{"id": "hiyouga_geometry3k_0", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_0_0.png"], "problem": "\nChords $\\overline{A C}$ and $\\overline{D F}$ are equidistant from the center. If the radius of $\\odot G$ is 26 find $A C$", "answer": "48"} {"id": "hiyouga_geometry3k_1", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_1_0.png"], "problem": "\nFind the length of $\\widehat {ZY}$. Round to the nearest hundredth.", "answer": "7.85"} {"id": "hiyouga_geometry3k_2", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_2_0.png"], "problem": "\nFind the area of the figure to the nearest tenth.", "answer": "31.1"} {"id": "hiyouga_geometry3k_3", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_3_0.png"], "problem": "\nIf pentagons $A B C D E$ and $P Q R S T$ are similar, find $S R$", "answer": "4 \\frac { 4 } { 11 }"} {"id": "hiyouga_geometry3k_4", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_4_0.png"], "problem": "\nIn $\\triangle PQR$, $\\overline{ST} \\| \\overline{R Q}$ . If $PS=12.5$, $SR=5$, and $PT=15$, find $TQ$.", "answer": "6"} {"id": "hiyouga_geometry3k_5", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_5_0.png"], "problem": "\n$a=14, b=48,$ and $c=50$ find $cosA$", "answer": "0.96"} {"id": "hiyouga_geometry3k_6", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_6_0.png"], "problem": "\n$\\overline{A C}$ is a diagonal of rhombus $A B C D$ If $m \\angle C D E$ is $116,$ what is $m \\angle A C D ?$", "answer": "58"} {"id": "hiyouga_geometry3k_7", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_7_0.png"], "problem": "\nUse parallelogram $JKLM$ to find $m \\angle KLM$", "answer": "71"} {"id": "hiyouga_geometry3k_8", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_8_0.png"], "problem": "\nFind the perimeter of the parallelogram.", "answer": "78"} {"id": "hiyouga_geometry3k_9", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_9_0.png"], "problem": "\nFind x.", "answer": "5 \\sqrt { 3 }"} {"id": "hiyouga_geometry3k_10", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_10_0.png"], "problem": "\nFind $PS$.", "answer": "9"} {"id": "hiyouga_geometry3k_11", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_11_0.png"], "problem": "\nIn the figure, $m∠1 = 50$ and $m∠3 = 60$. Find the measure of $\\angle 8$.", "answer": "120"} {"id": "hiyouga_geometry3k_12", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_12_0.png"], "problem": "\nFind x", "answer": "4"} {"id": "hiyouga_geometry3k_13", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_13_0.png"], "problem": "\nQuadrilateral $ABDC$ is a rectangle. If $m\\angle1 = 38$, find $m \\angle 2$", "answer": "52"} {"id": "hiyouga_geometry3k_14", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_14_0.png"], "problem": "\nWhat is the value of $x$ below to the nearest tenth?", "answer": "22.5"} {"id": "hiyouga_geometry3k_15", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_15_0.png"], "problem": "\nFind $m\\angle W$", "answer": "108"} {"id": "hiyouga_geometry3k_16", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_16_0.png"], "problem": "\nExpress the ratio of $\\cos B$ as a decimal to the nearest hundredth.", "answer": "0.38"} {"id": "hiyouga_geometry3k_17", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_17_0.png"], "problem": "\nFind the measure of $JK$.", "answer": "31"} {"id": "hiyouga_geometry3k_18", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_18_0.png"], "problem": "\nFor trapezoid $T R S V, M$ and $N$ are midpoints of the legs. If $T R=32$ and $M N=25,$ find $V S$", "answer": "18"} {"id": "hiyouga_geometry3k_19", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_19_0.png"], "problem": "\nFind $x$ so that each quadrilateral is a parallelogram.", "answer": "4"} {"id": "hiyouga_geometry3k_20", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_20_0.png"], "problem": "\nFind $WR$.", "answer": "8"} {"id": "hiyouga_geometry3k_21", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_21_0.png"], "problem": "\nFind the value of $x$", "answer": "74"} {"id": "hiyouga_geometry3k_22", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_22_0.png"], "problem": "\nFind the area of the trapezoid.", "answer": "678.5"} {"id": "hiyouga_geometry3k_23", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_23_0.png"], "problem": "\nThe diameters of $\\odot A, \\odot B,$ and $\\odot C$ are 10, 30 and 10 units, respectively. Find ZX if $\\overline{A Z} \\cong \\overline{C W}$ and $C W=2$.", "answer": "3"} {"id": "hiyouga_geometry3k_24", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_24_0.png"], "problem": "\nFind x", "answer": "6 \\sqrt { 6 }"} {"id": "hiyouga_geometry3k_25", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_25_0.png"], "problem": "\nFind x. Round to the nearest tenth.", "answer": "52.5"} {"id": "hiyouga_geometry3k_26", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_26_0.png"], "problem": "\nFind $y$ so that each quadrilateral is a parallelogram.", "answer": "31"} {"id": "hiyouga_geometry3k_27", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_27_0.png"], "problem": "\nFind $K J$ if $G J=8, G H=12,$ and $H I=4$", "answer": "2"} {"id": "hiyouga_geometry3k_28", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_28_0.png"], "problem": "\nFind $QP$.", "answer": "3.6"} {"id": "hiyouga_geometry3k_29", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_29_0.png"], "problem": "\nIn $\\odot T, Z V=1,$ and $T W=13$. Find XY", "answer": "10"} {"id": "hiyouga_geometry3k_30", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_30_0.png"], "problem": "\nIn the figure, $m∠11 = 62$ and $m∠14 = 38$. Find the measure of $\\angle 1$.", "answer": "38"} {"id": "hiyouga_geometry3k_31", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_31_0.png"], "problem": "\nThe two polygons are similar. Find UT.", "answer": "22.5"} {"id": "hiyouga_geometry3k_32", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_32_0.png"], "problem": "\nFind the measure of $∠A$ to the nearest tenth.", "answer": "41.8"} {"id": "hiyouga_geometry3k_33", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_33_0.png"], "problem": "\nFind $m \\angle H$.", "answer": "31"} {"id": "hiyouga_geometry3k_34", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_34_0.png"], "problem": "\nFind $x$.", "answer": "90"} {"id": "hiyouga_geometry3k_35", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_35_0.png"], "problem": "\n$m \\widehat{AC}=160$ and $m \\angle BEC=38$. What is $m \\angle AEB$?", "answer": "42"} {"id": "hiyouga_geometry3k_36", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_36_0.png"], "problem": "\nA plane travels from Des Moines to Phoenix, on to Atlanta, and back to Des Moines, as shown below. Find the distance in miles from Phoenix to Atlanta if the total trip was 3482 miles.", "answer": "1591"} {"id": "hiyouga_geometry3k_37", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_37_0.png"], "problem": "\nFind $x$.", "answer": "123"} {"id": "hiyouga_geometry3k_38", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_38_0.png"], "problem": "\nSolve for x in the figure. Round to the nearest tenth if necessary.", "answer": "3"} {"id": "hiyouga_geometry3k_39", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_39_0.png"], "problem": "\nIn the figure, $\\overline{A D}$ is perpendicular to $\\overline{B C}$ and $\\overline{A B}$ is perpendicular to $\\overline{A C}$. What is $B C ?$", "answer": "20"} {"id": "hiyouga_geometry3k_40", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_40_0.png"], "problem": "\nFind the area of the figure. Round to the nearest tenth.", "answer": "30.2"} {"id": "hiyouga_geometry3k_41", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_41_0.png"], "problem": "\nIf $c=5,$ find $b$", "answer": "2.5 \\sqrt { 3 }"} {"id": "hiyouga_geometry3k_42", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_42_0.png"], "problem": "\nFind $z$.", "answer": "12"} {"id": "hiyouga_geometry3k_43", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_43_0.png"], "problem": "\nFind the area of the shaded region. Assume that the polygon is regular unless otherwise stated. Round to the nearest tenth.", "answer": "216.6"} {"id": "hiyouga_geometry3k_44", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_44_0.png"], "problem": "\nFind $m \\angle 2$.", "answer": "39"} {"id": "hiyouga_geometry3k_45", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_45_0.png"], "problem": "\nFind x. Round to the nearest tenth.", "answer": "5.8"} {"id": "hiyouga_geometry3k_46", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_46_0.png"], "problem": "\n$m$ is the perpendicular bisector of $XZ$, $WZ=14.9$. Find $WX$.", "answer": "14.9"} {"id": "hiyouga_geometry3k_47", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_47_0.png"], "problem": "\n$m∠9 = 2x - 4$, $m∠10 = 2x + 4$. Find the measure of $∠10$.", "answer": "94"} {"id": "hiyouga_geometry3k_48", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_48_0.png"], "problem": "\nFind $JL$.", "answer": "14"} {"id": "hiyouga_geometry3k_49", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_49_0.png"], "problem": "\nFind the area of the parallelogram. Round to the nearest tenth if necessary.", "answer": "91.9"} {"id": "hiyouga_geometry3k_50", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_50_0.png"], "problem": "\nFind x.", "answer": "15"} {"id": "hiyouga_geometry3k_51", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_51_0.png"], "problem": "\nFind $ST$.", "answer": "19"} {"id": "hiyouga_geometry3k_52", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_52_0.png"], "problem": "\nFind x.", "answer": "18 \\sqrt { 6 }"} {"id": "hiyouga_geometry3k_53", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_53_0.png"], "problem": "\nFind $EG$ if $G$ is the incenter of $\\triangle ABC$.", "answer": "5"} {"id": "hiyouga_geometry3k_54", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_54_0.png"], "problem": "\nFind $x$ so that each quadrilateral is a parallelogram.", "answer": "13"} {"id": "hiyouga_geometry3k_55", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_55_0.png"], "problem": "\nFind $x$.", "answer": "3"} {"id": "hiyouga_geometry3k_56", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_56_0.png"], "problem": "\nFind x.", "answer": "1"} {"id": "hiyouga_geometry3k_57", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_57_0.png"], "problem": "\nTangent $\\overline{M P}$ is drawn to $\\odot O .$ Find $x$ if $M O=20$", "answer": "12"} {"id": "hiyouga_geometry3k_58", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_58_0.png"], "problem": "\nIn H, the diameter is $18$, $LM = 12$, and $m \\widehat {LM} = 84$. Find $HP$. Round to the nearest hundredth.", "answer": "6.71"} {"id": "hiyouga_geometry3k_59", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_59_0.png"], "problem": "\nFind x to the nearest tenth. Assume that segments that appear to be tangent are tangent.", "answer": "21.6"} {"id": "hiyouga_geometry3k_60", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_60_0.png"], "problem": "\nIf $m \\widehat{F E}=118, m \\widehat{A B}=108$, $m \\angle E G B=52,$ and $m \\angle E F B=30$, find $m \\widehat{C F}$", "answer": "44"} {"id": "hiyouga_geometry3k_61", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_61_0.png"], "problem": "\nIf $c=5,$ find $a$", "answer": "2.5"} {"id": "hiyouga_geometry3k_62", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_62_0.png"], "problem": "\nFind x.", "answer": "5"} {"id": "hiyouga_geometry3k_63", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_63_0.png"], "problem": "\nFind the length of $\\widehat {AB}$. Round to the nearest hundredth.", "answer": "9.77"} {"id": "hiyouga_geometry3k_64", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_64_0.png"], "problem": "\nIn the figure, line $l$ is parallel to line $m$. Line $n$ intersects both $l$ and $m$. Which of the following lists includes all of the angles that are supplementary to $ ∠1 $?", "answer": "angles 2,3, 6, and 7"} {"id": "hiyouga_geometry3k_65", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_65_0.png"], "problem": "\nIn the figure, $m∠3 = 43$. Find the measure of $\\angle 11$.", "answer": "43"} {"id": "hiyouga_geometry3k_66", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_66_0.png"], "problem": "\nIf AB || DC, find x.", "answer": "115"} {"id": "hiyouga_geometry3k_67", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_67_0.png"], "problem": "\nFind the measure of $\\angle 2$.", "answer": "33"} {"id": "hiyouga_geometry3k_68", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_68_0.png"], "problem": "\nThe diagram shows the layout of Elm, Plum, and Oak streets. Find the value of $x.$", "answer": "125"} {"id": "hiyouga_geometry3k_69", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_69_0.png"], "problem": "\nFind $y$.", "answer": "5 \\sqrt { 5 }"} {"id": "hiyouga_geometry3k_70", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_70_0.png"], "problem": "\nIn $\\odot P, m \\angle M P L=65$ and $\\overline{N P} \\perp \\overline{P L}$.\r\nFind $m \\widehat{N M}$", "answer": "25"} {"id": "hiyouga_geometry3k_71", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_71_0.png"], "problem": "\nEach pair of polygons is similar. Find y", "answer": "5"} {"id": "hiyouga_geometry3k_72", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_72_0.png"], "problem": "\nUse parallelogram $JKLM$ to find $m \\angle KJL$.", "answer": "30"} {"id": "hiyouga_geometry3k_73", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_73_0.png"], "problem": "\nFind the area of the figure. Round to the nearest tenth if necessary.", "answer": "63"} {"id": "hiyouga_geometry3k_74", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_74_0.png"], "problem": "\nFind the perimeter of the parallelogram. Round to the nearest tenth if necessary.", "answer": "76"} {"id": "hiyouga_geometry3k_75", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_75_0.png"], "problem": "\nTrapezoid $GHJK$ has an area of 75 square meters. Find the height.", "answer": "5"} {"id": "hiyouga_geometry3k_76", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_76_0.png"], "problem": "\nFind x", "answer": "58"} {"id": "hiyouga_geometry3k_77", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_77_0.png"], "problem": "\nFind x. Round to the nearest tenth.", "answer": "30.2"} {"id": "hiyouga_geometry3k_78", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_78_0.png"], "problem": "\nFor the pair of similar figures, find the area of the green figure.", "answer": "9"} {"id": "hiyouga_geometry3k_79", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_79_0.png"], "problem": "\nIn $\\odot X, A B=30, C D=30,$ and $m \\widehat{C Z}=40$\r\nFind $m\\widehat{C D}$", "answer": "80"} {"id": "hiyouga_geometry3k_80", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_80_0.png"], "problem": "\nQuadrilateral EFGH is a rectangle. If FK = 32 feet, find EG.", "answer": "64"} {"id": "hiyouga_geometry3k_81", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_81_0.png"], "problem": "\nFind $x$.", "answer": "7"} {"id": "hiyouga_geometry3k_82", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_82_0.png"], "problem": "\nIn the figure, $m \\angle 1=4 p+15$, $m \\angle 3=3 p-10$ and $m \\angle 4=6 r+5 $. Find the value of $p$.", "answer": "25"} {"id": "hiyouga_geometry3k_83", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_83_0.png"], "problem": "\nFind x.", "answer": "\\sqrt { 21 }"} {"id": "hiyouga_geometry3k_84", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_84_0.png"], "problem": "\nFind $BC$.", "answer": "13"} {"id": "hiyouga_geometry3k_85", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_85_0.png"], "problem": "\nFind x.", "answer": "24 \\sqrt { 3 }"} {"id": "hiyouga_geometry3k_86", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_86_0.png"], "problem": "\nIf $ZP = 4x - 9$ and $PY = 2x + 5$, find $ZX$.", "answer": "38"} {"id": "hiyouga_geometry3k_87", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_87_0.png"], "problem": "\nFind y", "answer": "6 \\sqrt { 3 }"} {"id": "hiyouga_geometry3k_88", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_88_0.png"], "problem": "\nFind the measure of $∠T$ to the nearest tenth.", "answer": "21.8"} {"id": "hiyouga_geometry3k_89", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_89_0.png"], "problem": "\nFind x to the nearest tenth. Assume that segments that appear to be tangent are tangent.", "answer": "7.2"} {"id": "hiyouga_geometry3k_90", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_90_0.png"], "problem": "\n$\\overline{AB} \\cong \\overline{DF}$. Find $x$.", "answer": "2"} {"id": "hiyouga_geometry3k_91", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_91_0.png"], "problem": "\nFind $m \\angle WYZ$.", "answer": "23"} {"id": "hiyouga_geometry3k_92", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_92_0.png"], "problem": "\nFind the area of the shaded region.", "answer": "22.1"} {"id": "hiyouga_geometry3k_93", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_93_0.png"], "problem": "\nFind x", "answer": "2"} {"id": "hiyouga_geometry3k_94", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_94_0.png"], "problem": "\nIn $\\odot O, \\overline{E C}$ and $\\overline{A B}$ are diameters, and $\\angle B O D \\cong \\angle D O E \\cong \\angle E O F \\cong \\angle F O A$\r\nFind $m\\widehat{A D}$", "answer": "135"} {"id": "hiyouga_geometry3k_95", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_95_0.png"], "problem": "\nFind $x$ if $AE=3, AB=2$, $BC=6,$ and $ED=2x-3$", "answer": "6"} {"id": "hiyouga_geometry3k_96", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_96_0.png"], "problem": "\nFind $A E$ if $A B=12, A C=16,$ and $E D=5$", "answer": "15"} {"id": "hiyouga_geometry3k_97", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_97_0.png"], "problem": "\nFind $x$ in the given parallelogram", "answer": "38"} {"id": "hiyouga_geometry3k_98", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_98_0.png"], "problem": "\nFind x", "answer": "115"} {"id": "hiyouga_geometry3k_99", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_99_0.png"], "problem": "\nFind the area of the figure. Round to the nearest tenth if necessary.", "answer": "129.9"} {"id": "hiyouga_geometry3k_100", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_100_0.png"], "problem": "\nFind $a$ in the given parallelogram", "answer": "9"} {"id": "hiyouga_geometry3k_101", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_101_0.png"], "problem": "\nFind $m\\angle B$", "answer": "120"} {"id": "hiyouga_geometry3k_102", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_102_0.png"], "problem": "\nFind GH in the kite", "answer": "\\sqrt { 369 }"} {"id": "hiyouga_geometry3k_103", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_103_0.png"], "problem": "\nFind the value of the variable $x$ in the figure.", "answer": "125"} {"id": "hiyouga_geometry3k_104", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_104_0.png"], "problem": "\nRefer to the figure at the right. Find the value of $m ∠FCE$ if $ p \\parallel q $.", "answer": "105"} {"id": "hiyouga_geometry3k_105", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_105_0.png"], "problem": "\nWhat is the measure of $\\angle B$ if $m \\angle A=10 ?$", "answer": "30"} {"id": "hiyouga_geometry3k_106", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_106_0.png"], "problem": "\nExpress the ratio of $\\cos N$ as a decimal to the nearest hundredth.", "answer": "0.38"} {"id": "hiyouga_geometry3k_107", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_107_0.png"], "problem": "\nFind $m \\angle R$", "answer": "29.1"} {"id": "hiyouga_geometry3k_108", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_108_0.png"], "problem": "\nFind $x$.", "answer": "8"} {"id": "hiyouga_geometry3k_109", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_109_0.png"], "problem": "\nFind the area of the figure. Round to the nearest tenth.", "answer": "50.2"} {"id": "hiyouga_geometry3k_110", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_110_0.png"], "problem": "\nFind y.", "answer": "21 \\sqrt { 3 }"} {"id": "hiyouga_geometry3k_111", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_111_0.png"], "problem": "\nFind the area of the shaded sector. Round to the nearest tenth.", "answer": "182.6"} {"id": "hiyouga_geometry3k_112", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_112_0.png"], "problem": "\n$\\triangle K L N$ and $\\triangle L M N$ are isosceles and $m \\angle J K N=130$. Find the measure of $\\angle J$.", "answer": "106"} {"id": "hiyouga_geometry3k_113", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_113_0.png"], "problem": "\nFind x.", "answer": "12"} {"id": "hiyouga_geometry3k_114", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_114_0.png"], "problem": "\n$ABCD$ is a rhombus. If $PB = 12$, $AB = 15$, and $m \\angle ABD = 24$, Find $m\\angle BDA$", "answer": "24"} {"id": "hiyouga_geometry3k_115", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_115_0.png"], "problem": "\nFind $y$.", "answer": "12"} {"id": "hiyouga_geometry3k_116", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_116_0.png"], "problem": "\nFind the value of $x$ in each diagram", "answer": "68"} {"id": "hiyouga_geometry3k_117", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_117_0.png"], "problem": "\nFind $m \\angle RST$.", "answer": "55"} {"id": "hiyouga_geometry3k_118", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_118_0.png"], "problem": "\n$∠6$ and $∠8$ are complementary, $m∠8 = 47$. Find the measure of $\\angle 7$.", "answer": "90"} {"id": "hiyouga_geometry3k_119", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_119_0.png"], "problem": "\nFind the measure of $m\\angle 1$. Assume that segments that appear\r\ntangent are tangent.", "answer": "129"} {"id": "hiyouga_geometry3k_120", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_120_0.png"], "problem": "\nLet $\\overline{G H}$ be the median of $R S B A .$ Find $G H$", "answer": "62"} {"id": "hiyouga_geometry3k_121", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_121_0.png"], "problem": "\nUse parallelogram PQRS to find $QP$", "answer": "5"} {"id": "hiyouga_geometry3k_122", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_122_0.png"], "problem": "\nQuadrilateral $WXYZ$ is inscribed in $\\odot V$. Find $m \\angle X$.", "answer": "120"} {"id": "hiyouga_geometry3k_123", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_123_0.png"], "problem": "\nFind the height of the parallelogram given its area with 2000 square units.", "answer": "40"} {"id": "hiyouga_geometry3k_124", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_124_0.png"], "problem": "\nFind $m \\angle A$ of quadrilateral ABCD", "answer": "135"} {"id": "hiyouga_geometry3k_125", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_125_0.png"], "problem": "\nFind y", "answer": "10"} {"id": "hiyouga_geometry3k_126", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_126_0.png"], "problem": "\nFind the measure of the altitude drawn to the hypotenuse.", "answer": "4 \\sqrt { 3 }"} {"id": "hiyouga_geometry3k_127", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_127_0.png"], "problem": "\nFind the area of the shaded region. Round to the nearest tenth.", "answer": "157.1"} {"id": "hiyouga_geometry3k_128", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_128_0.png"], "problem": "\nFind x. Round to the nearest tenth.", "answer": "30.7"} {"id": "hiyouga_geometry3k_129", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_129_0.png"], "problem": "\nFind $y$ in each figure.", "answer": "6"} {"id": "hiyouga_geometry3k_130", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_130_0.png"], "problem": "\nFind $m \\angle S$.", "answer": "34"} {"id": "hiyouga_geometry3k_131", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_131_0.png"], "problem": "\nIn the figure, $m∠3 = 110$ and $m ∠ 12 = 55$. Find the measure of $∠13$.", "answer": "55"} {"id": "hiyouga_geometry3k_132", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_132_0.png"], "problem": "\nFind x.", "answer": "3 \\sqrt { 35 }"} {"id": "hiyouga_geometry3k_133", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_133_0.png"], "problem": "\nQuadrilateral EFGH is a rectangle. If $m \\angle HGE = 13$, find $m\\angle FGE$.", "answer": "77"} {"id": "hiyouga_geometry3k_134", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_134_0.png"], "problem": "\nFind x in the parallelogram", "answer": "37"} {"id": "hiyouga_geometry3k_135", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_135_0.png"], "problem": "\nFind the side length in isosceles triangle $DEF$.", "answer": "11"} {"id": "hiyouga_geometry3k_136", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_136_0.png"], "problem": "\nFind the length of $\\widehat {JK}$. Round to the nearest hundredth.", "answer": "13.74"} {"id": "hiyouga_geometry3k_137", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_137_0.png"], "problem": "\nUse parallelogram to find $b$", "answer": "11"} {"id": "hiyouga_geometry3k_138", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_138_0.png"], "problem": "\nIf PR || KL, KN = 9, LN = 16, PM = 2 KP, find MN", "answer": "12"} {"id": "hiyouga_geometry3k_139", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_139_0.png"], "problem": "\nFind $x$. Round to the nearest tenth.", "answer": "14.1"} {"id": "hiyouga_geometry3k_140", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_140_0.png"], "problem": "\nFind the area of the rhombus.", "answer": "132"} {"id": "hiyouga_geometry3k_141", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_141_0.png"], "problem": "\nFind TX if $E X=24$ and $D E=7$", "answer": "32"} {"id": "hiyouga_geometry3k_142", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_142_0.png"], "problem": "\nFind $m \\widehat {LP}$.", "answer": "150"} {"id": "hiyouga_geometry3k_143", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_143_0.png"], "problem": "\nExpress the ratio of $\\sin N$ as a decimal to the nearest hundredth.", "answer": "0.92"} {"id": "hiyouga_geometry3k_144", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_144_0.png"], "problem": "\nFind x.", "answer": "1"} {"id": "hiyouga_geometry3k_145", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_145_0.png"], "problem": "\nFind the area of the figure. Round to the nearest hundredth, if necessary.", "answer": "4.8"} {"id": "hiyouga_geometry3k_146", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_146_0.png"], "problem": "\nFind $x$.", "answer": "3.5"} {"id": "hiyouga_geometry3k_147", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_147_0.png"], "problem": "\nUse parallelogram ABCD to find $m\\angle ADC$", "answer": "128"} {"id": "hiyouga_geometry3k_148", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_148_0.png"], "problem": "\nFind the measure of $\\angle 3$ if $\\overline{A B} \\perp \\overline{B C}$.", "answer": "76"} {"id": "hiyouga_geometry3k_149", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_149_0.png"], "problem": "\nIn $\\triangle DEF, m \\angle E=108, m \\angle F=26$, and $f=20$, Find $d$ to the nearest whole number.", "answer": "33"} {"id": "hiyouga_geometry3k_150", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_150_0.png"], "problem": "\nFind $y$ so that each quadrilateral is a parallelogram.", "answer": "4"} {"id": "hiyouga_geometry3k_151", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_151_0.png"], "problem": "\nFind $m \\angle 4$.", "answer": "33"} {"id": "hiyouga_geometry3k_152", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_152_0.png"], "problem": "\nFind $cos C$", "answer": "\\frac { 4 } { 5 }"} {"id": "hiyouga_geometry3k_153", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_153_0.png"], "problem": "\nIn rhombus $A B C D, m \\angle D A B=2, m \\angle A D C$ and $C B=6$. Find $m \\angle A C D$", "answer": "60"} {"id": "hiyouga_geometry3k_154", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_154_0.png"], "problem": "\nFind AB", "answer": "10"} {"id": "hiyouga_geometry3k_155", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_155_0.png"], "problem": "\nFind $x$ in the figure.", "answer": "14"} {"id": "hiyouga_geometry3k_156", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_156_0.png"], "problem": "\nCircle $O$ has a radius of 13 inches. Radius $\\overline{O B}$ is perpendicular to chord $\\overline{C D}$ which is 24 inches long.\r\nIf $m \\widehat{C D}=134,$ find $m \\widehat{C B}$", "answer": "67"} {"id": "hiyouga_geometry3k_157", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_157_0.png"], "problem": "\nIn $\\odot M$, $FL=24,HJ=48$, and $m \\widehat {HP}=65$. Find $FG$.", "answer": "48"} {"id": "hiyouga_geometry3k_158", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_158_0.png"], "problem": "\nCut four congruent triangles off the corners of a rectangle to make an octagon. What is the area of the octagon?", "answer": "528"} {"id": "hiyouga_geometry3k_159", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_159_0.png"], "problem": "\nFind $m\\angle A$", "answer": "60"} {"id": "hiyouga_geometry3k_160", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_160_0.png"], "problem": "\nUse parallelogram JKLM to find $m \\angle KJL$ if $J K=2 b+3$ and $J M=3 a$.", "answer": "30"} {"id": "hiyouga_geometry3k_161", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_161_0.png"], "problem": "\nFind x.", "answer": "\\frac { 17 } { 2 } \\sqrt { 3 }"} {"id": "hiyouga_geometry3k_162", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_162_0.png"], "problem": "\nFind $XZ$.", "answer": "34"} {"id": "hiyouga_geometry3k_163", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_163_0.png"], "problem": "\nFind $XW$.", "answer": "12"} {"id": "hiyouga_geometry3k_164", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_164_0.png"], "problem": "\nFind x so that $GJ \\parallel FK$. $G H=x+3.5, H J=x-8.5, F H=21, H K=7$.", "answer": "14.5"} {"id": "hiyouga_geometry3k_165", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_165_0.png"], "problem": "\nIn $\\odot P, m \\angle M P L=65$ and $\\overline{N P} \\perp \\overline{P L}$.\r\nFind $m \\widehat{N J K}$", "answer": "155"} {"id": "hiyouga_geometry3k_166", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_166_0.png"], "problem": "\nA square is inscribed in a circle having a radius of $6$ inches. Find the length of each side of the square.", "answer": "6 \\sqrt 2"} {"id": "hiyouga_geometry3k_167", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_167_0.png"], "problem": "\nOne diagonal of a rhombus is twice as long as the other diagonal. If the area of the rhombus is 169 square millimeters, what are the lengths of the diagonals?", "answer": "26"} {"id": "hiyouga_geometry3k_168", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_168_0.png"], "problem": "\nFind x", "answer": "9"} {"id": "hiyouga_geometry3k_169", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_169_0.png"], "problem": "\nIf $AB=12,AC=16$, and $ED=5$, find $AE$.", "answer": "15"} {"id": "hiyouga_geometry3k_170", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_170_0.png"], "problem": "\nFind $x$ so that $\\overline{BE}$ and $\\overline{AD}$ are perpendicular.", "answer": "10"} {"id": "hiyouga_geometry3k_171", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_171_0.png"], "problem": "\nFind DE", "answer": "9"} {"id": "hiyouga_geometry3k_172", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_172_0.png"], "problem": "\nFind the area of the shaded region formed by the circle and regular polygon. Round to the nearest tenth.", "answer": "76.4"} {"id": "hiyouga_geometry3k_173", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_173_0.png"], "problem": "\nIn the figure, $m ∠ 12 = 64$. Find the measure of $ \\angle 7$.", "answer": "64"} {"id": "hiyouga_geometry3k_174", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_174_0.png"], "problem": "\nFind $BC$.", "answer": "9"} {"id": "hiyouga_geometry3k_175", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_175_0.png"], "problem": "\nFind $m \\angle 1$.", "answer": "37.5"} {"id": "hiyouga_geometry3k_176", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_176_0.png"], "problem": "\nExpress the ratio of $\\sin P$ as a decimal to the nearest hundredth.", "answer": "0.88"} {"id": "hiyouga_geometry3k_177", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_177_0.png"], "problem": "\nFind $x$. $A=357$ in$^2$.", "answer": "21"} {"id": "hiyouga_geometry3k_178", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_178_0.png"], "problem": "\nFind $x$ so that $a ∥ b$.", "answer": "14"} {"id": "hiyouga_geometry3k_179", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_179_0.png"], "problem": "\n$\\overline{GJ}$ is a diameter of $\\odot K$. Find $m \\widehat {GLJ}$.", "answer": "180"} {"id": "hiyouga_geometry3k_180", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_180_0.png"], "problem": "\nFind $C F$ if $\\overline{B F}$ bisects $\\angle A B C$ and $\\overline{A C} \\| \\overline{E D}, B A=6, B C=7.5$, $A C=9,$ and $D E=9$", "answer": "5"} {"id": "hiyouga_geometry3k_181", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_181_0.png"], "problem": "\nFind $m \\angle K$", "answer": "100"} {"id": "hiyouga_geometry3k_182", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_182_0.png"], "problem": "\nFind the value of the variable $y$ in the figure.", "answer": "50"} {"id": "hiyouga_geometry3k_183", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_183_0.png"], "problem": "\nFind the value of $t$ in the parallelogram.", "answer": "7"} {"id": "hiyouga_geometry3k_184", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_184_0.png"], "problem": "\nFind the perimeter of the triangle. Round to the nearest hundredth.", "answer": "8.73"} {"id": "hiyouga_geometry3k_185", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_185_0.png"], "problem": "\nThe segment is tangent to the circle. Find the value of $x$.", "answer": "3"} {"id": "hiyouga_geometry3k_186", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_186_0.png"], "problem": "\nFind the area of the shaded region. Round to the nearest tenth.", "answer": "58.9"} {"id": "hiyouga_geometry3k_187", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_187_0.png"], "problem": "\nFind the measure of $m \\widehat{YXZ}$.", "answer": "166"} {"id": "hiyouga_geometry3k_188", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_188_0.png"], "problem": "\nFind x.", "answer": "14"} {"id": "hiyouga_geometry3k_189", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_189_0.png"], "problem": "\nFind $y$.", "answer": "2"} {"id": "hiyouga_geometry3k_190", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_190_0.png"], "problem": "\nFind x.", "answer": "8 \\sqrt { 5 }"} {"id": "hiyouga_geometry3k_191", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_191_0.png"], "problem": "\nFind y.", "answer": "48"} {"id": "hiyouga_geometry3k_192", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_192_0.png"], "problem": "\nUse parallelogram WXYZ to find $m\\angle XYZ$", "answer": "105"} {"id": "hiyouga_geometry3k_193", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_193_0.png"], "problem": "\nFind $x$.", "answer": "9.5"} {"id": "hiyouga_geometry3k_194", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_194_0.png"], "problem": "\nFind the measure of $m\\angle 2$. Assume that segments that appear\r\ntangent are tangent.", "answer": "157.5"} {"id": "hiyouga_geometry3k_195", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_195_0.png"], "problem": "\nFind the perimeter of the parallelogram. Round to the nearest tenth if necessary.", "answer": "64"} {"id": "hiyouga_geometry3k_196", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_196_0.png"], "problem": "\nQuadrilateral DEFG is a rectangle. If $m \\angle EFD = 2x - 3$ and $m \\angle DFG = x + 12$,\r\nfind $m \\angle EFD$.", "answer": "51"} {"id": "hiyouga_geometry3k_197", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_197_0.png"], "problem": "\nFind y", "answer": "4 \\sqrt { 2 }"} {"id": "hiyouga_geometry3k_198", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_198_0.png"], "problem": "\nCircle $O$ has a radius of 13 inches. Radius $\\overline{O B}$ is perpendicular to chord $\\overline{C D}$ which is 24 inches long.\r\nFind OX", "answer": "5"} {"id": "hiyouga_geometry3k_199", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_199_0.png"], "problem": "\nFind the area of $▱ JKLM$.", "answer": "24"} {"id": "hiyouga_geometry3k_200", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_200_0.png"], "problem": "\nFind $m \\angle 1$.", "answer": "108"} {"id": "hiyouga_geometry3k_201", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_201_0.png"], "problem": "\nFind $AB$.", "answer": "4.1"} {"id": "hiyouga_geometry3k_202", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_202_0.png"], "problem": "\nFind $RS$ if $\\triangle QRS$ is an equilateral triangle.", "answer": "2"} {"id": "hiyouga_geometry3k_203", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_203_0.png"], "problem": "\nIf two sides of a triangle measure 12 and 7, which of the following cannot be the perimeter of the triangle?", "answer": "38"} {"id": "hiyouga_geometry3k_204", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_204_0.png"], "problem": "\nFind the area of the triangle. Round to the nearest hundredth.", "answer": "7.51"} {"id": "hiyouga_geometry3k_205", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_205_0.png"], "problem": "\n$\\overline{AB}$ is a diameter, $AC=8$ inches, and $BC=15$ inches. Find the radius of the circle.", "answer": "8.5"} {"id": "hiyouga_geometry3k_206", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_206_0.png"], "problem": "\nFind $m \\angle 1$.", "answer": "70"} {"id": "hiyouga_geometry3k_207", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_207_0.png"], "problem": "\nFind $w$ in the given parallelogram", "answer": "5"} {"id": "hiyouga_geometry3k_208", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_208_0.png"], "problem": "\nFind $x$.", "answer": "\\frac { 5 } { 3 }"} {"id": "hiyouga_geometry3k_209", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_209_0.png"], "problem": "\nFind y", "answer": "5"} {"id": "hiyouga_geometry3k_210", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_210_0.png"], "problem": "\nIf $\\triangle L M N \\sim \\triangle Q R S, Q R=35, R S=37, S Q=12$, and $N L=5$, find the perimeter of $\\triangle L M N$.", "answer": "35"} {"id": "hiyouga_geometry3k_211", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_211_0.png"], "problem": "\nFind the measure of $\\angle 7$ if $m∠4= m∠5$.", "answer": "89"} {"id": "hiyouga_geometry3k_212", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_212_0.png"], "problem": "\n$\\overline{XY}$ and $\\overline{XZ}$ are midsegments of $\\triangle RST$. Find $ST$.", "answer": "14"} {"id": "hiyouga_geometry3k_213", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_213_0.png"], "problem": "\nIf $m∠5 = 7x - 5$ and $m∠4 = 2x + 23$, find $x$.", "answer": "18"} {"id": "hiyouga_geometry3k_214", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_214_0.png"], "problem": "\nFind the measure of $\\angle 2$.", "answer": "76"} {"id": "hiyouga_geometry3k_215", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_215_0.png"], "problem": "\nUse parallelogram ABCD to find $m\\angle ACD$", "answer": "29"} {"id": "hiyouga_geometry3k_216", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_216_0.png"], "problem": "\nFind $CD$ if $AC=x-3$, $BE=20, AB=16,$ and $CD=x+5$", "answer": "40"} {"id": "hiyouga_geometry3k_217", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_217_0.png"], "problem": "\n$UJ=9, VJ=3$, and $ZT=18$. Find $SV$.", "answer": "9"} {"id": "hiyouga_geometry3k_218", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_218_0.png"], "problem": "\nIn $\\odot O, \\overline{E C}$ and $\\overline{A B}$ are diameters, and $\\angle B O D \\cong \\angle D O E \\cong \\angle E O F \\cong \\angle F O A$\r\nFind $m\\widehat{A E}$", "answer": "90"} {"id": "hiyouga_geometry3k_219", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_219_0.png"], "problem": "\nIn $\\triangle PQR$, $ZQ=3a-11$, $ZP=a+5$, $PY=2 c-1$, $YR=4 c-11$, $m \\angle PRZ=4 b-17$, $m \\angle ZRQ=3 b-4$, $m \\angle QYR=7 b+6$, and $m \\angle PXR=2 a+10$. If $\\overline{RZ}$ is an angle bisector, find $m∠PRZ$.", "answer": "35"} {"id": "hiyouga_geometry3k_220", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_220_0.png"], "problem": "\nWhich segments are parallel?", "answer": "A D and B E"} {"id": "hiyouga_geometry3k_221", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_221_0.png"], "problem": "\nUse parallelogram MNPR to find $m \\angle RMN$", "answer": "109"} {"id": "hiyouga_geometry3k_222", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_222_0.png"], "problem": "\nIf WXYZ is a kite, find WP", "answer": "\\sqrt { 20 }"} {"id": "hiyouga_geometry3k_223", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_223_0.png"], "problem": "\nFind x.", "answer": "17"} {"id": "hiyouga_geometry3k_224", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_224_0.png"], "problem": "\nIn the figure below, $∠ABC$ is intersected by parallel lines $l$ and $m$. What is the measure of $∠ABC$? Express your answer in degrees.", "answer": "71"} {"id": "hiyouga_geometry3k_225", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_225_0.png"], "problem": "\nFind z", "answer": "6"} {"id": "hiyouga_geometry3k_226", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_226_0.png"], "problem": "\nIf DB = 24, AE = 3, and EC = 18, find AD", "answer": "4"} {"id": "hiyouga_geometry3k_227", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_227_0.png"], "problem": "\nFind the measure of $m∠1$.", "answer": "109"} {"id": "hiyouga_geometry3k_228", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_228_0.png"], "problem": "\nIn the figure, $m∠1 = 50$ and $m∠3 = 60$. Find the measure of $\\angle 6$.", "answer": "70"} {"id": "hiyouga_geometry3k_229", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_229_0.png"], "problem": "\nFind $x$.", "answer": "35"} {"id": "hiyouga_geometry3k_230", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_230_0.png"], "problem": "\nFind the perimeter of the parallelogram. Round to the nearest tenth if necessary.", "answer": "50"} {"id": "hiyouga_geometry3k_231", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_231_0.png"], "problem": "\nUse parallelogram ABCD to find $m\\angle DAC$", "answer": "72"} {"id": "hiyouga_geometry3k_232", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_232_0.png"], "problem": "\nIn the figure, $m∠1 = 123$. Find the measure of $\\angle 14$.", "answer": "57"} {"id": "hiyouga_geometry3k_233", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_233_0.png"], "problem": "\nUse parallelogram $JKLM$ to find $m \\angle JKL$.", "answer": "80"} {"id": "hiyouga_geometry3k_234", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_234_0.png"], "problem": "\nRefer to the figure at the right. Find y.", "answer": "6.75"} {"id": "hiyouga_geometry3k_235", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_235_0.png"], "problem": "\nFind the area of the figure. Round to the nearest tenth if necessary.", "answer": "95"} {"id": "hiyouga_geometry3k_236", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_236_0.png"], "problem": "\nFind $x$.", "answer": "6"} {"id": "hiyouga_geometry3k_237", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_237_0.png"], "problem": "\nFor the pair of similar figures, use the given areas to find $x$.", "answer": "16"} {"id": "hiyouga_geometry3k_238", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_238_0.png"], "problem": "\nFind x.", "answer": "8"} {"id": "hiyouga_geometry3k_239", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_239_0.png"], "problem": "\nFind $a,$ if $F G=18, G H=42,$ and $F K=15$", "answer": "57"} {"id": "hiyouga_geometry3k_240", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_240_0.png"], "problem": "\nFind the area of the figure. Round to the nearest tenth if necessary.", "answer": "22.1"} {"id": "hiyouga_geometry3k_241", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_241_0.png"], "problem": "\nFind PT", "answer": "\\frac { 20 } { 3 }"} {"id": "hiyouga_geometry3k_242", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_242_0.png"], "problem": "\nFind $GD$.", "answer": "14"} {"id": "hiyouga_geometry3k_243", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_243_0.png"], "problem": "\nFind the area of the regular polygon figure. Round to the nearest tenth.", "answer": "101.8"} {"id": "hiyouga_geometry3k_244", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_244_0.png"], "problem": "\nFind x", "answer": "120"} {"id": "hiyouga_geometry3k_245", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_245_0.png"], "problem": "\nFind y.", "answer": "45"} {"id": "hiyouga_geometry3k_246", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_246_0.png"], "problem": "\nFind the area of the rhombus.", "answer": "168"} {"id": "hiyouga_geometry3k_247", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_247_0.png"], "problem": "\nFind $AB$ if $\\triangle ABC$ is an isosceles triangle with $\\overline{AB} \\cong \\overline{BC}$.", "answer": "7"} {"id": "hiyouga_geometry3k_248", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_248_0.png"], "problem": "\nFind x. Round the side measure to the nearest tenth.", "answer": "69.8"} {"id": "hiyouga_geometry3k_249", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_249_0.png"], "problem": "\nCircle $J$ has a radius of $10$ units, $\\odot K$ has a radius of $8$ units, and $BC=5.4$ units. Find $JK$.", "answer": "12.6"} {"id": "hiyouga_geometry3k_250", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_250_0.png"], "problem": "\nThe perimeter of this polygon is 60 centimeters. Find the length of each side of the polygon.", "answer": "12"} {"id": "hiyouga_geometry3k_251", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_251_0.png"], "problem": "\nIf $XN=6,XM=2$, and $XY=10$, find $NZ$.", "answer": "24"} {"id": "hiyouga_geometry3k_252", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_252_0.png"], "problem": "\nFind $x$", "answer": "1"} {"id": "hiyouga_geometry3k_253", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_253_0.png"], "problem": "\nFind BC", "answer": "6"} {"id": "hiyouga_geometry3k_254", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_254_0.png"], "problem": "\nFind $x$.", "answer": "30"} {"id": "hiyouga_geometry3k_255", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_255_0.png"], "problem": "\nFind $\\widehat{\\mathrm{WN}}$ if $\\triangle \\mathrm{IWN}$ is equilateral and $W N=5$", "answer": "\\frac { 5 } { 3 } \\pi"} {"id": "hiyouga_geometry3k_256", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_256_0.png"], "problem": "\nFind x.", "answer": "4 \\sqrt { 15 }"} {"id": "hiyouga_geometry3k_257", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_257_0.png"], "problem": "\nFind x.", "answer": "4 \\sqrt { 2 }"} {"id": "hiyouga_geometry3k_258", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_258_0.png"], "problem": "\nFind the value of the variable $x$ in the figure.", "answer": "54"} {"id": "hiyouga_geometry3k_259", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_259_0.png"], "problem": "\nThe area $A$ of the shaded region is given. Find $x$. $A = 66$ cm$^2$ .", "answer": "13.0"} {"id": "hiyouga_geometry3k_260", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_260_0.png"], "problem": "\nFind the value of x.", "answer": "163"} {"id": "hiyouga_geometry3k_261", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_261_0.png"], "problem": "\n$\\overline{CH} \\cong \\overline{KJ}$. Find $x$.", "answer": "55"} {"id": "hiyouga_geometry3k_262", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_262_0.png"], "problem": "\nIn regular hexagon UVWXYZ, each side is 12 centimeters long. Find $W Y$.", "answer": "12 \\sqrt { 3 }"} {"id": "hiyouga_geometry3k_263", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_263_0.png"], "problem": "\nFind $\\angle 5$", "answer": "50"} {"id": "hiyouga_geometry3k_264", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_264_0.png"], "problem": "\nIn the figure, $m ∠1 = 58 $, $m ∠2 = 47 $, and $m ∠3 = 26 $. Find the measure of $∠9$.", "answer": "49"} {"id": "hiyouga_geometry3k_265", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_265_0.png"], "problem": "\nFind $m \\widehat {QTS}$.", "answer": "248"} {"id": "hiyouga_geometry3k_266", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_266_0.png"], "problem": "\nUse the Pythagorean Theorem to find the length of the hypotenuse of each right triangle.", "answer": "13"} {"id": "hiyouga_geometry3k_267", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_267_0.png"], "problem": "\n$∠1$ and $∠2$ form a linear pair and $m∠2 = 67$. Find the measure of $\\angle 1$.", "answer": "113"} {"id": "hiyouga_geometry3k_268", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_268_0.png"], "problem": "\nThe diameters of $\\odot A, \\odot B,$ and $\\odot C$ are 10, 30 and 10 units, respectively. Find YW if $\\overline{A Z} \\cong \\overline{C W}$ and $C W=2$.", "answer": "3"} {"id": "hiyouga_geometry3k_269", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_269_0.png"], "problem": "\nFind $m\\angle MPQ$.", "answer": "101"} {"id": "hiyouga_geometry3k_270", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_270_0.png"], "problem": "\nFind x to the nearest hundredth.", "answer": "43.86"} {"id": "hiyouga_geometry3k_271", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_271_0.png"], "problem": "\nFind x", "answer": "10.5"} {"id": "hiyouga_geometry3k_272", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_272_0.png"], "problem": "\nFind $\\angle 9$", "answer": "120"} {"id": "hiyouga_geometry3k_273", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_273_0.png"], "problem": "\nFind $x$.", "answer": "9.6"} {"id": "hiyouga_geometry3k_274", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_274_0.png"], "problem": "\nFind z.", "answer": "6 \\sqrt { 5 }"} {"id": "hiyouga_geometry3k_275", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_275_0.png"], "problem": "\nUse rectangle LMNP, parallelogram LKMJ to solve the problem.\r\nIf $L N=10, L J=2 x+1,$ and $P J=3 x-1,$ find $x$", "answer": "2"} {"id": "hiyouga_geometry3k_276", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_276_0.png"], "problem": "\nIn $\\odot P$, $JK=10$ and $\\widehat {JKL}=134$. Find $m \\widehat{JL}$.", "answer": "67"} {"id": "hiyouga_geometry3k_277", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_277_0.png"], "problem": "\nFind $m \\angle N C L$", "answer": "120"} {"id": "hiyouga_geometry3k_278", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_278_0.png"], "problem": "\nFind $m \\angle 1$.", "answer": "79"} {"id": "hiyouga_geometry3k_279", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_279_0.png"], "problem": "\nThe pair of polygons is similar. Find x", "answer": "6"} {"id": "hiyouga_geometry3k_280", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_280_0.png"], "problem": "\n$m \\angle 3=x-12$ and $m \\angle 6=72$. Find $x$.", "answer": "84"} {"id": "hiyouga_geometry3k_281", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_281_0.png"], "problem": "\nFind the perimeter of $\\triangle D E F,$ if $\\triangle D E F \\sim \\triangle C B F,$ perimeter of $\\triangle C B F=27, D F=6,$ and $F C=8$", "answer": "20.25"} {"id": "hiyouga_geometry3k_282", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_282_0.png"], "problem": "\nFind $TQ$.", "answer": "12"} {"id": "hiyouga_geometry3k_283", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_283_0.png"], "problem": "\nQuadrilateral ABCD is a rectangle. $m\\angle 2 = 40$. Find $m \\angle 3$", "answer": "40"} {"id": "hiyouga_geometry3k_284", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_284_0.png"], "problem": "\nFind $h$ in the triangle.", "answer": "8"} {"id": "hiyouga_geometry3k_285", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_285_0.png"], "problem": "\nThe diameters of $\\odot A, \\odot B,$ and $\\odot C$ are 10, 30 and 10 units, respectively. Find AC if $\\overline{A Z} \\cong \\overline{C W}$ and $C W=2$.", "answer": "34"} {"id": "hiyouga_geometry3k_286", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_286_0.png"], "problem": "\nFind $m∠1$.", "answer": "53"} {"id": "hiyouga_geometry3k_287", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_287_0.png"], "problem": "\nIn rhombus $A B C D, m \\angle D A B=2, m \\angle A D C$ and $C B=6$. Find $m \\angle A D B$", "answer": "30"} {"id": "hiyouga_geometry3k_288", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_288_0.png"], "problem": "\n$\\overline{WTY} \\cong \\overline{TWY}$. Find $x$.", "answer": "5"} {"id": "hiyouga_geometry3k_289", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_289_0.png"], "problem": "\nQuadrilateral $WXYZ$ is a rectangle. Find the measure of $\\angle 6$ if $m∠1 = 30$.", "answer": "60"} {"id": "hiyouga_geometry3k_290", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_290_0.png"], "problem": "\nIn $\\odot Z, \\angle W Z X \\cong \\angle X Z Y, m \\angle V Z U=4 x$, $m \\angle U Z Y=2 x+24,$ and $\\overline{V Y}$ and $\\overline{W U}$ are diameters.\r\nFind $m\\widehat{W U X}$", "answer": "308"} {"id": "hiyouga_geometry3k_291", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_291_0.png"], "problem": "\nFind x.", "answer": "10"} {"id": "hiyouga_geometry3k_292", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_292_0.png"], "problem": "\nFind x. Assume that segments that appear to be tangent are tangent. Round to the nearest tenth if necessary.", "answer": "10"} {"id": "hiyouga_geometry3k_293", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_293_0.png"], "problem": "\nFind the perimeter of the figure.", "answer": "32"} {"id": "hiyouga_geometry3k_294", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_294_0.png"], "problem": "\nFind the measure of the altitude drawn to the hypotenuse.", "answer": "\\sqrt { 336 }"} {"id": "hiyouga_geometry3k_295", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_295_0.png"], "problem": "\nUse parallelogram MNPR to find $m \\angle MNP$", "answer": "71"} {"id": "hiyouga_geometry3k_296", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_296_0.png"], "problem": "\nIn the figure, $\\triangle A B C \\sim \\triangle D E F . \\overline{B G}$ is a median of $\\triangle A B C,$ and $\\overline{E H}$ is a median of $\\triangle D E F .$ Find $E H$ if $B C=30, B G=15,$ and $E F=15$", "answer": "7.5"} {"id": "hiyouga_geometry3k_297", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_297_0.png"], "problem": "\nFind x. Round to the nearest tenth if necessary. Assume that segments that appear\r\nto be tangent are tangent.", "answer": "2"} {"id": "hiyouga_geometry3k_298", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_298_0.png"], "problem": "\nFind $m \\angle Y$", "answer": "80"} {"id": "hiyouga_geometry3k_299", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_299_0.png"], "problem": "\nEquilateral pentagon $P Q R S T$ is inscribed in $\\odot U$. Find $m \\widehat{Q R}$", "answer": "72"} {"id": "hiyouga_geometry3k_300", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_300_0.png"], "problem": "\nIn the figure, $m ∠9 = 75$. Find the measure of $\\angle 6$.", "answer": "105"} {"id": "hiyouga_geometry3k_301", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_301_0.png"], "problem": "\nGiven that the perimeter of $\\triangle A B C=25,$ find $x$. Assume that segments that appear tangent to circles are tangent.", "answer": "3"} {"id": "hiyouga_geometry3k_302", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_302_0.png"], "problem": "\n$\\overline{HK}$ and $\\overline{IG}$ are diameters of $\\odot L$. Find $m \\widehat {IHJ}$.", "answer": "270"} {"id": "hiyouga_geometry3k_303", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_303_0.png"], "problem": "\nFind the scale factor from $W$ to $W'$.", "answer": "\\frac { 1 } { 3 }"} {"id": "hiyouga_geometry3k_304", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_304_0.png"], "problem": "\nFind x.", "answer": "\\sqrt { 7 }"} {"id": "hiyouga_geometry3k_305", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_305_0.png"], "problem": "\nFind tan X", "answer": "\\frac { 5 } { 12 }"} {"id": "hiyouga_geometry3k_306", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_306_0.png"], "problem": "\nFind the area of the parallelogram. Round to the nearest tenth if necessary.", "answer": "1440"} {"id": "hiyouga_geometry3k_307", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_307_0.png"], "problem": "\nIf $A B C D$ is a rhombus, and $m \\angle A B C=70^{\\circ}$, what is $m \\angle 1 ?$", "answer": "55"} {"id": "hiyouga_geometry3k_308", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_308_0.png"], "problem": "\n$MC=7,RM=4$, and $AT=16$. Find $MS$.", "answer": "3.5"} {"id": "hiyouga_geometry3k_309", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_309_0.png"], "problem": "\nFor trapezoid $ABCD$, $S$ and $T$ are midpoints of the legs. If $CD=14$, $ST=10$, and $AB=2x$, find $x$.", "answer": "3"} {"id": "hiyouga_geometry3k_310", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_310_0.png"], "problem": "\nFind $m \\angle 4$.", "answer": "71.5"} {"id": "hiyouga_geometry3k_311", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_311_0.png"], "problem": "\nCircles $G, J,$ and $K$ all intersect at $L$ If $G H=10$, find FH", "answer": "20"} {"id": "hiyouga_geometry3k_312", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_312_0.png"], "problem": "\nFind DE", "answer": "10"} {"id": "hiyouga_geometry3k_313", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_313_0.png"], "problem": "\n$\\triangle ABC \\sim \\triangle FDG$. Find the value of $x$.", "answer": "10"} {"id": "hiyouga_geometry3k_314", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_314_0.png"], "problem": "\nFind x. Assume that segments that appear to be tangent are tangent.", "answer": "5"} {"id": "hiyouga_geometry3k_315", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_315_0.png"], "problem": "\nFor trapezoid QRTU, V and S are midpoints of the legs. If QR = 4 and UT = 16, find VS.", "answer": "10"} {"id": "hiyouga_geometry3k_316", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_316_0.png"], "problem": "\nFind z", "answer": "36 \\sqrt { 7 }"} {"id": "hiyouga_geometry3k_317", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_317_0.png"], "problem": "\nLines $l$, $m$, and $n$ are perpendicular bisectors of $\\triangle PQR$ and meet at $T$. If $TQ = 2x$, $PT = 3y - 1$, and $TR = 8$, find $z$.", "answer": "3"} {"id": "hiyouga_geometry3k_318", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_318_0.png"], "problem": "\nUse parallelogram JKLM to find $m \\angle JML$", "answer": "109"} {"id": "hiyouga_geometry3k_319", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_319_0.png"], "problem": "\nFind $x$.", "answer": "12.75"} {"id": "hiyouga_geometry3k_320", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_320_0.png"], "problem": "\nFind $\\angle C$ of quadrilateral ABCD", "answer": "90"} {"id": "hiyouga_geometry3k_321", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_321_0.png"], "problem": "\n$P Q R S$ is a rhombus inscribed in a circle. Find $m \\widehat{SP}$", "answer": "90"} {"id": "hiyouga_geometry3k_322", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_322_0.png"], "problem": "\nFind the variable of $x$ to the nearest tenth. Assume that segments that appear to be tangent are tangent.", "answer": "6.0"} {"id": "hiyouga_geometry3k_323", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_323_0.png"], "problem": "\nThe segment is tangent to the circle. Find $x$. Round to the nearest tenth.", "answer": "8.5"} {"id": "hiyouga_geometry3k_324", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_324_0.png"], "problem": "\nFind $x$.", "answer": "16"} {"id": "hiyouga_geometry3k_325", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_325_0.png"], "problem": "\nIf $ST=8, TR=4$, and $PT=6$, find $QR$.", "answer": "9"} {"id": "hiyouga_geometry3k_326", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_326_0.png"], "problem": "\nFind the value of $x$ in each diagram", "answer": "71"} {"id": "hiyouga_geometry3k_327", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_327_0.png"], "problem": "\n$m \\angle 2=2 x, m \\angle 3=x$ Find $m\\angle 2$", "answer": "60"} {"id": "hiyouga_geometry3k_328", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_328_0.png"], "problem": "\nFind the perimeter of the parallelogram. Round to the nearest tenth if necessary.", "answer": "76"} {"id": "hiyouga_geometry3k_329", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_329_0.png"], "problem": "\n$\\triangle JKL \\sim \\triangle WYZ$. Find $x$.", "answer": "21"} {"id": "hiyouga_geometry3k_330", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_330_0.png"], "problem": "\nFind $KL$.", "answer": "12"} {"id": "hiyouga_geometry3k_331", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_331_0.png"], "problem": "\nFind $QS$.", "answer": "25"} {"id": "hiyouga_geometry3k_332", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_332_0.png"], "problem": "\nparallelogram MNPQ with $m \\angle M=10 x$ and $m \\angle N=20 x$, find $\\angle M$", "answer": "60"} {"id": "hiyouga_geometry3k_333", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_333_0.png"], "problem": "\nFind $x$.", "answer": "90"} {"id": "hiyouga_geometry3k_334", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_334_0.png"], "problem": "\nFind y.", "answer": "2 \\sqrt { 6 }"} {"id": "hiyouga_geometry3k_335", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_335_0.png"], "problem": "\n$\\overline{AB} \\perp \\overline{DC}$ and $\\overline{GH} \\perp \\overline{FE}$.\r\nIf $\\triangle ACD \\sim \\triangle GEF$, find $AB$.", "answer": "2.2"} {"id": "hiyouga_geometry3k_336", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_336_0.png"], "problem": "\nFind $JQ$ if $Q$ is the incenter of $\\triangle JLN$. Rounded to the nearest hundredth.", "answer": "18.79"} {"id": "hiyouga_geometry3k_337", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_337_0.png"], "problem": "\nIf $FGHJ$ is a kite, find $m\\angle GFJ$.", "answer": "80"} {"id": "hiyouga_geometry3k_338", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_338_0.png"], "problem": "\nFind $x$ so that $m || n$.", "answer": "20"} {"id": "hiyouga_geometry3k_339", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_339_0.png"], "problem": "\nFind x.", "answer": "2 \\sqrt { 11 }"} {"id": "hiyouga_geometry3k_340", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_340_0.png"], "problem": "\nFor the pair of similar figures, use the given areas to find the scale factor from the blue to the green figure.", "answer": "\\frac { 1 } { 2 }"} {"id": "hiyouga_geometry3k_341", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_341_0.png"], "problem": "\nFind the value of the variable $y$ in the figure.", "answer": "10"} {"id": "hiyouga_geometry3k_342", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_342_0.png"], "problem": "\nFind $m \\widehat {XZ}$.", "answer": "88"} {"id": "hiyouga_geometry3k_343", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_343_0.png"], "problem": "\nExpress the ratio of $\\tan M$ as a decimal to the nearest hundredth.", "answer": "0.42"} {"id": "hiyouga_geometry3k_344", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_344_0.png"], "problem": "\nExpress the ratio of $\\tan L$ as a decimal to the nearest hundredth.", "answer": "0.42"} {"id": "hiyouga_geometry3k_345", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_345_0.png"], "problem": "\nIn $\\odot S$, $m \\widehat {PQR}=98$, Find $m \\widehat {PQ}$.", "answer": "49"} {"id": "hiyouga_geometry3k_346", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_346_0.png"], "problem": "\nFind $h$ in each triangle.", "answer": "11"} {"id": "hiyouga_geometry3k_347", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_347_0.png"], "problem": "\nFind x", "answer": "93"} {"id": "hiyouga_geometry3k_348", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_348_0.png"], "problem": "\n$m \\angle 4=2 y+32$ and $m \\angle 5=3 y-3$. Find $y$.", "answer": "35"} {"id": "hiyouga_geometry3k_349", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_349_0.png"], "problem": "\nIn the figure, square $ABDC$ is inscribed in $\\odot K$. Find the measure of a central angle.", "answer": "90"} {"id": "hiyouga_geometry3k_350", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_350_0.png"], "problem": "\nCircle $J$ has a radius of $10$ units, $\\odot K$ has a radius of $8$ units, and $BC=5.4$ units. Find $CK$.", "answer": "2.6"} {"id": "hiyouga_geometry3k_351", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_351_0.png"], "problem": "\nFind $x$ so that the quadrilateral is a parallelogram.", "answer": "5"} {"id": "hiyouga_geometry3k_352", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_352_0.png"], "problem": "\nFind x.", "answer": "14"} {"id": "hiyouga_geometry3k_353", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_353_0.png"], "problem": "\nFind x. Assume that segments that appear to be tangent are tangent.", "answer": "\\frac { 14 } { 3 }"} {"id": "hiyouga_geometry3k_354", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_354_0.png"], "problem": "\nFind x. Round to the nearest hundredth.", "answer": "27.44"} {"id": "hiyouga_geometry3k_355", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_355_0.png"], "problem": "\nIn $\\odot M$, $FL=24,HJ=48$, and $m \\widehat {HP}=65$. Find $NJ$.", "answer": "24"} {"id": "hiyouga_geometry3k_356", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_356_0.png"], "problem": "\nFind the length of $AC$ in the isosceles triangle ABC.", "answer": "7"} {"id": "hiyouga_geometry3k_357", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_357_0.png"], "problem": "\nFind $m \\angle D$.", "answer": "80"} {"id": "hiyouga_geometry3k_358", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_358_0.png"], "problem": "\nThe degree measures of minor arc $\\widehat{A C}$ and major arc $\\widehat{A D C}$ are $x$ and $y$ respectively. If $m∠ABC = 70°$, find $x$.", "answer": "110"} {"id": "hiyouga_geometry3k_359", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_359_0.png"], "problem": "\nCircles $G, J,$ and $K$ all intersect at $L$ If $G H=10,$ find each measure.\r\nFind JL", "answer": "5"} {"id": "hiyouga_geometry3k_360", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_360_0.png"], "problem": "\nQuadrilateral DEFG is a rectangle. If $m\\angle EDF = 5x - 3$ and $m\\angle DFG = 3x + 7$, find $m\\angle EDF$.", "answer": "22"} {"id": "hiyouga_geometry3k_361", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_361_0.png"], "problem": "\nFind the area of the figure.", "answer": "120"} {"id": "hiyouga_geometry3k_362", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_362_0.png"], "problem": "\nFind z", "answer": "\\frac { 40 } { 3 }"} {"id": "hiyouga_geometry3k_363", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_363_0.png"], "problem": "\nFind $m \\angle B$.", "answer": "61"} {"id": "hiyouga_geometry3k_364", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_364_0.png"], "problem": "\nFor trapezoid $Q R S T, A$ and $B$ are midpoints of the legs. Find $m \\angle S$", "answer": "135"} {"id": "hiyouga_geometry3k_365", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_365_0.png"], "problem": "\nIf $CE=t-2$. $EB=t+1$, $CD=2$, and $CA=10$, find $CE$.", "answer": "1"} {"id": "hiyouga_geometry3k_366", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_366_0.png"], "problem": "\nUse parallelogram MNPR to find $m \\angle RNP$", "answer": "38"} {"id": "hiyouga_geometry3k_367", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_367_0.png"], "problem": "\nFind $x$. Assume that segments that appear to be tangent are tangent.", "answer": "6"} {"id": "hiyouga_geometry3k_368", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_368_0.png"], "problem": "\nFind the measure of $\\angle 3$ in the figure.", "answer": "68"} {"id": "hiyouga_geometry3k_369", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_369_0.png"], "problem": "\n$\\triangle LMN \\cong \\triangle QRS$. Find $x$.", "answer": "5"} {"id": "hiyouga_geometry3k_370", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_370_0.png"], "problem": "\nFind the area of the triangle. Round to the nearest tenth if necessary.", "answer": "54"} {"id": "hiyouga_geometry3k_371", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_371_0.png"], "problem": "\n$\\triangle RST \\cong \\triangle ABC$. Find $x$.", "answer": "10"} {"id": "hiyouga_geometry3k_372", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_372_0.png"], "problem": "\nFind the area of the regular polygon. Round to the nearest tenth.", "answer": "23.4"} {"id": "hiyouga_geometry3k_373", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_373_0.png"], "problem": "\nUse parallelogram $ABCD$ to find $AD$", "answer": "18"} {"id": "hiyouga_geometry3k_374", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_374_0.png"], "problem": "\nFind the area of the parallelogram. Round to the nearest tenth if necessary.", "answer": "10.2"} {"id": "hiyouga_geometry3k_375", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_375_0.png"], "problem": "\nTrapezoid $GHJK$ has an area of 188.35 square feet. If $HJ$ is 16.5 feet, find $GK$.", "answer": "26.8"} {"id": "hiyouga_geometry3k_376", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_376_0.png"], "problem": "\nWhich of the following facts would be sufficient to prove that line $d$ is parallel to $\\overline {XZ}$?", "answer": "\\angle 3 \\cong \\angle Z"} {"id": "hiyouga_geometry3k_377", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_377_0.png"], "problem": "\nIf $LK=4,MP=3,PQ=6,KJ=2,RS=6$, and $LP=2$, find $ML$.", "answer": "2"} {"id": "hiyouga_geometry3k_378", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_378_0.png"], "problem": "\nFind x", "answer": "4 \\sqrt { 6 }"} {"id": "hiyouga_geometry3k_379", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_379_0.png"], "problem": "\nFind $x$. $A=148$ $m^2$.", "answer": "18.5"} {"id": "hiyouga_geometry3k_380", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_380_0.png"], "problem": "\nABCD is a parallelogram with side lengths as indicated in the figure at the right. The perimeter of ABCD is 22. Find AB", "answer": "7"} {"id": "hiyouga_geometry3k_381", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_381_0.png"], "problem": "\nFind x to the nearest tenth. Assume that segments that appear to be tangent are tangent.", "answer": "11.2"} {"id": "hiyouga_geometry3k_382", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_382_0.png"], "problem": "\nFind $x$.", "answer": "30"} {"id": "hiyouga_geometry3k_383", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_383_0.png"], "problem": "\nIf $XM=4,XN=6$, and $NZ=9$, find $XY$.", "answer": "10"} {"id": "hiyouga_geometry3k_384", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_384_0.png"], "problem": "\nIn $\\odot O, \\overline{E C}$ and $\\overline{A B}$ are diameters, and $\\angle B O D \\cong \\angle D O E \\cong \\angle E O F \\cong \\angle F O A$\r\nFind $m\\widehat{A C}$", "answer": "90"} {"id": "hiyouga_geometry3k_385", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_385_0.png"], "problem": "\nFind z.", "answer": "3 \\sqrt { 19 }"} {"id": "hiyouga_geometry3k_386", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_386_0.png"], "problem": "\nIn $\\odot F, \\overline{F H} \\cong \\overline{F L}$ and $\\mathrm{FK}=17$.\r\nFind JG", "answer": "30"} {"id": "hiyouga_geometry3k_387", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_387_0.png"], "problem": "\n$\\overrightarrow{BA}$ and $\\overrightarrow{BC}$ are opposite rays and $\\overrightarrow{BD}$ bisects $\\angle ABF$. If $m \\angle FBC=2x+25$ and $m \\angle ABF=10x-1$, find $m \\angle DBF$.", "answer": "64.5"} {"id": "hiyouga_geometry3k_388", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_388_0.png"], "problem": "\nFind $XY$ of isosceles $\\triangle XYZ$", "answer": "7"} {"id": "hiyouga_geometry3k_389", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_389_0.png"], "problem": "\nFind $z$ in the given parallelogram", "answer": "4.5"} {"id": "hiyouga_geometry3k_390", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_390_0.png"], "problem": "\n$\\overline{MN} \\| \\overline{BC}$. Solve for $x$.", "answer": "9"} {"id": "hiyouga_geometry3k_391", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_391_0.png"], "problem": "\nFind y.", "answer": "28"} {"id": "hiyouga_geometry3k_392", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_392_0.png"], "problem": "\nFind the scale factor from $Q$ to $Q'$.", "answer": "3"} {"id": "hiyouga_geometry3k_393", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_393_0.png"], "problem": "\n$MC=7,RM=4$, and $AT = 16$. Find $MB$.", "answer": "8"} {"id": "hiyouga_geometry3k_394", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_394_0.png"], "problem": "\nFind the perimeter of $\\triangle B C D,$ if $\\triangle B C D \\sim \\triangle F D E, C D=12$, $F D=5, F E=4,$ and $D E=8$.", "answer": "25.5"} {"id": "hiyouga_geometry3k_395", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_395_0.png"], "problem": "\nIn rhombus LMPQ, $m \\angle Q L M=2 x^{2}-10$, $m \\angle Q P M=8 x$, and $M P=10$ . \r\nFind the perimeter of $LMPQ$", "answer": "40"} {"id": "hiyouga_geometry3k_396", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_396_0.png"], "problem": "\nFind $BD$ if $\\overline{B F}$ bisects $\\angle A B C$ and $\\overline{A C} \\| \\overline{E D}, B A=6, B C=7.5$, $A C=9,$ and $D E=9$", "answer": "13.5"} {"id": "hiyouga_geometry3k_397", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_397_0.png"], "problem": "\nFind y.", "answer": "12 \\sqrt { 2 }"} {"id": "hiyouga_geometry3k_398", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_398_0.png"], "problem": "\nQuadrilateral EFGH is a rectangle. If EF = 4x - 6 and HG = x + 3, find EF.", "answer": "6"} {"id": "hiyouga_geometry3k_399", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_399_0.png"], "problem": "\nFind $m \\angle R C M$", "answer": "43"} {"id": "hiyouga_geometry3k_400", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_400_0.png"], "problem": "\nUse parallelogram ABCD to find $m \\angle CDF $", "answer": "43"} {"id": "hiyouga_geometry3k_401", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_401_0.png"], "problem": "\nPoint $D$ is the center of the circle. What is $m \\angle A B C ?$", "answer": "90"} {"id": "hiyouga_geometry3k_402", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_402_0.png"], "problem": "\nFind the measure of $\\angle 3$.", "answer": "95"} {"id": "hiyouga_geometry3k_403", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_403_0.png"], "problem": "\nQuadrilateral $WXYZ$ is a rectangle. Find the measure of $\\angle 3$ if $m∠1 = 30$.", "answer": "60"} {"id": "hiyouga_geometry3k_404", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_404_0.png"], "problem": "\nFind x. Assume that segments that appear to be tangent are tangent.", "answer": "4"} {"id": "hiyouga_geometry3k_405", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_405_0.png"], "problem": "\nFind $m \\angle 2$ if $m \\widehat{B C}=30$ and $m \\widehat{A D}=20$", "answer": "155"} {"id": "hiyouga_geometry3k_406", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_406_0.png"], "problem": "\nFind x. Assume that any segment that appears to be tangent is tangent.", "answer": "25"} {"id": "hiyouga_geometry3k_407", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_407_0.png"], "problem": "\nFind the area of the shaded region. Assume that all polygons that appear to be regular are regular. Round to the nearest tenth.", "answer": "56.9"} {"id": "hiyouga_geometry3k_408", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_408_0.png"], "problem": "\nFind x. Round to the nearest tenth.", "answer": "37.2"} {"id": "hiyouga_geometry3k_409", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_409_0.png"], "problem": "\nIf RL = 5, RT = 9, and WS = 6, find RW.", "answer": "7.5"} {"id": "hiyouga_geometry3k_410", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_410_0.png"], "problem": "\nFind the measure of $\\angle AFB$ on $\\odot F$ with diameter $\\overline{AC} $.", "answer": "108"} {"id": "hiyouga_geometry3k_411", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_411_0.png"], "problem": "\nFind x.", "answer": "4 \\sqrt { 6 }"} {"id": "hiyouga_geometry3k_412", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_412_0.png"], "problem": "\nFind the area of the parallelogram. Round to the nearest tenth if necessary.", "answer": "207.8"} {"id": "hiyouga_geometry3k_413", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_413_0.png"], "problem": "\nFind the area of the parallelogram. Round to the nearest tenth if necessary.", "answer": "178.2"} {"id": "hiyouga_geometry3k_414", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_414_0.png"], "problem": "\nFind the area of the regular polygon figure. Round to the nearest tenth.", "answer": "65.0"} {"id": "hiyouga_geometry3k_415", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_415_0.png"], "problem": "\nA regular pentagon and a square share a mutual vertex $X$. The sides $\\overline{X Y}$ and $\\overline{X Z}$ are sides of a third regular polygon with a vertex at $X .$ How many sides does this polygon have?", "answer": "20"} {"id": "hiyouga_geometry3k_416", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_416_0.png"], "problem": "\nFind $x$ if $\\triangle JLM \\sim \\triangle QST$.", "answer": "1.5"} {"id": "hiyouga_geometry3k_417", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_417_0.png"], "problem": "\n$\\triangle WXY \\cong \\triangle WXZ$. Find $y$.", "answer": "4"} {"id": "hiyouga_geometry3k_418", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_418_0.png"], "problem": "\nPolygon ABCD ~ polygon AEFG, $m\\angle AGF = 108$, GF = 14, AD = 12, DG = 4.5, EF = 8, and AB = 26.\r\nFind $m\\angle ADC$", "answer": "108"} {"id": "hiyouga_geometry3k_419", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_419_0.png"], "problem": "\nFind the measure of $\\angle 3$ if $m∠4= m∠5$.", "answer": "116"} {"id": "hiyouga_geometry3k_420", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_420_0.png"], "problem": "\nUse parallelogram MNPR to find $x$", "answer": "8"} {"id": "hiyouga_geometry3k_421", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_421_0.png"], "problem": "\nThe segment is tangent to the circle. Find $x$.", "answer": "16"} {"id": "hiyouga_geometry3k_422", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_422_0.png"], "problem": "\nJKLM is a rectangle. MLPR is a rhombus. $\\angle J M K \\cong \\angle R M P$, $m \\angle J M K=55, \\text { and } m \\angle M R P=70 . Find $m \\angle K M L$", "answer": "35"} {"id": "hiyouga_geometry3k_423", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_423_0.png"], "problem": "\nQuadrilateral ABCD is a rectangle. $m\\angle 2 = 40$. Find $m \\angle 8$", "answer": "100"} {"id": "hiyouga_geometry3k_424", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_424_0.png"], "problem": "\nFind $m \\angle 3$.", "answer": "38"} {"id": "hiyouga_geometry3k_425", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_425_0.png"], "problem": "\nFind y.", "answer": "8 \\sqrt { 3 }"} {"id": "hiyouga_geometry3k_426", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_426_0.png"], "problem": "\nEach pair of polygons is similar. Find AC", "answer": "7.6"} {"id": "hiyouga_geometry3k_427", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_427_0.png"], "problem": "\n$\\odot P \\cong \\odot Q$, Find $x$.", "answer": "11"} {"id": "hiyouga_geometry3k_428", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_428_0.png"], "problem": "\n$\\overline{AD}$ and $\\overline{CG}$ are diameters of $\\odot B$. Find $m \\widehat {AG}$.", "answer": "55"} {"id": "hiyouga_geometry3k_429", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_429_0.png"], "problem": "\nRefer to the triangle shown below. Find $y$ to the nearest tenth.", "answer": "2 \\sqrt { 41 }"} {"id": "hiyouga_geometry3k_430", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_430_0.png"], "problem": "\nFind $PN$.", "answer": "30"} {"id": "hiyouga_geometry3k_431", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_431_0.png"], "problem": "\nFind $m \\angle A B C$\r\nif $m \\angle C D A=61$", "answer": "140"} {"id": "hiyouga_geometry3k_432", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_432_0.png"], "problem": "\nFind $m\\angle 2$", "answer": "90"} {"id": "hiyouga_geometry3k_433", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_433_0.png"], "problem": "\nThe diagonals of rhombus FGHJ intersect at K. If $GH = x + 9$ and $JH = 5x - 2$, find $x$.", "answer": "2.75"} {"id": "hiyouga_geometry3k_434", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_434_0.png"], "problem": "\n$\\triangle RSV \\cong \\triangle TVS$. Find $x$.", "answer": "12"} {"id": "hiyouga_geometry3k_435", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_435_0.png"], "problem": "\nIn $\\odot M$, $FL=24,HJ=48$, and $m \\widehat {HP}=65$. Find $m \\widehat {HJ}$.", "answer": "130"} {"id": "hiyouga_geometry3k_436", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_436_0.png"], "problem": "\nFind x. Round to the nearest tenth.", "answer": "17.4"} {"id": "hiyouga_geometry3k_437", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_437_0.png"], "problem": "\nIf $\\frac{I J}{X J}=\\frac{HJ}{YJ}, m \\angle W X J=130$\r\nand $m \\angle WZG=20,$ find $m \\angle J$", "answer": "60"} {"id": "hiyouga_geometry3k_438", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_438_0.png"], "problem": "\nThe ratio of the measures of the angles of the triangle below is 3 : 2 : 1. Which of the following is not an angle measure of the triangle?", "answer": "45"} {"id": "hiyouga_geometry3k_439", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_439_0.png"], "problem": "\nFind $G I$ if $G H=9, G K=6,$ and $K J=4$", "answer": "15"} {"id": "hiyouga_geometry3k_440", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_440_0.png"], "problem": "\nFind $AB$.", "answer": "6.25"} {"id": "hiyouga_geometry3k_441", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_441_0.png"], "problem": "\nIn the figure, a regular polygon is inscribed in a circle. Find the measure of a central angle.", "answer": "60"} {"id": "hiyouga_geometry3k_442", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_442_0.png"], "problem": "\nIn rhombus $A B C D, A B=2 x+3$ and $B C=5 x$. Find AD.", "answer": "5"} {"id": "hiyouga_geometry3k_443", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_443_0.png"], "problem": "\nIn the figure, $m∠3 = 110$ and $m ∠ 12 = 55$. Find the measure of $∠1$.", "answer": "110"} {"id": "hiyouga_geometry3k_444", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_444_0.png"], "problem": "\nQuadrilateral $WXYZ$ is a rectangle. Find the measure of $\\angle 5$ if $m∠1 = 30$.", "answer": "30"} {"id": "hiyouga_geometry3k_445", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_445_0.png"], "problem": "\nEach pair of polygons is similar. Find GF", "answer": "7.5"} {"id": "hiyouga_geometry3k_446", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_446_0.png"], "problem": "\n$a=14, b=48,$ and $c=50$ find $sinA$", "answer": "0.28"} {"id": "hiyouga_geometry3k_447", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_447_0.png"], "problem": "\nFind x", "answer": "10 \\sqrt { 3 }"} {"id": "hiyouga_geometry3k_448", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_448_0.png"], "problem": "\nFind $m \\angle JKL$.", "answer": "37"} {"id": "hiyouga_geometry3k_449", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_449_0.png"], "problem": "\nFind $m \\widehat {JKL}$.", "answer": "232"} {"id": "hiyouga_geometry3k_450", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_450_0.png"], "problem": "\nFind the area of the kite.", "answer": "336"} {"id": "hiyouga_geometry3k_451", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_451_0.png"], "problem": "\nFind the area of the figure in feet. Round to the nearest tenth, if necessary.", "answer": "34.6"} {"id": "hiyouga_geometry3k_452", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_452_0.png"], "problem": "\nFind $x$.", "answer": "\\frac { 97 } { 6 }"} {"id": "hiyouga_geometry3k_453", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_453_0.png"], "problem": "\nIn $\\odot F, m \\angle D F A=50$ and $\\overline{C F} \\perp \\overline{F B}$. Find $m \\widehat{A C E}$", "answer": "230"} {"id": "hiyouga_geometry3k_454", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_454_0.png"], "problem": "\nFind x", "answer": "8 \\sqrt { 3 }"} {"id": "hiyouga_geometry3k_455", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_455_0.png"], "problem": "\nFind the area of the trapezoid.", "answer": "132"} {"id": "hiyouga_geometry3k_456", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_456_0.png"], "problem": "\nFind the area of the shaded region. Assume that the polygon is regular unless otherwise stated. Round to the nearest tenth.", "answer": "1208.1"} {"id": "hiyouga_geometry3k_457", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_457_0.png"], "problem": "\nIf $PR \\parallel KL$, KN = 9, LN = 16, PM = 2 KP, find PR", "answer": "\\frac { 50 } { 3 }"} {"id": "hiyouga_geometry3k_458", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_458_0.png"], "problem": "\nFind $m \\angle CAD$.", "answer": "44"} {"id": "hiyouga_geometry3k_459", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_459_0.png"], "problem": "\nThe rectangle is inscribed into the circle. Find the exact circumference of the circle.", "answer": "10 \\pi"} {"id": "hiyouga_geometry3k_460", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_460_0.png"], "problem": "\nFind x. Assume that segments that appear to be tangent are tangent.", "answer": "12"} {"id": "hiyouga_geometry3k_461", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_461_0.png"], "problem": "\nFind $x$.", "answer": "5"} {"id": "hiyouga_geometry3k_462", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_462_0.png"], "problem": "\nThe diameter of $\\odot S$ is $30$ units, the diameter of $\\odot R$ is $20$ units, and $DS=9$ units. Find $RC$.", "answer": "4"} {"id": "hiyouga_geometry3k_463", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_463_0.png"], "problem": "\nFind the area of the figure. Round to the nearest tenth.", "answer": "28.3"} {"id": "hiyouga_geometry3k_464", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_464_0.png"], "problem": "\nIn $\\odot M$, $FL=24,HJ=48$, and $m \\widehat {HP}=65$. Find $m \\widehat {PJ}$.", "answer": "65"} {"id": "hiyouga_geometry3k_465", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_465_0.png"], "problem": "\n$\\overline{AB}$ is a diameter, $AC=8$ inches, and $BC=15$ inches. Find the circumference of the circle.", "answer": "17 \\pi"} {"id": "hiyouga_geometry3k_466", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_466_0.png"], "problem": "\nFind $x$.", "answer": "70"} {"id": "hiyouga_geometry3k_467", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_467_0.png"], "problem": "\nFind $x$.", "answer": "65"} {"id": "hiyouga_geometry3k_468", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_468_0.png"], "problem": "\n$m \\angle BAC=38$, $BC=5$, and $DC=5$, find $m \\angle DAC$.", "answer": "38"} {"id": "hiyouga_geometry3k_469", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_469_0.png"], "problem": "\nJKLM is a rectangle. MLPR is a rhombus. $\\angle J M K \\cong \\angle R M P$, $m \\angle J M K=55, \\text { and } m \\angle M R P=70 . Find $m \\angle K L P$", "answer": "160"} {"id": "hiyouga_geometry3k_470", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_470_0.png"], "problem": "\nIn $\\odot P$, the radius is $2$ inches, find the length of $\\widehat {RS}$. Round to the nearest hundredth.", "answer": "4.54"} {"id": "hiyouga_geometry3k_471", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_471_0.png"], "problem": "\nFind the perimeter of $\\triangle W Z X$, if $\\triangle W Z X \\sim \\triangle S R T, S T=6$, $W X=5,$ and the perimeter of $\\triangle S R T=15$.", "answer": "12.5"} {"id": "hiyouga_geometry3k_472", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_472_0.png"], "problem": "\nEquilateral pentagon $P Q R S T$ is inscribed in $\\odot U$.\r\nFind $m \\angle P S R$", "answer": "72"} {"id": "hiyouga_geometry3k_473", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_473_0.png"], "problem": "\n$\\overline{EB} \\| \\overline{DC}$. Find $AB$.", "answer": "7.5"} {"id": "hiyouga_geometry3k_474", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_474_0.png"], "problem": "\nQuadrilateral ABCD is a rectangle. Find x", "answer": "12"} {"id": "hiyouga_geometry3k_475", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_475_0.png"], "problem": "\nExpress the ratio of $\\cos P$ as a decimal to the nearest hundredth.", "answer": "0.47"} {"id": "hiyouga_geometry3k_476", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_476_0.png"], "problem": "\nFind the area of the shaded sector. Round to the nearest tenth.", "answer": "1.8"} {"id": "hiyouga_geometry3k_477", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_477_0.png"], "problem": "\nFind y. Round to the nearest tenth, if necessary.", "answer": "7.4"} {"id": "hiyouga_geometry3k_478", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_478_0.png"], "problem": "\n$Q$ is the centroid and $BE=9$. Find $BQ$.", "answer": "6"} {"id": "hiyouga_geometry3k_479", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_479_0.png"], "problem": "\nFind the measure of $\\angle CFD$ on $\\odot F$ with diameter $\\overline{AC} $.", "answer": "123"} {"id": "hiyouga_geometry3k_480", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_480_0.png"], "problem": "\nFind x.", "answer": "33 \\sqrt { 3 }"} {"id": "hiyouga_geometry3k_481", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_481_0.png"], "problem": "\nFind the perimeter of $\\triangle R U W$ if $\\triangle R U W \\sim \\triangle S T V$, $S T=24, V S=12, V T=18$ and $U W=21$", "answer": "63"} {"id": "hiyouga_geometry3k_482", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_482_0.png"], "problem": "\nFind the perimeter of the parallelogram. Round to the nearest tenth if necessary.", "answer": "44"} {"id": "hiyouga_geometry3k_483", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_483_0.png"], "problem": "\nFind x. Assume that segments that appear to be tangent are tangent.", "answer": "2"} {"id": "hiyouga_geometry3k_484", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_484_0.png"], "problem": "\nUse a Pythagorean Triple to find x.", "answer": "70"} {"id": "hiyouga_geometry3k_485", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_485_0.png"], "problem": "\nFind the area of the parallelogram.", "answer": "552"} {"id": "hiyouga_geometry3k_486", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_486_0.png"], "problem": "\nFind $x$.", "answer": "12.5"} {"id": "hiyouga_geometry3k_487", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_487_0.png"], "problem": "\nFind $m\\angle R$", "answer": "58"} {"id": "hiyouga_geometry3k_488", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_488_0.png"], "problem": "\nFind x. Round to the nearest hundredth.", "answer": "16.64"} {"id": "hiyouga_geometry3k_489", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_489_0.png"], "problem": "\nWhat is the area of $▱ ABCD$?", "answer": "48"} {"id": "hiyouga_geometry3k_490", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_490_0.png"], "problem": "\nFind the area of the parallelogram. Round to the nearest tenth if necessary.", "answer": "180"} {"id": "hiyouga_geometry3k_491", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_491_0.png"], "problem": "\nUse a calculator to find the measure of $∠J$ to the nearest degree.", "answer": "40"} {"id": "hiyouga_geometry3k_492", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_492_0.png"], "problem": "\nFind y", "answer": "6 \\sqrt { 2 }"} {"id": "hiyouga_geometry3k_493", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_493_0.png"], "problem": "\nFind x.", "answer": "4 \\sqrt { 2 }"} {"id": "hiyouga_geometry3k_494", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_494_0.png"], "problem": "\nEach pair of polygons is similar. Find x", "answer": "8"} {"id": "hiyouga_geometry3k_495", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_495_0.png"], "problem": "\nIn the figure, $m∠1 = 50$ and $m∠3 = 60$. Find the measure of $\\angle 4$.", "answer": "50"} {"id": "hiyouga_geometry3k_496", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_496_0.png"], "problem": "\nFind $KL$.", "answer": "12"} {"id": "hiyouga_geometry3k_497", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_497_0.png"], "problem": "\nUse parallelogram ABCD to find $m\\angle DAB$", "answer": "101"} {"id": "hiyouga_geometry3k_498", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_498_0.png"], "problem": "\nFind $m \\angle ABC$.", "answer": "51"} {"id": "hiyouga_geometry3k_499", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_499_0.png"], "problem": "\nFind BC", "answer": "4"} {"id": "hiyouga_geometry3k_500", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_500_0.png"], "problem": "\nFind the area of the parallelogram. Round to the nearest tenth if necessary.", "answer": "528"} {"id": "hiyouga_geometry3k_501", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_501_0.png"], "problem": "\n$UJ=9, VJ=3$, and $ZT=18$. Find $SJ$.", "answer": "6"} {"id": "hiyouga_geometry3k_502", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_502_0.png"], "problem": "\nFind $x$.", "answer": "30"} {"id": "hiyouga_geometry3k_503", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_503_0.png"], "problem": "\nFind the measure of $\\angle 1$.", "answer": "65"} {"id": "hiyouga_geometry3k_504", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_504_0.png"], "problem": "\nFind the value of the variable t.", "answer": "5"} {"id": "hiyouga_geometry3k_505", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_505_0.png"], "problem": "\nFind $x$ so that the quadrilateral is a parallelogram.", "answer": "4"} {"id": "hiyouga_geometry3k_506", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_506_0.png"], "problem": "\nFind $AB$.", "answer": "23"} {"id": "hiyouga_geometry3k_507", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_507_0.png"], "problem": "\nFind $m \\angle 1$ in the figure.", "answer": "113"} {"id": "hiyouga_geometry3k_508", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_508_0.png"], "problem": "\nQuadrilateral ABCD is a rhombus. If $AB = 2x + 3$ and $BC = x + 7$, find $CD$.", "answer": "11"} {"id": "hiyouga_geometry3k_509", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_509_0.png"], "problem": "\nIn the figure, KL is tangent to $\\odot M$ at K. Find the value of x.", "answer": "9.45"} {"id": "hiyouga_geometry3k_510", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_510_0.png"], "problem": "\nin $\\triangle XYZ$, $P$ is the centroid, $KP=3$, and $XJ=8$. Find $YJ$.", "answer": "8"} {"id": "hiyouga_geometry3k_511", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_511_0.png"], "problem": "\nFind $QM$.", "answer": "12"} {"id": "hiyouga_geometry3k_512", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_512_0.png"], "problem": "\nFind the area of the figure. Round to the nearest tenth if necessary.", "answer": "2256"} {"id": "hiyouga_geometry3k_513", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_513_0.png"], "problem": "\nFind $m \\angle 6$", "answer": "35"} {"id": "hiyouga_geometry3k_514", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_514_0.png"], "problem": "\nIf $LK=4,MP=3,PQ=6,KJ=2,RS=6$, and $LP=2$, find $JH$.", "answer": "4"} {"id": "hiyouga_geometry3k_515", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_515_0.png"], "problem": "\nFind $m\\angle V X W$", "answer": "65"} {"id": "hiyouga_geometry3k_516", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_516_0.png"], "problem": "\nIn the figure, $m ∠1 = 58 $, $m ∠2 = 47 $, and $m ∠3 = 26 $. Find the measure of $∠5$.", "answer": "47"} {"id": "hiyouga_geometry3k_517", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_517_0.png"], "problem": "\nQuadrilateral $A B C D$ is inscribed in $\\odot Z$ such that $m \\angle B Z A=104, m \\widehat{C B}=94,$ and $\\overline{A B} \\| \\overline{D C} .$\r\nFind $m \\angle Z A C$", "answer": "9"} {"id": "hiyouga_geometry3k_518", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_518_0.png"], "problem": "\nFind $x$.", "answer": "22.5"} {"id": "hiyouga_geometry3k_519", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_519_0.png"], "problem": "\nFind $m \\angle 3$.", "answer": "66"} {"id": "hiyouga_geometry3k_520", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_520_0.png"], "problem": "\nFind $x$.", "answer": "1.4"} {"id": "hiyouga_geometry3k_521", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_521_0.png"], "problem": "\nFind y.", "answer": "16 \\sqrt { 5 }"} {"id": "hiyouga_geometry3k_522", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_522_0.png"], "problem": "\nFind the area of the rhombus.", "answer": "136"} {"id": "hiyouga_geometry3k_523", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_523_0.png"], "problem": "\nFind x. Round the angle measure to the nearest degree", "answer": "98"} {"id": "hiyouga_geometry3k_524", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_524_0.png"], "problem": "\nFind y", "answer": "6"} {"id": "hiyouga_geometry3k_525", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_525_0.png"], "problem": "\nFind $x$.", "answer": "4.5"} {"id": "hiyouga_geometry3k_526", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_526_0.png"], "problem": "\nFind $y$ so that the quadrilateral is a parallelogram", "answer": "14"} {"id": "hiyouga_geometry3k_527", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_527_0.png"], "problem": "\nFind y.", "answer": "\\frac { 28 \\sqrt 3 } { 3 }"} {"id": "hiyouga_geometry3k_528", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_528_0.png"], "problem": "\n$\\triangle BCD \\cong \\triangle WXY$. Find $x$.", "answer": "3"} {"id": "hiyouga_geometry3k_529", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_529_0.png"], "problem": "\nQuadrilateral $WXYZ$ is a rectangle. Find the measure of $\\angle 2$ if $m∠1 = 30$.", "answer": "60"} {"id": "hiyouga_geometry3k_530", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_530_0.png"], "problem": "\nRefer to the figure at the right. Find x.", "answer": "5.17"} {"id": "hiyouga_geometry3k_531", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_531_0.png"], "problem": "\n$m \\angle 2=2 x, m \\angle 3=x$ Find $m\\angle 3$", "answer": "30"} {"id": "hiyouga_geometry3k_532", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_532_0.png"], "problem": "\nUse parallelogram ABCD to find $m \\angle AFD $", "answer": "97"} {"id": "hiyouga_geometry3k_533", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_533_0.png"], "problem": "\nFor the pair of similar figures, use the given areas to find $x$.", "answer": "8"} {"id": "hiyouga_geometry3k_534", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_534_0.png"], "problem": "\nThe square is circumscribed to the circle. Find the exact circumference of the circle.", "answer": "14 \\pi"} {"id": "hiyouga_geometry3k_535", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_535_0.png"], "problem": "\nIn $\\odot R$, find $TV$. Round to the nearest hundredth.", "answer": "18.44"} {"id": "hiyouga_geometry3k_536", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_536_0.png"], "problem": "\nThe area of trapezoid $JKLM$ is 138 square feet. The area of trapezoid $QRST$ is 5.52 square feet. If trapezoid $J K L M$ $ \\sim$ trapezoid $QRST$, find the value of $x$.", "answer": "1"} {"id": "hiyouga_geometry3k_537", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_537_0.png"], "problem": "\nFind $m \\angle Z$", "answer": "110"} {"id": "hiyouga_geometry3k_538", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_538_0.png"], "problem": "\n$\\Delta EFG$ is equilateral, and $\\overline{E H}$ bisects $\\angle E$. Find $m \\angle 2$.", "answer": "30"} {"id": "hiyouga_geometry3k_539", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_539_0.png"], "problem": "\nCircle $A$ has diameters $\\overline{D F}$ and $\\overline{P G}$\r\nIf $D F=10$, find $D A$", "answer": "5"} {"id": "hiyouga_geometry3k_540", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_540_0.png"], "problem": "\nFind the area of the triangle.", "answer": "285"} {"id": "hiyouga_geometry3k_541", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_541_0.png"], "problem": "\nFind the length of $\\widehat {JK}$. Round to the nearest hundredth.", "answer": "1.05"} {"id": "hiyouga_geometry3k_542", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_542_0.png"], "problem": "\nTriangle $LMN$ is equilateral, and $\\overline{MP}$ bisects $\\overline{LN}$. Find the measure of each side of $\\triangle LMN$.", "answer": "10"} {"id": "hiyouga_geometry3k_543", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_543_0.png"], "problem": "\nIn the figure, $m∠4 = 101$. Find the measure of $\\angle 6$.", "answer": "101"} {"id": "hiyouga_geometry3k_544", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_544_0.png"], "problem": "\nIn rhombus $A B C D, A B=2 x+3$ and $B C=5 x$. Find $m \\angle AEB$.", "answer": "90"} {"id": "hiyouga_geometry3k_545", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_545_0.png"], "problem": "\nIf $\\frac{I J}{X J}=\\frac{HJ}{YJ}, m \\angle W X J=130$\r\nand $m \\angle WZG=20,$ find $m \\angle YIZ$", "answer": "50"} {"id": "hiyouga_geometry3k_546", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_546_0.png"], "problem": "\nFind x. Round to the nearest tenth if necessary. Assume that segments that appear\r\nto be tangent are tangent.", "answer": "5.6"} {"id": "hiyouga_geometry3k_547", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_547_0.png"], "problem": "\nFind $m \\angle B G E$", "answer": "60"} {"id": "hiyouga_geometry3k_548", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_548_0.png"], "problem": "\nIn the figure, $\\overline{CP}$ is an altitude, $\\overline{CQ}$ is the angle bisector of $∠ACB$, and $R$ is the midpoint of $\\overline{AB}$. Find $m∠ACQ$ if $m∠ACB=123-x$ and $m∠QCB = 42 + x$.", "answer": "55"} {"id": "hiyouga_geometry3k_549", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_549_0.png"], "problem": "\nFind x", "answer": "10 \\sqrt { 3 }"} {"id": "hiyouga_geometry3k_550", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_550_0.png"], "problem": "\nFind $m\\angle CAM$", "answer": "28"} {"id": "hiyouga_geometry3k_551", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_551_0.png"], "problem": "\nTriangle $LMN$ is equilateral, and $\\overline{MP}$ bisects $\\overline{LN}$. Find $y$.", "answer": "18"} {"id": "hiyouga_geometry3k_552", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_552_0.png"], "problem": "\nFind x in the figure.", "answer": "34"} {"id": "hiyouga_geometry3k_553", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_553_0.png"], "problem": "\nFind y", "answer": "23.4"} {"id": "hiyouga_geometry3k_554", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_554_0.png"], "problem": "\nFind the area of the shaded region. Round to the nearest tenth.", "answer": "10.7"} {"id": "hiyouga_geometry3k_555", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_555_0.png"], "problem": "\nFind x. Round to the nearest tenth.", "answer": "18.8"} {"id": "hiyouga_geometry3k_556", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_556_0.png"], "problem": "\nFind the measure of $\\angle 2$.", "answer": "28"} {"id": "hiyouga_geometry3k_557", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_557_0.png"], "problem": "\nFind the area of the rhombus.", "answer": "264"} {"id": "hiyouga_geometry3k_558", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_558_0.png"], "problem": "\nFind the value of x.", "answer": "23"} {"id": "hiyouga_geometry3k_559", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_559_0.png"], "problem": "\nFind the area of the parallelogram.", "answer": "315"} {"id": "hiyouga_geometry3k_560", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_560_0.png"], "problem": "\n$\\overrightarrow{QP}$ and $\\overrightarrow{QR}$ are opposite rays, and $\\overrightarrow{QT}$ bisects $\\angle SOR$. If $m \\angle SOR=6x+8$ and $m \\angle TOR=4x-14,$ find $m \\angle SQT$.", "answer": "58"} {"id": "hiyouga_geometry3k_561", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_561_0.png"], "problem": "\nFind $m\\angle W$", "answer": "76"} {"id": "hiyouga_geometry3k_562", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_562_0.png"], "problem": "\nFind the area of the trapezoid.", "answer": "180"} {"id": "hiyouga_geometry3k_563", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_563_0.png"], "problem": "\nIn $\\triangle CDF$, $K$ is the centroid and $DK=16$. Find $CD$.", "answer": "18"} {"id": "hiyouga_geometry3k_564", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_564_0.png"], "problem": "\nFind PQ", "answer": "6"} {"id": "hiyouga_geometry3k_565", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_565_0.png"], "problem": "\nFind the area of the parallelogram. Round to the nearest tenth if necessary.", "answer": "169.7"} {"id": "hiyouga_geometry3k_566", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_566_0.png"], "problem": "\nIn RSTV, RS $=6, V T=3$ and $R X$ is twice the length of $X V .$ Find $X Y .$", "answer": "4"} {"id": "hiyouga_geometry3k_567", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_567_0.png"], "problem": "\nFor trapezoid $ABCD$, $S$ and $T$ are midpoints of the legs. If $AB=x+4$, $CD=3x+2$, and $ST=9$, find $AB$.", "answer": "7"} {"id": "hiyouga_geometry3k_568", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_568_0.png"], "problem": "\nFind $x$ for the equilateral triangle $RST$ if $RS = x + 9$, $ST = 2x$, and $RT = 3x - 9$.", "answer": "9"} {"id": "hiyouga_geometry3k_569", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_569_0.png"], "problem": "\nFind x. Assume that any segment that appears to be tangent is tangent.", "answer": "10"} {"id": "hiyouga_geometry3k_570", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_570_0.png"], "problem": "\n$\\overline{EB} \\| \\overline{DC}$. Find $x$.", "answer": "9.5"} {"id": "hiyouga_geometry3k_571", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_571_0.png"], "problem": "\nExpress the ratio of $\\cos X$ as a decimal to the nearest hundredth.", "answer": "0.28"} {"id": "hiyouga_geometry3k_572", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_572_0.png"], "problem": "\nIn $\\odot X, A B=30, C D=30,$ and $m \\widehat{C Z}=40$\r\nFind ND", "answer": "15"} {"id": "hiyouga_geometry3k_573", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_573_0.png"], "problem": "\nFind z.", "answer": "3"} {"id": "hiyouga_geometry3k_574", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_574_0.png"], "problem": "\nIf $CW=WF$ and $ED=30$, what is $DF$?", "answer": "15"} {"id": "hiyouga_geometry3k_575", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_575_0.png"], "problem": "\nA square is inscribed in a circle of area 18$\\pi$ square units. Find the length of a side of the square.", "answer": "6"} {"id": "hiyouga_geometry3k_576", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_576_0.png"], "problem": "\nFind the scale from $B$ to $B'$.", "answer": "\\frac { 4 } { 3 }"} {"id": "hiyouga_geometry3k_577", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_577_0.png"], "problem": "\nFind $m\\angle H$", "answer": "97"} {"id": "hiyouga_geometry3k_578", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_578_0.png"], "problem": "\nFind the area of the figure. Round to the nearest tenth if necessary.", "answer": "35.7"} {"id": "hiyouga_geometry3k_579", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_579_0.png"], "problem": "\nFind x. Round to the nearest tenth, if necessary.", "answer": "3"} {"id": "hiyouga_geometry3k_580", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_580_0.png"], "problem": "\nFind the area of the figure.", "answer": "60"} {"id": "hiyouga_geometry3k_581", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_581_0.png"], "problem": "\nFind the area of the figure.", "answer": "144"} {"id": "hiyouga_geometry3k_582", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_582_0.png"], "problem": "\nIf $A E=m-2, E C=m+4$， $A D=4,$ and $A B=20,$ find $m$", "answer": "4"} {"id": "hiyouga_geometry3k_583", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_583_0.png"], "problem": "\nFind y", "answer": "\\frac { 5 \\sqrt { 2 } } { 2 }"} {"id": "hiyouga_geometry3k_584", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_584_0.png"], "problem": "\nFind the perimeter of the figure. Round to the nearest tenth if necessary.", "answer": "24"} {"id": "hiyouga_geometry3k_585", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_585_0.png"], "problem": "\nFind the measure of $\\angle 2$ if $\\overline{A B} \\perp \\overline{B C}$.", "answer": "68"} {"id": "hiyouga_geometry3k_586", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_586_0.png"], "problem": "\nFind x", "answer": "9.3"} {"id": "hiyouga_geometry3k_587", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_587_0.png"], "problem": "\nIn $\\odot B$, $CE=13.5$. Find $BD$. Round to the nearest hundredth.", "answer": "4.29"} {"id": "hiyouga_geometry3k_588", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_588_0.png"], "problem": "\nIf $\\overline{PR} \\| \\overline{KL}, KN=9, LN=16,$ and $PM=2KP$, find $KM$.", "answer": "15"} {"id": "hiyouga_geometry3k_589", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_589_0.png"], "problem": "\nFind $m \\angle ABC$.", "answer": "22"} {"id": "hiyouga_geometry3k_590", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_590_0.png"], "problem": "\nExpress the ratio of $\\cos A$ as a decimal to the nearest hundredth.", "answer": "0.60"} {"id": "hiyouga_geometry3k_591", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_591_0.png"], "problem": "\nFind $AD$.", "answer": "7.5"} {"id": "hiyouga_geometry3k_592", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_592_0.png"], "problem": "\n$\\triangle LMN \\cong \\triangle QRS$. Find $x$.", "answer": "20"} {"id": "hiyouga_geometry3k_593", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_593_0.png"], "problem": "\nFind the circumference of the figure. Round to the nearest tenth.", "answer": "19.5"} {"id": "hiyouga_geometry3k_594", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_594_0.png"], "problem": "\nfind $sinS$", "answer": "0.6"} {"id": "hiyouga_geometry3k_595", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_595_0.png"], "problem": "\nFind $BC$ if $AB=6, AF=8, BC=x, CD=y$, $DE=2y-3$, and $FE=x+\\frac{10}{3}$.", "answer": "10"} {"id": "hiyouga_geometry3k_596", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_596_0.png"], "problem": "\nFind $x$ so that each quadrilateral is a parallelogram.", "answer": "34"} {"id": "hiyouga_geometry3k_597", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_597_0.png"], "problem": "\n$P$ is the incenter of $\\triangle AEC$. Find $m \\angle DEP$.", "answer": "28.5"} {"id": "hiyouga_geometry3k_598", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_598_0.png"], "problem": "\nFind $x$.", "answer": "5"} {"id": "hiyouga_geometry3k_599", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_599_0.png"], "problem": "\n$m \\angle 4=42$. Find $m \\angle 7$.", "answer": "138"} {"id": "hiyouga_geometry3k_600", "image_paths": ["/inspire/hdd/project/autoregressive-video-generation/czxs253130312/EasyR1/eval/data/images/hiyouga_geometry3k/hiyouga_geometry3k_600_0.png"], "problem": "\nFind the measure of $∠Z$ to the nearest tenth.", "answer": "33.7"}