id int32 1 6.98k | annotation stringclasses 132
values | source stringlengths 7 17 | problem_level int32 0 28 | problem_text_cn stringlengths 20 201 | problem_text_en stringlengths 58 424 | problem_img stringlengths 5 8 | construction_cdl listlengths 1 28 | text_cdl listlengths 0 16 | image_cdl listlengths 0 16 | goal_cdl stringlengths 8 131 | problem_answer stringclasses 906
values | theorem_seqs listlengths 0 28 | theorem_seqs_dag_json stringlengths 13 3.3k | image imagewidth (px) 48 1.6k |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
901 | XiaokaiZhang_2023-04-09 | Geometry3k-930 | 1 | 如图所示，弧AJL的角度为92。求∠LKJ的大小。 | As shown in the diagram, the measure of arc AJL is 92. Find the measure of ∠LKJ. | 901.png | [
"Shape(AKJ,JK)",
"Shape(AJL,LK,KJ)",
"Shape(ALK,KL)",
"Cocircular(A,KJL)"
] | [
"Equal(MeasureOfArc(AJL),92)"
] | [
"Equal(MeasureOfArc(AJL),92)"
] | Value(MeasureOfAngle(LKJ)) | 46 | [
"arc_property_circumference_angle_external(1,AJL,K)"
] | {"START": ["arc_property_circumference_angle_external(1,AJL,K)"]} | |
902 | XiaokaiZhang_2023-04-09 | Geometry3k-931 | 2 | 如图所示，∠WZY=35°，∠XWZ=13*x+14°，∠YXW=13*x+24°，XWZY是风筝形。求∠ZYX的大小。 | As shown in the diagram, ∠WZY=35°, ∠XWZ=13*x+14°, ∠YXW=13*x+24°, quadrilateral XWZY is a kite. Find the measure of ∠ZYX. | 902.png | [
"Shape(XW,WU,UX)",
"Shape(UW,WZ,ZU)",
"Shape(UZ,ZY,YU)",
"Shape(UY,YX,XU)",
"Collinear(ZUX)",
"Collinear(WUY)"
] | [
"Equal(MeasureOfAngle(WZY),35)",
"Equal(MeasureOfAngle(XWZ),13*x+14)",
"Equal(MeasureOfAngle(YXW),13*x+24)",
"Kite(XWZY)"
] | [
"Equal(MeasureOfAngle(WZY),35)",
"Equal(MeasureOfAngle(XWZ),13*x+14)",
"Equal(MeasureOfAngle(YXW),13*x+24)"
] | Value(MeasureOfAngle(ZYX)) | 105 | [
"kite_property_opposite_angle_equal(1,XWZY)",
"quadrilateral_property_angle_sum(1,XWZY)"
] | {"START": ["kite_property_opposite_angle_equal(1,XWZY)", "quadrilateral_property_angle_sum(1,XWZY)"]} | |
903 | XiaokaiZhang_2023-03-19 | Geometry3k-932 | 2 | 如图所示，AC=b，BA=c，BC=a，∠ABC=60°，∠CAB=30°，a=4，BC⊥AC。求b的值。 | As shown in the diagram, AC=b, BA=c, BC=a, ∠ABC=60°, ∠CAB=30°, a=4, BC is perpendicular to AC. Find the value of b. | 903.png | [
"Shape(BC,CA,AB)"
] | [
"Equal(LengthOfLine(AC),b)",
"Equal(LengthOfLine(BA),c)",
"Equal(LengthOfLine(BC),a)",
"Equal(MeasureOfAngle(ABC),60)",
"Equal(MeasureOfAngle(CAB),30)",
"Equal(a,4)",
"PerpendicularBetweenLine(BC,AC)"
] | [
"Equal(LengthOfLine(AC),b)",
"Equal(LengthOfLine(BA),c)",
"Equal(LengthOfLine(BC),a)",
"Equal(MeasureOfAngle(ABC),60)",
"Equal(MeasureOfAngle(CAB),30)",
"PerpendicularBetweenLine(BC,AC)"
] | Value(b) | 4*sqrt(3) | [
"sine_theorem(1,BCA)",
"sine_theorem(1,ABC)"
] | {"START": ["sine_theorem(1,BCA)", "sine_theorem(1,ABC)"]} | |
904 | XiaokaiZhang_2023-03-19 | Geometry3k-933 | 2 | 如图所示，JM=6，KJ=KL，LM垂直于KM。求直线JL的长度。 | As shown in the diagram, JM=6, KJ=KL, LM is perpendicular to KM. Find the length of line JL. | 904.png | [
"Shape(JK,KM,MJ)",
"Shape(MK,KL,LM)",
"Collinear(JML)"
] | [
"Equal(LengthOfLine(JM),6)",
"Equal(LengthOfLine(KJ),LengthOfLine(KL))",
"PerpendicularBetweenLine(LM,KM)"
] | [
"Equal(LengthOfLine(JM),6)",
"Equal(LengthOfLine(KJ),LengthOfLine(KL))",
"PerpendicularBetweenLine(LM,KM)"
] | Value(LengthOfLine(JL)) | 12 | [
"perpendicular_bisector_judgment_distance_equal(1,KM,LJ)",
"line_addition(1,JM,ML)"
] | {"START": ["perpendicular_bisector_judgment_distance_equal(1,KM,LJ)", "line_addition(1,JM,ML)"]} | |
905 | XiaokaiZhang_2023-03-19 | Geometry3k-934 | 3 | 如图所示，AB=26，AD=10，BC=16，DC=8，AD垂直于CD。求△ACB的周长。 | As shown in the diagram, AB=26, AD=10, BC=16, DC=8, AD⊥CD. Find the perimeter of triangle ACB. | 905.png | [
"Shape(AD,DC,CA)",
"Shape(AC,CB,BA)",
"Collinear(DCB)"
] | [
"Equal(LengthOfLine(AB),26)",
"Equal(LengthOfLine(AD),10)",
"Equal(LengthOfLine(BC),16)",
"Equal(LengthOfLine(DC),8)",
"PerpendicularBetweenLine(AD,CD)"
] | [
"Equal(LengthOfLine(AB),26)",
"Equal(LengthOfLine(AD),10)",
"Equal(LengthOfLine(BC),16)",
"Equal(LengthOfLine(DC),8)",
"PerpendicularBetweenLine(AD,CD)"
] | Value(PerimeterOfTriangle(ACB)) | 2*sqrt(41)+42 | [
"right_triangle_judgment_angle(1,ADC)",
"right_triangle_property_pythagorean(1,ADC)",
"triangle_perimeter_formula(1,ACB)"
] | {"START": ["right_triangle_judgment_angle(1,ADC)", "triangle_perimeter_formula(1,ACB)"], "right_triangle_judgment_angle(1,ADC)": ["right_triangle_property_pythagorean(1,ADC)"]} | |
906 | XiaokaiZhang_2023-03-19 | Geometry3k-935 | 8 | 如图所示，AB=x，AC=19，AD=15，BC=z，BD=y，CA⊥BA，DB⊥CB。求y的值。 | As shown in the diagram, AB=x, AC=19, AD=15, BC=z, BD=y, CA is perpendicular to BA, DB is perpendicular to CB. Find the value of y. | 906.png | [
"Shape(DB,BA,AD)",
"Shape(AB,BC,CA)",
"Collinear(DAC)"
] | [
"Equal(LengthOfLine(AB),x)",
"Equal(LengthOfLine(AC),19)",
"Equal(LengthOfLine(AD),15)",
"Equal(LengthOfLine(BC),z)",
"Equal(LengthOfLine(BD),y)",
"PerpendicularBetweenLine(CA,BA)",
"PerpendicularBetweenLine(DB,CB)"
] | [
"Equal(LengthOfLine(AB),x)",
"Equal(LengthOfLine(AC),19)",
"Equal(LengthOfLine(AD),15)",
"Equal(LengthOfLine(BC),z)",
"Equal(LengthOfLine(BD),y)",
"PerpendicularBetweenLine(CA,BA)",
"PerpendicularBetweenLine(DB,CB)"
] | Value(y) | sqrt(510) | [
"adjacent_complementary_angle(1,CAB,BAD)",
"right_triangle_judgment_angle(1,DBC)",
"right_triangle_judgment_angle(1,CAB)",
"right_triangle_judgment_angle(1,BAD)",
"line_addition(1,DA,AC)",
"right_triangle_property_pythagorean(1,DBC)",
"right_triangle_property_pythagorean(1,CAB)",
"right_triangle_prope... | {"START": ["adjacent_complementary_angle(1,CAB,BAD)", "right_triangle_judgment_angle(1,DBC)", "right_triangle_judgment_angle(1,CAB)", "line_addition(1,DA,AC)"], "adjacent_complementary_angle(1,CAB,BAD)": ["right_triangle_judgment_angle(1,BAD)"], "right_triangle_judgment_angle(1,BAD)": ["right_triangle_property_pythagor... | |
907 | XiaokaiZhang_2023-03-19 | Geometry3k-936 | 2 | 如图所示，AB=11，AC=x，BC=9，AC垂直于BC。求x的值。 | As shown in the diagram, AB=11, AC=x, BC=9, AC is perpendicular to BC. Find the value of x. | 907.png | [
"Shape(AC,CB,BA)"
] | [
"Equal(LengthOfLine(AB),11)",
"Equal(LengthOfLine(AC),x)",
"Equal(LengthOfLine(BC),9)",
"PerpendicularBetweenLine(AC,BC)"
] | [
"Equal(LengthOfLine(AB),11)",
"Equal(LengthOfLine(AC),x)",
"Equal(LengthOfLine(BC),9)",
"PerpendicularBetweenLine(AC,BC)"
] | Value(x) | 2*sqrt(10) | [
"right_triangle_judgment_angle(1,ACB)",
"right_triangle_property_pythagorean(1,ACB)"
] | {"START": ["right_triangle_judgment_angle(1,ACB)"], "right_triangle_judgment_angle(1,ACB)": ["right_triangle_property_pythagorean(1,ACB)"]} | |
908 | XiaokaiZhang_2023-04-09 | Geometry3k-937 | 2 | 如图所示，TU=14，圆Q的圆心为Q，TU是圆Q的直径。求圆Q的半径。 | As shown in the diagram, TU=14, the center of circle Q is Q, the diameter of ⊙Q is TU. Find the radius of ⊙Q. | 908.png | [
"Shape(QT,QTU,UQ)",
"Shape(QV,QVT,TQ)",
"Shape(QU,QUV,VQ)",
"Collinear(TQU)",
"Cocircular(Q,TUV)"
] | [
"Equal(LengthOfLine(TU),14)",
"IsCentreOfCircle(Q,Q)",
"IsDiameterOfCircle(TU,Q)"
] | [
"Equal(LengthOfLine(TU),14)",
"IsCentreOfCircle(Q,Q)",
"IsDiameterOfCircle(TU,Q)"
] | Value(RadiusOfCircle(Q)) | 7 | [
"diameter_of_circle_property_length_equal(1,TU,Q)",
"circle_property_length_of_radius_and_diameter(1,Q)"
] | {"START": ["diameter_of_circle_property_length_equal(1,TU,Q)", "circle_property_length_of_radius_and_diameter(1,Q)"]} | |
909 | XiaokaiZhang_2023-03-19 | Geometry3k-938 | 2 | 如图所示，∠VWY=67°，∠XWZ=∠WZX，∠XZY=65°，∠ZYW=58°。求∠ZXW的大小。 | As shown in the diagram, ∠VWY=67°, ∠XWZ=∠WZX, ∠XZY=65°, ∠ZYW=58°. Find the measure of ∠ZXW. | 909.png | [
"Shape(VW,WX,XV)",
"Shape(XW,WZ,ZX)",
"Shape(XZ,ZY,YX)",
"Collinear(VXZ)",
"Collinear(WXY)"
] | [
"Equal(MeasureOfAngle(VWY),67)",
"Equal(MeasureOfAngle(XWZ),MeasureOfAngle(WZX))",
"Equal(MeasureOfAngle(XZY),65)",
"Equal(MeasureOfAngle(ZYW),58)"
] | [
"Equal(MeasureOfAngle(VWY),67)",
"Equal(MeasureOfAngle(XWZ),MeasureOfAngle(WZX))",
"Equal(MeasureOfAngle(XZY),65)",
"Equal(MeasureOfAngle(ZYW),58)"
] | Value(MeasureOfAngle(ZXW)) | 123 | [
"triangle_property_angle_sum(1,YXZ)",
"adjacent_complementary_angle(1,YXZ,ZXW)"
] | {"START": ["triangle_property_angle_sum(1,YXZ)", "adjacent_complementary_angle(1,YXZ,ZXW)"]} | |
910 | XiaokaiZhang_2023-04-09 | Geometry3k-939 | 1 | 如图所示，∠CAY=2*x°，∠YAF=x°。求x的值。 | As shown in the diagram, ∠CAY=2*x°, ∠YAF=x°. Find the value of x. | 910.png | [
"Shape(YA,AF)",
"Shape(FA,AD)",
"Shape(DA,AC)",
"Shape(CA,AY)",
"Collinear(YAD)",
"Collinear(CAF)"
] | [
"Equal(MeasureOfAngle(CAY),2*x)",
"Equal(MeasureOfAngle(YAF),x)"
] | [
"Equal(MeasureOfAngle(CAY),2*x)",
"Equal(MeasureOfAngle(YAF),x)"
] | Value(x) | 60 | [
"adjacent_complementary_angle(1,CAY,YAF)"
] | {"START": ["adjacent_complementary_angle(1,CAY,YAF)"]} | |
911 | XiaokaiZhang_2023-04-09 | Geometry3k-940 | 2 | 如图所示，∠AED=3*x°，∠EBN=2*x+45°，ET平行于BN。求x的值。 | As shown in the diagram, ∠AED=3*x°, ∠EBN=2*x+45°, ET is parallel to BN. Find the value of x. | 911.png | [
"Shape(DE,ET)",
"Shape(TE,EB)",
"Shape(EB,BN)",
"Shape(NB,BF)",
"Shape(FB,BC)",
"Shape(CB,BE)",
"Shape(BE,EA)",
"Shape(AE,ED)",
"Collinear(DEBF)",
"Collinear(TEA)",
"Collinear(NBC)"
] | [
"Equal(MeasureOfAngle(AED),3*x)",
"Equal(MeasureOfAngle(EBN),2*x+45)",
"ParallelBetweenLine(ET,BN)"
] | [
"Equal(MeasureOfAngle(AED),3*x)",
"Equal(MeasureOfAngle(EBN),2*x+45)",
"ParallelBetweenLine(ET,BN)"
] | Value(x) | 27 | [
"vertical_angle(1,AED,TEB)",
"parallel_property_ipsilateral_internal_angle(1,ET,BN)"
] | {"START": ["vertical_angle(1,AED,TEB)", "parallel_property_ipsilateral_internal_angle(1,ET,BN)"]} | |
912 | XiaokaiZhang_2023-04-09 | Geometry3k-941 | 8 | 如图所示，AC=12，∠DBC=45°，D是⊙D的圆心，AB是⊙D的直径，⊙D的直径为BA。求⊙D的面积减去三角形CAB的面积。 | As shown in the diagram, AC=12, ∠DBC=45°, the center of ⊙D is D, AB is the diameter of circle D, the diameter of circle D is BA. Find the area of the circle D minus the area of triangle CAB. | 912.png | [
"Shape(DCA,AC)",
"Shape(DA,DAB,BD)",
"Shape(CA,AD,DB,BC)",
"Shape(DBC,CB)",
"Collinear(ADB)",
"Cocircular(D,ABC)"
] | [
"Equal(LengthOfLine(AC),12)",
"Equal(MeasureOfAngle(DBC),45)",
"IsCentreOfCircle(D,D)",
"IsDiameterOfCircle(AB,D)",
"IsDiameterOfCircle(BA,D)"
] | [
"Equal(LengthOfLine(AC),12)",
"Equal(MeasureOfAngle(DBC),45)",
"IsCentreOfCircle(D,D)",
"IsDiameterOfCircle(AB,D)",
"IsDiameterOfCircle(BA,D)"
] | Value(Sub(AreaOfCircle(D),AreaOfTriangle(CAB))) | -72+72*pi | [
"diameter_of_circle_property_right_angle(1,BCA,D)",
"triangle_property_angle_sum(1,CAB)",
"sine_theorem(1,ABC)",
"sine_theorem(1,BCA)",
"diameter_of_circle_property_length_equal(1,AB,D)",
"circle_property_length_of_radius_and_diameter(1,D)",
"triangle_area_formula_sine(1,CAB)",
"circle_area_formula(1,... | {"START": ["diameter_of_circle_property_right_angle(1,BCA,D)", "triangle_property_angle_sum(1,CAB)", "sine_theorem(1,ABC)", "sine_theorem(1,BCA)", "diameter_of_circle_property_length_equal(1,AB,D)", "circle_property_length_of_radius_and_diameter(1,D)", "triangle_area_formula_sine(1,CAB)", "circle_area_formula(1,D)"]} | |
913 | XiaokaiZhang_2023-04-09 | Geometry3k-942 | 4 | 如图所示，弧OAB的角度为143，弧ODC的角度为75。求∠BEA的大小。 | As shown in the diagram, the measure of arc OAB is 143, the measure of arc ODC is 75. Find the measure of ∠BEA. | 913.png | [
"Shape(OAB,BE,EA)",
"Shape(OBD,DB)",
"Shape(ODC,CE,ED)",
"Shape(OCA,AE,EC)",
"Shape(EB,BD,DE)",
"Collinear(AED)",
"Collinear(CEB)",
"Cocircular(O,ABDC)"
] | [
"Equal(MeasureOfArc(OAB),143)",
"Equal(MeasureOfArc(ODC),75)"
] | [
"Equal(MeasureOfArc(OAB),143)",
"Equal(MeasureOfArc(ODC),75)"
] | Value(MeasureOfAngle(BEA)) | 109 | [
"arc_property_circumference_angle_external(1,OAB,D)",
"arc_property_circumference_angle_external(1,ODC,B)",
"triangle_property_angle_sum(1,EBD)",
"adjacent_complementary_angle(1,DEB,BEA)"
] | {"START": ["arc_property_circumference_angle_external(1,OAB,D)", "arc_property_circumference_angle_external(1,ODC,B)", "triangle_property_angle_sum(1,EBD)", "adjacent_complementary_angle(1,DEB,BEA)"]} | |
914 | XiaokaiZhang_2023-03-19 | Geometry3k-943 | 2 | 如图所示，AZ=4，∠XYA=∠AYZ，AX⊥YX，YZ⊥AZ。求直线XA的长度。 | As shown in the diagram, AZ=4, ∠XYA=∠AYZ, AX⊥YX, YZ⊥AZ. Find the length of line XA. | 914.png | [
"Shape(XY,YA,AX)",
"Shape(AY,YZ,ZA)"
] | [
"Equal(LengthOfLine(AZ),4)",
"Equal(MeasureOfAngle(XYA),MeasureOfAngle(AYZ))",
"PerpendicularBetweenLine(AX,YX)",
"PerpendicularBetweenLine(YZ,AZ)"
] | [
"Equal(LengthOfLine(AZ),4)",
"Equal(MeasureOfAngle(XYA),MeasureOfAngle(AYZ))",
"PerpendicularBetweenLine(AX,YX)",
"PerpendicularBetweenLine(YZ,AZ)"
] | Value(LengthOfLine(XA)) | 4 | [
"mirror_congruent_triangle_judgment_aas(3,AXY,AYZ)",
"mirror_congruent_triangle_property_line_equal(1,YAX,YZA)"
] | {"START": ["mirror_congruent_triangle_judgment_aas(3,AXY,AYZ)"], "mirror_congruent_triangle_judgment_aas(3,AXY,AYZ)": ["mirror_congruent_triangle_property_line_equal(1,YAX,YZA)"]} | |
915 | XiaokaiZhang_2023-04-09 | Geometry3k-944 | 3 | 如图所示，DB=x，DF=5，FB=15，⊙D的圆心为D，BF是圆O的切线。求x的值。 | As shown in the diagram, DB=x, DF=5, FB=15, the center of circle D is D, the tangent to ⊙D is BF. Find the value of x. | 915.png | [
"Shape(BF,DAF,AB)",
"Shape(DA,DAF,FD)",
"Shape(DF,DFA,AD)",
"Collinear(DAB)",
"Cocircular(D,FA)"
] | [
"Equal(LengthOfLine(DB),x)",
"Equal(LengthOfLine(DF),5)",
"Equal(LengthOfLine(FB),15)",
"IsCentreOfCircle(D,D)",
"IsTangentOfCircle(BF,D)"
] | [
"Equal(LengthOfLine(DB),x)",
"Equal(LengthOfLine(DF),5)",
"Equal(LengthOfLine(FB),15)",
"IsCentreOfCircle(D,D)"
] | Value(x) | 5*sqrt(10) | [
"tangent_of_circle_property_perpendicular(2,BF,D,D)",
"right_triangle_judgment_angle(1,BFD)",
"right_triangle_property_pythagorean(1,BFD)"
] | {"START": ["tangent_of_circle_property_perpendicular(2,BF,D,D)"], "right_triangle_judgment_angle(1,BFD)": ["right_triangle_property_pythagorean(1,BFD)"], "tangent_of_circle_property_perpendicular(2,BF,D,D)": ["right_triangle_judgment_angle(1,BFD)"]} | |
916 | XiaokaiZhang_2023-03-19 | Geometry3k-945 | 2 | 如图所示，三角形CDE的面积为13，AB=8，CE=6，三角形CDE与三角形ATB是相似三角形。求三角形ATB的面积。 | As shown in the diagram, the area of triangle CDE is 13, AB=8, CE=6, triangle CDE is similar to triangle ATB.. Find the area of △ATB. | 916.png | [
"Shape(CD,DE,EC)",
"Shape(AT,TB,BA)"
] | [
"Equal(AreaOfTriangle(CDE),13)",
"Equal(LengthOfLine(AB),8)",
"Equal(LengthOfLine(CE),6)",
"SimilarBetweenTriangle(CDE,ATB)"
] | [
"Equal(AreaOfTriangle(CDE),13)",
"Equal(LengthOfLine(AB),8)",
"Equal(LengthOfLine(CE),6)"
] | Value(AreaOfTriangle(ATB)) | 208/9 | [
"similar_triangle_property_line_ratio(1,DEC,TBA)",
"similar_triangle_property_area_square_ratio(1,DEC,TBA)"
] | {"START": ["similar_triangle_property_line_ratio(1,DEC,TBA)", "similar_triangle_property_area_square_ratio(1,DEC,TBA)"]} | |
917 | XiaokaiZhang_2023-03-19 | Geometry3k-946 | 1 | 如图所示，RW=14，RZ=18，UZ=5，Z是△RST的重心。求直线SZ的长度。 | As shown in the diagram, RW=14, RZ=18, UZ=5, the centroid of △RST is Z. Find the length of line SZ. | 917.png | [
"Shape(RW,WZ,ZR)",
"Shape(ZW,WS,SZ)",
"Shape(ZS,SV,VZ)",
"Shape(ZV,VT,TZ)",
"Shape(ZT,TU,UZ)",
"Shape(ZU,UR,RZ)",
"Collinear(RWS)",
"Collinear(SVT)",
"Collinear(TUR)",
"Collinear(WZT)",
"Collinear(SZU)",
"Collinear(RZV)"
] | [
"Equal(LengthOfLine(RW),14)",
"Equal(LengthOfLine(RZ),18)",
"Equal(LengthOfLine(UZ),5)",
"IsCentroidOfTriangle(Z,RST)"
] | [
"Equal(LengthOfLine(RW),14)",
"Equal(LengthOfLine(RZ),18)",
"Equal(LengthOfLine(UZ),5)",
"IsCentroidOfTriangle(Z,RST)"
] | Value(LengthOfLine(SZ)) | 10 | [
"centroid_of_triangle_property_line_ratio(1,Z,STR,U)"
] | {"START": ["centroid_of_triangle_property_line_ratio(1,Z,STR,U)"]} | |
918 | XiaokaiZhang_2023-04-09 | Geometry3k-947 | 1 | 如图所示，⌒AJH的角度为114，GB⊥HB，JH⊥GH。求∠HGB的大小。 | As shown in the diagram, the measure of ⌒AJH is 114, GB⊥HB, JH is perpendicular to GH. Find the measure of ∠HGB. | 918.png | [
"Shape(AGF,FB,BG)",
"Shape(AB,BF,AFJ,JA)",
"Shape(BA,AJ,JH,HB)",
"Shape(AJH,HJ)",
"Shape(GB,BH,HG)",
"Shape(AHG,GH)",
"Collinear(FBH)",
"Collinear(GBAJ)",
"Cocircular(A,GFJH)"
] | [
"Equal(MeasureOfArc(AJH),114)",
"PerpendicularBetweenLine(GB,HB)",
"PerpendicularBetweenLine(JH,GH)"
] | [
"Equal(MeasureOfArc(AJH),114)",
"PerpendicularBetweenLine(GB,HB)",
"PerpendicularBetweenLine(JH,GH)"
] | Value(MeasureOfAngle(HGB)) | 57 | [
"arc_property_circumference_angle_external(1,AJH,G)"
] | {"START": ["arc_property_circumference_angle_external(1,AJH,G)"]} | |
919 | XiaokaiZhang_2023-04-09 | Geometry3k-948 | 1 | 如图所示，∠QRS=x°，∠RST=2*x+7°，∠STQ=x°，∠TQR=2*x+5°。求∠STQ的大小。 | As shown in the diagram, ∠QRS=x°, ∠RST=2*x+7°, ∠STQ=x°, ∠TQR=2*x+5°. Find the measure of ∠STQ. | 919.png | [
"Shape(QR,RS,ST,TQ)"
] | [
"Equal(MeasureOfAngle(QRS),x)",
"Equal(MeasureOfAngle(RST),2*x+7)",
"Equal(MeasureOfAngle(STQ),x)",
"Equal(MeasureOfAngle(TQR),2*x+5)"
] | [
"Equal(MeasureOfAngle(QRS),x)",
"Equal(MeasureOfAngle(RST),2*x+7)",
"Equal(MeasureOfAngle(STQ),x)",
"Equal(MeasureOfAngle(TQR),2*x+5)"
] | Value(MeasureOfAngle(STQ)) | 58 | [
"quadrilateral_property_angle_sum(1,QRST)"
] | {"START": ["quadrilateral_property_angle_sum(1,QRST)"]} | |
920 | XiaokaiZhang_2023-04-09 | Geometry3k-949 | 5 | 如图所示，AC=4，CD=3，E是⊙E的圆心，DA是⊙E的直径，DC垂直于AC。求⊙E的周长。 | As shown in the diagram, AC=4, CD=3, E is the center of ⊙E, DA is the diameter of circle E, DC⊥AC. Find the circumference of the ⊙E. | 920.png | [
"Shape(EDC,CD)",
"Shape(ECA,AC)",
"Shape(DC,CA,AE,ED)",
"Shape(DE,EA,EAD)",
"Collinear(DEA)",
"Cocircular(E,DCA)"
] | [
"Equal(LengthOfLine(AC),4)",
"Equal(LengthOfLine(CD),3)",
"IsCentreOfCircle(E,E)",
"IsDiameterOfCircle(DA,E)",
"PerpendicularBetweenLine(DC,AC)"
] | [
"Equal(LengthOfLine(AC),4)",
"Equal(LengthOfLine(CD),3)",
"IsCentreOfCircle(E,E)",
"IsDiameterOfCircle(DA,E)",
"PerpendicularBetweenLine(DC,AC)"
] | Value(PerimeterOfCircle(E)) | 5*pi | [
"right_triangle_judgment_angle(1,DCA)",
"right_triangle_property_pythagorean(1,DCA)",
"diameter_of_circle_property_length_equal(1,DA,E)",
"circle_property_length_of_radius_and_diameter(1,E)",
"circle_perimeter_formula(1,E)"
] | {"START": ["right_triangle_judgment_angle(1,DCA)", "diameter_of_circle_property_length_equal(1,DA,E)", "circle_property_length_of_radius_and_diameter(1,E)", "circle_perimeter_formula(1,E)"], "right_triangle_judgment_angle(1,DCA)": ["right_triangle_property_pythagorean(1,DCA)"]} | |
921 | XiaokaiZhang_2023-04-09 | Geometry3k-950 | 6 | 如图所示，AD=12，FE=18，D是圆D的圆心，圆O的切线为EA。求直线AE的长度。 | As shown in the diagram, AD=12, FE=18, D is the center of circle D, the tangent to circle D is EA. Find the length of line AE. | 921.png | [
"Shape(DAB,BA)",
"Shape(DBJ,JK,KB)",
"Shape(BK,KM,MA,AB)",
"Shape(AM,MF,DFA)",
"Shape(DFA,FE,EA)",
"Shape(DJC,CK,KJ)",
"Shape(MK,KC,CD,DM)",
"Shape(MD,DF,FM)",
"Shape(DC,DCH,HD)",
"Shape(DH,DHF,FD)",
"Shape(DHF,HG,GF)",
"Collinear(JKMF)",
"Collinear(BKC)",
"Collinear(AMDC)",
"Collinear(D... | [
"Equal(LengthOfLine(AD),12)",
"Equal(LengthOfLine(FE),18)",
"IsCentreOfCircle(D,D)",
"IsTangentOfCircle(EA,D)"
] | [
"Equal(LengthOfLine(AD),12)",
"Equal(LengthOfLine(FE),18)",
"IsCentreOfCircle(D,D)",
"IsTangentOfCircle(EA,D)"
] | Value(LengthOfLine(AE)) | 6*sqrt(21) | [
"radius_of_circle_property_length_equal(1,DA,D)",
"radius_of_circle_property_length_equal(1,DF,D)",
"line_addition(1,DF,FE)",
"tangent_of_circle_property_perpendicular(2,EA,D,D)",
"right_triangle_judgment_angle(1,EAD)",
"right_triangle_property_pythagorean(1,EAD)"
] | {"START": ["radius_of_circle_property_length_equal(1,DA,D)", "radius_of_circle_property_length_equal(1,DF,D)", "line_addition(1,DF,FE)", "tangent_of_circle_property_perpendicular(2,EA,D,D)"], "right_triangle_judgment_angle(1,EAD)": ["right_triangle_property_pythagorean(1,EAD)"], "tangent_of_circle_property_perpendicula... | |
922 | XiaokaiZhang_2023-03-19 | Geometry3k-951 | 1 | 如图所示，BA=15，BC=20，CA=25，CB垂直于AB。求tan(BA)的值。 | As shown in the diagram, BA=15, BC=20, CA=25, CB⊥AB. Find the value of tan(BA). | 922.png | [
"Shape(AC,CB,BA)"
] | [
"Equal(LengthOfLine(BA),15)",
"Equal(LengthOfLine(BC),20)",
"Equal(LengthOfLine(CA),25)",
"PerpendicularBetweenLine(CB,AB)"
] | [
"Equal(LengthOfLine(BA),15)",
"Equal(LengthOfLine(BC),20)",
"Equal(LengthOfLine(CA),25)",
"PerpendicularBetweenLine(CB,AB)"
] | Value(Tan(MeasureOfAngle(BAC))) | 4/3 | [
"cosine_theorem(1,ACB)"
] | {"START": ["cosine_theorem(1,ACB)"]} | |
923 | XiaokaiZhang_2023-04-09 | Geometry3k-952 | 3 | 如图所示，四边形MQPN的面积为360，NE=18，QP=26，NE垂直于PE，MQPN是梯形。求直线MN的长度。 | As shown in the diagram, the area of MQPN is 360, NE=18, QP=26, NE⊥PE, MN and QP are the parallel sides of trapezoid MQPN. Find the length of line MN. | 923.png | [
"Shape(MQ,QE,EN,NM)",
"Shape(NE,EP,PN)",
"Collinear(QEP)"
] | [
"Equal(AreaOfQuadrilateral(MQPN),360)",
"Equal(LengthOfLine(NE),18)",
"Equal(LengthOfLine(QP),26)",
"PerpendicularBetweenLine(NE,PE)",
"Trapezoid(MQPN)"
] | [
"Equal(LengthOfLine(NE),18)",
"Equal(LengthOfLine(QP),26)",
"PerpendicularBetweenLine(NE,PE)"
] | Value(LengthOfLine(MN)) | 14 | [
"adjacent_complementary_angle(1,QEN,NEP)",
"altitude_of_quadrilateral_judgment_right_vertex(2,NE,MQPN)",
"trapezoid_area_formula(1,MQPN)"
] | {"START": ["adjacent_complementary_angle(1,QEN,NEP)", "trapezoid_area_formula(1,MQPN)"], "adjacent_complementary_angle(1,QEN,NEP)": ["altitude_of_quadrilateral_judgment_right_vertex(2,NE,MQPN)"]} | |
924 | XiaokaiZhang_2023-03-19 | Geometry3k-953 | 0 | 如图所示，MJ=2*x-5，NJ=x-2，NM=3*x-9，三角形MJN为等腰三角形。求直线JN的长度。 | As shown in the diagram, MJ=2*x-5, NJ=x-2, NM=3*x-9, △MJN is an isosceles △. Find the length of line JN. | 924.png | [
"Shape(MJ,JN,NM)"
] | [
"Equal(LengthOfLine(MJ),2*x-5)",
"Equal(LengthOfLine(NJ),x-2)",
"Equal(LengthOfLine(NM),3*x-9)",
"IsoscelesTriangle(MJN)"
] | [
"Equal(LengthOfLine(MJ),2*x-5)",
"Equal(LengthOfLine(NJ),x-2)",
"Equal(LengthOfLine(NM),3*x-9)",
"IsoscelesTriangle(MJN)"
] | Value(LengthOfLine(JN)) | 2 | [] | {"START": []} | |
925 | XiaokaiZhang_2023-04-09 | Geometry3k-954 | 2 | 如图所示，QV=8，⊙Q的圆心为Q。求圆Q的直径。 | As shown in the diagram, QV=8, Q is the center of circle Q. Find the diameter of circle Q. | 925.png | [
"Shape(QT,QTU,UQ)",
"Shape(QVT,TQ,QV)",
"Shape(QUV,VQ,QU)",
"Collinear(TQU)",
"Cocircular(Q,TUV)"
] | [
"Equal(LengthOfLine(QV),8)",
"IsCentreOfCircle(Q,Q)"
] | [
"Equal(LengthOfLine(QV),8)",
"IsCentreOfCircle(Q,Q)"
] | Value(DiameterOfCircle(Q)) | 16 | [
"radius_of_circle_property_length_equal(1,QV,Q)",
"circle_property_length_of_radius_and_diameter(1,Q)"
] | {"START": ["radius_of_circle_property_length_equal(1,QV,Q)", "circle_property_length_of_radius_and_diameter(1,Q)"]} | |
926 | XiaokaiZhang_2023-04-09 | Geometry3k-955 | 1 | 如图所示，∠TZY=30*x°，∠TZY=∠ZYW，∠WTZ=20*x°，∠WTZ=∠YWT，四边形TZYW是等腰梯形。求∠TZY的大小。 | As shown in the diagram, ∠TZY=30*x°, ∠TZY=∠ZYW, ∠WTZ=20*x°, ∠WTZ=∠YWT, quadrilateral TZYW is a isosceles trapezoid. Find the measure of ∠TZY. | 926.png | [
"Shape(TZ,ZY,YW,WT)"
] | [
"Equal(MeasureOfAngle(TZY),30*x)",
"Equal(MeasureOfAngle(TZY),MeasureOfAngle(ZYW))",
"Equal(MeasureOfAngle(WTZ),20*x)",
"Equal(MeasureOfAngle(WTZ),MeasureOfAngle(YWT))",
"IsoscelesTrapezoid(TZYW)"
] | [
"Equal(MeasureOfAngle(TZY),MeasureOfAngle(ZYW))",
"Equal(MeasureOfAngle(WTZ),MeasureOfAngle(YWT))"
] | Value(MeasureOfAngle(TZY)) | 108 | [
"parallel_property_ipsilateral_internal_angle(1,TW,ZY)"
] | {"START": ["parallel_property_ipsilateral_internal_angle(1,TW,ZY)"]} | |
927 | XiaokaiZhang_2023-04-09 | Geometry3k-956 | 1 | 如图所示，BA=6，DA=9，DC=6.86，∠BAF=32°，∠CBF=40.1°，∠FAD=20°，CD和BA是▱DCBA的一组对边。求直线BC的长度。 | As shown in the diagram, BA=6, DA=9, DC=6.86, ∠BAF=32°, ∠CBF=40.1°, ∠FAD=20°, quadrilateral DCBA is a ▱. Find the length of line BC. | 927.png | [
"Shape(DC,CF,FD)",
"Shape(FC,CB,BF)",
"Shape(FB,BA,AF)",
"Shape(DF,FA,AD)",
"Collinear(DFB)",
"Collinear(CFA)"
] | [
"Equal(LengthOfLine(BA),6)",
"Equal(LengthOfLine(DA),9)",
"Equal(LengthOfLine(DC),6.86)",
"Equal(MeasureOfAngle(BAF),32)",
"Equal(MeasureOfAngle(CBF),40.1)",
"Equal(MeasureOfAngle(FAD),20)",
"Parallelogram(DCBA)"
] | [
"Equal(LengthOfLine(BA),6)",
"Equal(LengthOfLine(DA),9)",
"Equal(LengthOfLine(DC),6.86)",
"Equal(MeasureOfAngle(BAF),32)",
"Equal(MeasureOfAngle(CBF),40.1)",
"Equal(MeasureOfAngle(FAD),20)"
] | Value(LengthOfLine(BC)) | 9 | [
"parallelogram_property_opposite_line_equal(1,ADCB)"
] | {"START": ["parallelogram_property_opposite_line_equal(1,ADCB)"]} | |
928 | XiaokaiZhang_2023-03-19 | Geometry3k-957 | 4 | 如图所示，BC=15，BE=6，DA=10，DE=3*x-2，EC=12，∠ADE=∠CBE。求直线AE的长度。 | As shown in the diagram, BC=15, BE=6, DA=10, DE=3*x-2, EC=12, ∠ADE=∠CBE. Find the length of line AE. | 928.png | [
"Shape(AD,DE,EA)",
"Shape(BE,EC,CB)",
"Collinear(AEC)",
"Collinear(BED)"
] | [
"Equal(LengthOfLine(BC),15)",
"Equal(LengthOfLine(BE),6)",
"Equal(LengthOfLine(DA),10)",
"Equal(LengthOfLine(DE),3*x-2)",
"Equal(LengthOfLine(EC),12)",
"Equal(MeasureOfAngle(ADE),MeasureOfAngle(CBE))"
] | [
"Equal(LengthOfLine(BC),15)",
"Equal(LengthOfLine(BE),6)",
"Equal(LengthOfLine(DA),10)",
"Equal(LengthOfLine(DE),3*x-2)",
"Equal(LengthOfLine(EC),12)",
"Equal(MeasureOfAngle(ADE),MeasureOfAngle(CBE))"
] | Value(LengthOfLine(AE)) | 8 | [
"vertical_angle(1,DEA,BEC)",
"similar_triangle_judgment_aa(1,ADE,CBE)",
"similar_triangle_property_line_ratio(1,EAD,ECB)",
"similar_triangle_property_line_ratio(1,DEA,BEC)"
] | {"START": ["vertical_angle(1,DEA,BEC)"], "similar_triangle_judgment_aa(1,ADE,CBE)": ["similar_triangle_property_line_ratio(1,DEA,BEC)", "similar_triangle_property_line_ratio(1,EAD,ECB)"], "vertical_angle(1,DEA,BEC)": ["similar_triangle_judgment_aa(1,ADE,CBE)"]} | |
929 | XiaokaiZhang_2023-04-09 | Geometry3k-958 | 7 | 如图所示，QR=4，SA=5，ST=x，⊙Q的圆心为Q，⊙O的切线为SR，ST是⊙O的切线。求x的值。 | As shown in the diagram, QR=4, SA=5, ST=x, Q is the center of ⊙Q, SR is the tangent to circle Q, ST is the tangent to ⊙Q. Find the value of x. | 929.png | [
"Shape(SR,QAR,AS)",
"Shape(RQ,QA,QAR)",
"Shape(QT,QTA,AQ)",
"Shape(QTA,TS,SA)",
"Shape(QR,QRT,TQ)",
"Collinear(QAS)",
"Cocircular(Q,TAR)"
] | [
"Equal(LengthOfLine(QR),4)",
"Equal(LengthOfLine(SA),5)",
"Equal(LengthOfLine(ST),x)",
"IsCentreOfCircle(Q,Q)",
"IsTangentOfCircle(SR,Q)",
"IsTangentOfCircle(ST,Q)"
] | [
"Equal(LengthOfLine(QR),4)",
"Equal(LengthOfLine(SA),5)",
"Equal(LengthOfLine(ST),x)",
"IsCentreOfCircle(Q,Q)"
] | Value(x) | sqrt(65) | [
"radius_of_circle_property_length_equal(1,QR,Q)",
"radius_of_circle_property_length_equal(1,QA,Q)",
"radius_of_circle_property_length_equal(1,QT,Q)",
"line_addition(1,QA,AS)",
"tangent_of_circle_property_perpendicular(1,ST,Q,Q)",
"right_triangle_judgment_angle(1,QTS)",
"right_triangle_property_pythagore... | {"START": ["radius_of_circle_property_length_equal(1,QR,Q)", "radius_of_circle_property_length_equal(1,QA,Q)", "radius_of_circle_property_length_equal(1,QT,Q)", "line_addition(1,QA,AS)", "tangent_of_circle_property_perpendicular(1,ST,Q,Q)"], "right_triangle_judgment_angle(1,QTS)": ["right_triangle_property_pythagorean(... | |
930 | XiaokaiZhang_2023-04-09 | Geometry3k-959 | 2 | 如图所示，四边形BLAN的面积为72，EFGH的面积为50，BN=6，EH=x，四边形EFGH相似于四边形BLAN。求x的值。 | As shown in the diagram, the area of BLAN is 72, the area of quadrilateral EFGH is 50, BN=6, EH=x, EFGH is similar to BLAN. Find the value of x. | 930.png | [
"Shape(EF,FG,GH,HE)",
"Shape(BL,LA,AN,NB)"
] | [
"Equal(AreaOfQuadrilateral(BLAN),72)",
"Equal(AreaOfQuadrilateral(EFGH),50)",
"Equal(LengthOfLine(BN),6)",
"Equal(LengthOfLine(EH),x)",
"SimilarBetweenQuadrilateral(EFGH,BLAN)"
] | [
"Equal(LengthOfLine(BN),6)",
"Equal(LengthOfLine(EH),x)"
] | Value(x) | 5 | [
"similar_quadrilateral_property_area_square_ratio(1,EFGH,BLAN)",
"similar_quadrilateral_property_line_ratio(1,HEFG,NBLA)"
] | {"START": ["similar_quadrilateral_property_area_square_ratio(1,EFGH,BLAN)", "similar_quadrilateral_property_line_ratio(1,HEFG,NBLA)"]} | |
931 | XiaokaiZhang_2023-03-19 | Geometry3k-960 | 4 | 如图所示，HQ=y，JQ=2*z，KQ=7，LQ=3，QM=4，QP=2*x-6，J是线段HK的中点，L是线段KM的中点，P是线段MH的中点。求z的值。 | As shown in the diagram, HQ=y, JQ=2*z, KQ=7, LQ=3, QM=4, QP=2*x-6, J is the midpoint of segment HK, L bisects segment KM, P bisects segment MH. Find the value of z. | 931.png | [
"Shape(HJ,JQ,QH)",
"Shape(JK,KQ,QJ)",
"Shape(QK,KL,LQ)",
"Shape(QL,LM,MQ)",
"Shape(QM,MP,PQ)",
"Shape(QP,PH,HQ)",
"Collinear(HJK)",
"Collinear(KLM)",
"Collinear(MPH)",
"Collinear(HQL)",
"Collinear(JQM)",
"Collinear(KQP)"
] | [
"Equal(LengthOfLine(HQ),y)",
"Equal(LengthOfLine(JQ),2*z)",
"Equal(LengthOfLine(KQ),7)",
"Equal(LengthOfLine(LQ),3)",
"Equal(LengthOfLine(QM),4)",
"Equal(LengthOfLine(QP),2*x-6)",
"IsMidpointOfLine(J,HK)",
"IsMidpointOfLine(L,KM)",
"IsMidpointOfLine(P,MH)"
] | [
"Equal(LengthOfLine(HQ),y)",
"Equal(LengthOfLine(JQ),2*z)",
"Equal(LengthOfLine(KQ),7)",
"Equal(LengthOfLine(LQ),3)",
"Equal(LengthOfLine(QM),4)",
"Equal(LengthOfLine(QP),2*x-6)"
] | Value(z) | 1 | [
"median_of_triangle_judgment(1,KP,KMH)",
"median_of_triangle_judgment(1,HL,HKM)",
"centroid_of_triangle_judgment_intersection(1,Q,MHK,P,L)",
"centroid_of_triangle_property_line_ratio(1,Q,MHK,J)"
] | {"START": ["median_of_triangle_judgment(1,KP,KMH)", "median_of_triangle_judgment(1,HL,HKM)"], "centroid_of_triangle_judgment_intersection(1,Q,MHK,P,L)": ["centroid_of_triangle_property_line_ratio(1,Q,MHK,J)"], "median_of_triangle_judgment(1,HL,HKM)": ["centroid_of_triangle_judgment_intersection(1,Q,MHK,P,L)"], "median_... | |
932 | XiaokaiZhang_2023-03-19 | Geometry3k-961 | 4 | 如图所示，AF=24，AH=25，BH=11，∠DBH=30°，∠GCH=28°，三角形ABC的内切圆圆心为H，BG垂直于HG，HD⊥BD，HF⊥AF。求∠CAH的大小。 | As shown in the diagram, AF=24, AH=25, BH=11, ∠DBH=30°, ∠GCH=28°, H is the incenter of △ABC, BG⊥HG, HD is perpendicular to BD, HF⊥AF. Find the measure of ∠CAH. | 932.png | [
"Shape(AD,DH,HA)",
"Shape(HD,DB,BH)",
"Shape(HB,BG,GH)",
"Shape(HG,GC,CH)",
"Shape(HC,CF,FH)",
"Shape(HF,FA,AH)",
"Collinear(ADB)",
"Collinear(BGC)",
"Collinear(CFA)"
] | [
"Equal(LengthOfLine(AF),24)",
"Equal(LengthOfLine(AH),25)",
"Equal(LengthOfLine(BH),11)",
"Equal(MeasureOfAngle(DBH),30)",
"Equal(MeasureOfAngle(GCH),28)",
"IsIncenterOfTriangle(H,ABC)",
"PerpendicularBetweenLine(BG,HG)",
"PerpendicularBetweenLine(HD,BD)",
"PerpendicularBetweenLine(HF,AF)"
] | [
"Equal(LengthOfLine(AF),24)",
"Equal(LengthOfLine(AH),25)",
"Equal(LengthOfLine(BH),11)",
"Equal(MeasureOfAngle(DBH),30)",
"Equal(MeasureOfAngle(GCH),28)",
"PerpendicularBetweenLine(BG,HG)",
"PerpendicularBetweenLine(HD,BD)",
"PerpendicularBetweenLine(HF,AF)"
] | Value(MeasureOfAngle(CAH)) | 32 | [
"angle_addition(1,DBH,HBG)",
"angle_addition(1,GCH,HCF)",
"angle_addition(1,FAH,HAD)",
"triangle_property_angle_sum(1,ABC)"
] | {"START": ["angle_addition(1,DBH,HBG)", "angle_addition(1,GCH,HCF)", "angle_addition(1,FAH,HAD)", "triangle_property_angle_sum(1,ABC)"]} | |
933 | XiaokaiZhang_2023-04-09 | Geometry3k-962 | 1 | 如图所示，AB=2*x+2，AC=y+10，BD=2*y+5，CD=x+5，四边形CABD是平行四边形。求x的值。 | As shown in the diagram, AB=2*x+2, AC=y+10, BD=2*y+5, CD=x+5, CD and AB are opposite sides of the ▱ CABD. Find the value of x. | 933.png | [
"Shape(CA,AB,BD,DC)"
] | [
"Equal(LengthOfLine(AB),2*x+2)",
"Equal(LengthOfLine(AC),y+10)",
"Equal(LengthOfLine(BD),2*y+5)",
"Equal(LengthOfLine(CD),x+5)",
"Parallelogram(CABD)"
] | [
"Equal(LengthOfLine(AB),2*x+2)",
"Equal(LengthOfLine(AC),y+10)",
"Equal(LengthOfLine(BD),2*y+5)",
"Equal(LengthOfLine(CD),x+5)"
] | Value(x) | 3 | [
"parallelogram_property_opposite_line_equal(1,ABDC)"
] | {"START": ["parallelogram_property_opposite_line_equal(1,ABDC)"]} | |
934 | XiaokaiZhang_2023-03-19 | Geometry3k-963 | 1 | 如图所示，AB=c，AC=b，CB=a，a=8，b=15，c=17，BC垂直于AC。求tan(AB)的值。 | As shown in the diagram, AB=c, AC=b, CB=a, a=8, b=15, c=17, BC is perpendicular to AC. Find the value of tan(AB). | 934.png | [
"Shape(BC,CA,AB)"
] | [
"Equal(LengthOfLine(AB),c)",
"Equal(LengthOfLine(AC),b)",
"Equal(LengthOfLine(CB),a)",
"Equal(a,8)",
"Equal(b,15)",
"Equal(c,17)",
"PerpendicularBetweenLine(BC,AC)"
] | [
"Equal(LengthOfLine(AB),c)",
"Equal(LengthOfLine(AC),b)",
"Equal(LengthOfLine(CB),a)",
"PerpendicularBetweenLine(BC,AC)"
] | Value(Tan(MeasureOfAngle(ABC))) | 15/8 | [
"cosine_theorem(1,BCA)"
] | {"START": ["cosine_theorem(1,BCA)"]} | |
935 | XiaokaiZhang_2023-04-09 | Geometry3k-964 | 1 | 如图所示，AB=2*x+6，AD=4*y+6，BC=6*y-8，DC=3*x-2，BC和AD是平行四边形CBAD的一组对边。求x的值。 | As shown in the diagram, AB=2*x+6, AD=4*y+6, BC=6*y-8, DC=3*x-2, BC and AD are opposite sides of the ▱ CBAD. Find the value of x. | 935.png | [
"Shape(CB,BA,AD,DC)"
] | [
"Equal(LengthOfLine(AB),2*x+6)",
"Equal(LengthOfLine(AD),4*y+6)",
"Equal(LengthOfLine(BC),6*y-8)",
"Equal(LengthOfLine(DC),3*x-2)",
"Parallelogram(CBAD)"
] | [
"Equal(LengthOfLine(AB),2*x+6)",
"Equal(LengthOfLine(AD),4*y+6)",
"Equal(LengthOfLine(BC),6*y-8)",
"Equal(LengthOfLine(DC),3*x-2)"
] | Value(x) | 8 | [
"parallelogram_property_opposite_line_equal(1,BADC)"
] | {"START": ["parallelogram_property_opposite_line_equal(1,BADC)"]} | |
936 | XiaokaiZhang_2023-03-19 | Geometry3k-965 | 3 | 如图所示，AB=16，AC=12，BA垂直于CA。求三角形CBA的周长。 | As shown in the diagram, AB=16, AC=12, BA is perpendicular to CA. Find the perimeter of triangle CBA. | 936.png | [
"Shape(AC,CB,BA)"
] | [
"Equal(LengthOfLine(AB),16)",
"Equal(LengthOfLine(AC),12)",
"PerpendicularBetweenLine(BA,CA)"
] | [
"Equal(LengthOfLine(AB),16)",
"Equal(LengthOfLine(AC),12)",
"PerpendicularBetweenLine(BA,CA)"
] | Value(PerimeterOfTriangle(CBA)) | 48 | [
"right_triangle_judgment_angle(1,BAC)",
"right_triangle_property_pythagorean(1,BAC)",
"triangle_perimeter_formula(1,CBA)"
] | {"START": ["right_triangle_judgment_angle(1,BAC)", "triangle_perimeter_formula(1,CBA)"], "right_triangle_judgment_angle(1,BAC)": ["right_triangle_property_pythagorean(1,BAC)"]} | |
937 | XiaokaiZhang_2023-03-19 | Geometry3k-966 | 4 | 如图所示，AC=10，AD=x，BC=z，BD=y，CD=4，BD⊥AD，CA⊥BA。求z的值。 | As shown in the diagram, AC=10, AD=x, BC=z, BD=y, CD=4, BD is perpendicular to AD, CA⊥BA. Find the value of z. | 937.png | [
"Shape(AB,BD,DA)",
"Shape(AD,DC,CA)",
"Collinear(BDC)"
] | [
"Equal(LengthOfLine(AC),10)",
"Equal(LengthOfLine(AD),x)",
"Equal(LengthOfLine(BC),z)",
"Equal(LengthOfLine(BD),y)",
"Equal(LengthOfLine(CD),4)",
"PerpendicularBetweenLine(BD,AD)",
"PerpendicularBetweenLine(CA,BA)"
] | [
"Equal(LengthOfLine(AC),10)",
"Equal(LengthOfLine(AD),x)",
"Equal(LengthOfLine(BC),z)",
"Equal(LengthOfLine(BD),y)",
"Equal(LengthOfLine(CD),4)",
"PerpendicularBetweenLine(BD,AD)",
"PerpendicularBetweenLine(CA,BA)"
] | Value(z) | 25 | [
"adjacent_complementary_angle(1,BDA,ADC)",
"mirror_similar_triangle_judgment_aa(1,ADC,BCA)",
"mirror_similar_triangle_property_line_ratio(1,ADC,BCA)",
"mirror_similar_triangle_property_line_ratio(1,DCA,ABC)"
] | {"START": ["adjacent_complementary_angle(1,BDA,ADC)"], "adjacent_complementary_angle(1,BDA,ADC)": ["mirror_similar_triangle_judgment_aa(1,ADC,BCA)"], "mirror_similar_triangle_judgment_aa(1,ADC,BCA)": ["mirror_similar_triangle_property_line_ratio(1,ADC,BCA)", "mirror_similar_triangle_property_line_ratio(1,DCA,ABC)"]} | |
938 | XiaokaiZhang_2023-04-09 | Geometry3k-967 | 4 | 如图所示，PY=3，XZ=18，ZY=XW，XY∥WZ。求直线PW的长度。 | As shown in the diagram, PY=3, XZ=18, ZY=XW, XY is parallel to WZ. Find the length of line PW. | 938.png | [
"Shape(XW,WP,PX)",
"Shape(PW,WZ,ZP)",
"Shape(XP,PY,YX)",
"Shape(PZ,ZY,YP)",
"Collinear(XPZ)",
"Collinear(WPY)"
] | [
"Equal(LengthOfLine(PY),3)",
"Equal(LengthOfLine(XZ),18)",
"Equal(LengthOfLine(ZY),LengthOfLine(XW))",
"ParallelBetweenLine(XY,WZ)"
] | [
"Equal(LengthOfLine(ZY),LengthOfLine(XW))",
"ParallelBetweenLine(XY,WZ)"
] | Value(LengthOfLine(PW)) | 15 | [
"trapezoid_judgment_parallel(1,XWZY)",
"isosceles_trapezoid_judgment_line_equal(1,XWZY)",
"isosceles_trapezoid_property_diagonal_equal(1,XWZY)",
"line_addition(1,WP,PY)"
] | {"START": ["trapezoid_judgment_parallel(1,XWZY)", "line_addition(1,WP,PY)"], "isosceles_trapezoid_judgment_line_equal(1,XWZY)": ["isosceles_trapezoid_property_diagonal_equal(1,XWZY)"], "trapezoid_judgment_parallel(1,XWZY)": ["isosceles_trapezoid_judgment_line_equal(1,XWZY)"]} | |
939 | XiaokaiZhang_2023-04-09 | Geometry3k-968 | 1 | 如图所示，∠ABC=y°，∠ACD=z°，∠BCA=48°，∠CAB=42°，∠DAC=3*x°，AD平行于BC，BA平行于CD。求x的值。 | As shown in the diagram, ∠ABC=y°, ∠ACD=z°, ∠BCA=48°, ∠CAB=42°, ∠DAC=3*x°, AD is parallel to BC, BA∥CD. Find the value of x. | 939.png | [
"Shape(AB,BC,CA)",
"Shape(AC,CD,DA)"
] | [
"Equal(MeasureOfAngle(ABC),y)",
"Equal(MeasureOfAngle(ACD),z)",
"Equal(MeasureOfAngle(BCA),48)",
"Equal(MeasureOfAngle(CAB),42)",
"Equal(MeasureOfAngle(DAC),3*x)",
"ParallelBetweenLine(AD,BC)",
"ParallelBetweenLine(BA,CD)"
] | [
"Equal(MeasureOfAngle(ABC),y)",
"Equal(MeasureOfAngle(ACD),z)",
"Equal(MeasureOfAngle(BCA),48)",
"Equal(MeasureOfAngle(CAB),42)",
"Equal(MeasureOfAngle(DAC),3*x)",
"ParallelBetweenLine(AD,BC)",
"ParallelBetweenLine(BA,CD)"
] | Value(x) | 16 | [
"parallel_property_alternate_interior_angle(1,AD,BC)"
] | {"START": ["parallel_property_alternate_interior_angle(1,AD,BC)"]} | |
940 | XiaokaiZhang_2023-03-19 | Geometry3k-969 | 7 | 如图所示，GK=HK，HK=KJ，∠HGK=28°。求∠KJH的大小。 | As shown in the diagram, GK=HK, HK=KJ, ∠HGK=28°. Find the measure of ∠KJH. | 940.png | [
"Shape(HG,GK,KH)",
"Shape(HK,KJ,JH)",
"Collinear(GKJ)"
] | [
"Equal(LengthOfLine(GK),LengthOfLine(HK))",
"Equal(LengthOfLine(HK),LengthOfLine(KJ))",
"Equal(MeasureOfAngle(HGK),28)"
] | [
"Equal(MeasureOfAngle(HGK),28)"
] | Value(MeasureOfAngle(KJH)) | 62 | [
"isosceles_triangle_judgment_line_equal(1,KHG)",
"isosceles_triangle_property_angle_equal(1,KHG)",
"triangle_property_angle_sum(1,KHG)",
"adjacent_complementary_angle(1,GKH,HKJ)",
"isosceles_triangle_judgment_line_equal(1,KJH)",
"isosceles_triangle_property_angle_equal(1,KJH)",
"triangle_property_angle_... | {"START": ["isosceles_triangle_judgment_line_equal(1,KHG)", "triangle_property_angle_sum(1,KHG)", "adjacent_complementary_angle(1,GKH,HKJ)", "isosceles_triangle_judgment_line_equal(1,KJH)", "triangle_property_angle_sum(1,KJH)"], "isosceles_triangle_judgment_line_equal(1,KHG)": ["isosceles_triangle_property_angle_equal(... | |
941 | XiaokaiZhang_2023-04-09 | Geometry3k-970 | 1 | 如图所示，ML=w，NM=2*y+5，NQ=3*x+2，QL=12，RM=4*x-2，RQ=3*y，RM和QN是平行四边形MRQN的一组对边。求直线NQ的长度。 | As shown in the diagram, ML=w, NM=2*y+5, NQ=3*x+2, QL=12, RM=4*x-2, RQ=3*y, RM and QN are opposite sides of the parallelogram MRQN. Find the length of line NQ. | 941.png | [
"Shape(NM,ML,LN)",
"Shape(LM,MR,RL)",
"Shape(LR,RQ,QL)",
"Shape(NL,LQ,QN)",
"Collinear(NLR)",
"Collinear(MLQ)"
] | [
"Equal(LengthOfLine(ML),w)",
"Equal(LengthOfLine(NM),2*y+5)",
"Equal(LengthOfLine(NQ),3*x+2)",
"Equal(LengthOfLine(QL),12)",
"Equal(LengthOfLine(RM),4*x-2)",
"Equal(LengthOfLine(RQ),3*y)",
"Parallelogram(MRQN)"
] | [
"Equal(LengthOfLine(ML),w)",
"Equal(LengthOfLine(NM),2*y+5)",
"Equal(LengthOfLine(NQ),3*x+2)",
"Equal(LengthOfLine(QL),12)",
"Equal(LengthOfLine(RM),4*x-2)",
"Equal(LengthOfLine(RQ),3*y)"
] | Value(LengthOfLine(NQ)) | 14 | [
"parallelogram_property_opposite_line_equal(1,MRQN)"
] | {"START": ["parallelogram_property_opposite_line_equal(1,MRQN)"]} | |
942 | XiaokaiZhang_2023-04-09 | Geometry3k-971 | 19 | 如图所示，AC=32，O是⊙O的圆心，AE是⊙O的切线，AG是圆O的切线，圆O的切线为BF，圆O的切线为BH，圆O的切线为CE，圆O的切线为CF，DG是圆O的切线，圆O的切线为DH，EC垂直于FC，FB⊥HB，GA垂直于EA，HD⊥GD。求⊙O的周长。 | As shown in the diagram, AC=32, the center of ⊙O is O, the tangent to circle O is AE, AG is the tangent to ⊙O, BF is the tangent to ⊙O, BH is the tangent to circle O, the tangent to circle O is CE, CF is the tangent to ⊙O, the tangent to ⊙O is DG, DH is the tangent to circle O, EC is perpendicular to FC, FB⊥HB, GA is p... | 942.png | [
"Shape(OHF,FB,BH)",
"Shape(HD,DG,OHG)",
"Shape(GA,AE,OGE)",
"Shape(OG,OGE,EO)",
"Shape(FO,OE,OEF)",
"Shape(EC,CF,OEF)",
"Shape(OF,OFH,OHG,GO)",
"Collinear(BHD)",
"Collinear(FOG)",
"Collinear(CEA)",
"Collinear(BFC)",
"Collinear(DGA)",
"Cocircular(O,FHGE)"
] | [
"Equal(LengthOfLine(AC),32)",
"IsCentreOfCircle(O,O)",
"IsTangentOfCircle(AE,O)",
"IsTangentOfCircle(AG,O)",
"IsTangentOfCircle(BF,O)",
"IsTangentOfCircle(BH,O)",
"IsTangentOfCircle(CE,O)",
"IsTangentOfCircle(CF,O)",
"IsTangentOfCircle(DG,O)",
"IsTangentOfCircle(DH,O)",
"PerpendicularBetweenLine... | [
"Equal(LengthOfLine(AC),32)",
"IsCentreOfCircle(O,O)",
"IsTangentOfCircle(AE,O)",
"IsTangentOfCircle(AG,O)",
"IsTangentOfCircle(BF,O)",
"IsTangentOfCircle(BH,O)",
"IsTangentOfCircle(CE,O)",
"IsTangentOfCircle(CF,O)",
"IsTangentOfCircle(DG,O)",
"IsTangentOfCircle(DH,O)",
"PerpendicularBetweenLine... | Value(PerimeterOfCircle(O)) | 32*pi | [
"tangent_of_circle_property_perpendicular(2,AE,O,O)",
"tangent_of_circle_property_perpendicular(1,AG,O,O)",
"tangent_of_circle_property_length_equal(1,AE,AG,O)",
"radius_of_circle_property_length_equal(1,OE,O)",
"radius_of_circle_property_length_equal(1,OG,O)",
"quadrilateral_property_angle_sum(1,OGAE)",
... | {"START": ["tangent_of_circle_property_perpendicular(2,AE,O,O)", "tangent_of_circle_property_perpendicular(1,AG,O,O)", "tangent_of_circle_property_length_equal(1,AE,AG,O)", "radius_of_circle_property_length_equal(1,OE,O)", "radius_of_circle_property_length_equal(1,OG,O)", "quadrilateral_property_angle_sum(1,OGAE)", "ta... | |
943 | XiaokaiZhang_2023-04-09 | Geometry3k-972 | 3 | 如图所示，AE=10，NB=7，NC=12，四边形ABNC是平行四边形，AE⊥NE。求ABNC的周长。 | As shown in the diagram, AE=10, NB=7, NC=12, ABNC is a parallelogram, AE is perpendicular to NE. Find the perimeter of ABNC. | 943.png | [
"Shape(AB,BE,EA)",
"Shape(AE,EN,NC,CA)",
"Collinear(BEN)"
] | [
"Equal(LengthOfLine(AE),10)",
"Equal(LengthOfLine(NB),7)",
"Equal(LengthOfLine(NC),12)",
"Parallelogram(ABNC)",
"PerpendicularBetweenLine(AE,NE)"
] | [
"Equal(LengthOfLine(AE),10)",
"Equal(LengthOfLine(NB),7)",
"Equal(LengthOfLine(NC),12)",
"PerpendicularBetweenLine(AE,NE)"
] | Value(PerimeterOfQuadrilateral(ABNC)) | 38 | [
"parallelogram_property_opposite_line_equal(1,ABNC)",
"parallelogram_property_opposite_line_equal(1,BNCA)",
"quadrilateral_perimeter_formula(1,ABNC)"
] | {"START": ["parallelogram_property_opposite_line_equal(1,ABNC)", "parallelogram_property_opposite_line_equal(1,BNCA)", "quadrilateral_perimeter_formula(1,ABNC)"]} | |
944 | XiaokaiZhang_2023-04-09 | Geometry3k-973 | 1 | 如图所示，∠ADC=40°，弧BED的角度为98。求⌒BCF的角度。 | As shown in the diagram, ∠ADC=40°, the measure of ⌒BED is 98. Find the measure of arc BCF. | 944.png | [
"Shape(BDC,CD)",
"Shape(AD,DC,CA)",
"Shape(BCF,FA,AC)",
"Shape(AF,BFE,EA)",
"Shape(AE,BED,DA)",
"Collinear(CAE)",
"Collinear(DAF)",
"Cocircular(B,DCFE)"
] | [
"Equal(MeasureOfAngle(ADC),40)",
"Equal(MeasureOfArc(BED),98)"
] | [
"Equal(MeasureOfAngle(ADC),40)",
"Equal(MeasureOfArc(BED),98)"
] | Value(MeasureOfArc(BCF)) | 80 | [
"arc_property_circumference_angle_external(1,BCF,D)"
] | {"START": ["arc_property_circumference_angle_external(1,BCF,D)"]} | |
945 | XiaokaiZhang_2023-04-09 | Geometry3k-974 | 1 | 如图所示，AC=30-x，BD=4*x-60，DABC是长方形。求x的值。 | As shown in the diagram, AC=30-x, BD=4*x-60, quadrilateral DABC is a rectangle. Find the value of x. | 945.png | [
"Shape(DA,AE,ED)",
"Shape(EA,AB,BE)",
"Shape(EB,BC,CE)",
"Shape(DE,EC,CD)",
"Collinear(DEB)",
"Collinear(AEC)"
] | [
"Equal(LengthOfLine(AC),30-x)",
"Equal(LengthOfLine(BD),4*x-60)",
"Rectangle(DABC)"
] | [
"Equal(LengthOfLine(AC),30-x)",
"Equal(LengthOfLine(BD),4*x-60)"
] | Value(x) | 18 | [
"rectangle_property_diagonal_equal(1,DABC)"
] | {"START": ["rectangle_property_diagonal_equal(1,DABC)"]} | |
946 | XiaokaiZhang_2023-03-19 | Geometry3k-975 | 5 | 如图所示，AB=12，AD=10，BC=y，BD=x，CD=z，AB⊥CB，BD⊥AD。求y的值。 | As shown in the diagram, AB=12, AD=10, BC=y, BD=x, CD=z, AB⊥CB, BD is perpendicular to AD. Find the value of y. | 946.png | [
"Shape(BC,CD,DB)",
"Shape(BD,DA,AB)",
"Collinear(CDA)"
] | [
"Equal(LengthOfLine(AB),12)",
"Equal(LengthOfLine(AD),10)",
"Equal(LengthOfLine(BC),y)",
"Equal(LengthOfLine(BD),x)",
"Equal(LengthOfLine(CD),z)",
"PerpendicularBetweenLine(AB,CB)",
"PerpendicularBetweenLine(BD,AD)"
] | [
"Equal(LengthOfLine(AB),12)",
"Equal(LengthOfLine(AD),10)",
"Equal(LengthOfLine(BC),y)",
"Equal(LengthOfLine(BD),x)",
"Equal(LengthOfLine(CD),z)",
"PerpendicularBetweenLine(AB,CB)",
"PerpendicularBetweenLine(BD,AD)"
] | Value(y) | 12*sqrt(11)/5 | [
"mirror_similar_triangle_judgment_aa(1,BDA,CAB)",
"right_triangle_judgment_angle(1,BDA)",
"right_triangle_property_pythagorean(1,BDA)",
"mirror_similar_triangle_property_line_ratio(1,BDA,CAB)",
"mirror_similar_triangle_property_line_ratio(1,ABD,ABC)"
] | {"START": ["mirror_similar_triangle_judgment_aa(1,BDA,CAB)", "right_triangle_judgment_angle(1,BDA)"], "mirror_similar_triangle_judgment_aa(1,BDA,CAB)": ["mirror_similar_triangle_property_line_ratio(1,BDA,CAB)", "mirror_similar_triangle_property_line_ratio(1,ABD,ABC)"], "right_triangle_judgment_angle(1,BDA)": ["right_tr... | |
947 | XiaokaiZhang_2023-03-19 | Geometry3k-976 | 2 | 如图所示，AR=RC，AT=16，CT=TB，MC=7，RM=4，SA=SB，三角形ACB的重心为O。求直线RB的长度。 | As shown in the diagram, AR=RC, AT=16, CT=TB, MC=7, RM=4, SA=SB, the centroid of △ACB is M. Find the length of line RB. | 947.png | [
"Shape(AR,RM,MA)",
"Shape(MR,RC,CM)",
"Shape(MC,CT,TM)",
"Shape(MT,TB,BM)",
"Shape(MB,BS,SM)",
"Shape(MS,SA,AM)",
"Collinear(ARC)",
"Collinear(CTB)",
"Collinear(BSA)",
"Collinear(AMT)",
"Collinear(BMR)",
"Collinear(CMS)"
] | [
"Equal(LengthOfLine(AR),LengthOfLine(RC))",
"Equal(LengthOfLine(AT),16)",
"Equal(LengthOfLine(CT),LengthOfLine(TB))",
"Equal(LengthOfLine(MC),7)",
"Equal(LengthOfLine(RM),4)",
"Equal(LengthOfLine(SA),LengthOfLine(SB))",
"IsCentroidOfTriangle(M,ACB)"
] | [
"Equal(LengthOfLine(AR),LengthOfLine(RC))",
"Equal(LengthOfLine(CT),LengthOfLine(TB))",
"Equal(LengthOfLine(MC),7)",
"Equal(LengthOfLine(RM),4)",
"Equal(LengthOfLine(SA),LengthOfLine(SB))",
"IsCentroidOfTriangle(M,ACB)"
] | Value(LengthOfLine(RB)) | 12 | [
"centroid_of_triangle_property_line_ratio(1,M,BAC,R)",
"line_addition(1,RM,MB)"
] | {"START": ["centroid_of_triangle_property_line_ratio(1,M,BAC,R)", "line_addition(1,RM,MB)"]} | |
948 | XiaokaiZhang_2023-04-09 | Geometry3k-977 | 14 | 如图所示，⊙O的直径为5，BY=5/2，⊙O的圆心为O，DY是⊙O的直径，D平分线段AC，E是线段CB的中点，F是线段AB的中点，AD是圆O的切线，圆O的切线为AF，⊙O的切线为BE，⊙O的切线为BF，⊙O的切线为CD，圆O的切线为CE。求三角形ACB的周长。 | As shown in the diagram, the diameter of ⊙O is 5, BY=5/2, the center of ⊙O is O, the diameter of ⊙O is DY, D bisects segment AC, E bisects segment CB, F is the midpoint of segment AB, the tangent to ⊙O is AD, the tangent to circle O is AF, BE is the tangent to circle O, the tangent to ⊙O is BF, CD is the tangent to ⊙O,... | 948.png | [
"Shape(AD,OXD,XA)",
"Shape(OX,OXD,DO)",
"Shape(AX,OFX,FA)",
"Shape(XO,OF,OFX)",
"Shape(OD,ODZ,ZO)",
"Shape(DC,CZ,ODZ)",
"Shape(OZ,OZE,EO)",
"Shape(ZC,CE,OZE)",
"Shape(OE,OEY,YO)",
"Shape(OEY,EB,BY)",
"Shape(OY,OYF,FO)",
"Shape(YB,BF,OYF)",
"Collinear(ADC)",
"Collinear(CEB)",
"Collinear(B... | [
"Equal(DiameterOfCircle(O),5)",
"Equal(LengthOfLine(BY),5/2)",
"IsCentreOfCircle(O,O)",
"IsDiameterOfCircle(DY,O)",
"IsMidpointOfLine(D,AC)",
"IsMidpointOfLine(E,CB)",
"IsMidpointOfLine(F,AB)",
"IsTangentOfCircle(AD,O)",
"IsTangentOfCircle(AF,O)",
"IsTangentOfCircle(BE,O)",
"IsTangentOfCircle(BF... | [
"IsCentreOfCircle(O,O)",
"IsDiameterOfCircle(DY,O)"
] | Value(PerimeterOfTriangle(ACB)) | 15*sqrt(3) | [
"diameter_of_circle_property_length_equal(1,DY,O)",
"line_addition(1,DY,YB)",
"line_addition(1,AD,DC)",
"line_addition(1,CE,EB)",
"line_addition(1,AF,FB)",
"tangent_of_circle_property_length_equal(1,AD,AF,O)",
"tangent_of_circle_property_length_equal(1,CD,CE,O)",
"isosceles_triangle_judgment_line_equa... | {"START": ["diameter_of_circle_property_length_equal(1,DY,O)", "line_addition(1,DY,YB)", "line_addition(1,AD,DC)", "line_addition(1,CE,EB)", "line_addition(1,AF,FB)", "tangent_of_circle_property_length_equal(1,AD,AF,O)", "tangent_of_circle_property_length_equal(1,CD,CE,O)", "tangent_of_circle_property_perpendicular(1,C... | |
949 | XiaokaiZhang_2023-04-09 | Geometry3k-978 | 2 | 如图所示，∠GMC=10*x°，∠IMG=8*y+2°，∠MGJ=25*y-20°，MI∥GJ。求x的值。 | As shown in the diagram, ∠GMC=10*x°, ∠IMG=8*y+2°, ∠MGJ=25*y-20°, MI is parallel to GJ. Find the value of x. | 949.png | [
"Shape(HM,MI)",
"Shape(IM,MG)",
"Shape(MG,GJ)",
"Shape(JG,GF)",
"Shape(FG,GD)",
"Shape(DG,GM)",
"Shape(GM,MC)",
"Shape(CM,MH)",
"Collinear(HMGF)",
"Collinear(IMC)",
"Collinear(JGD)"
] | [
"Equal(MeasureOfAngle(GMC),10*x)",
"Equal(MeasureOfAngle(IMG),8*y+2)",
"Equal(MeasureOfAngle(MGJ),25*y-20)",
"ParallelBetweenLine(MI,GJ)"
] | [
"Equal(MeasureOfAngle(GMC),10*x)",
"Equal(MeasureOfAngle(IMG),8*y+2)",
"Equal(MeasureOfAngle(MGJ),25*y-20)",
"ParallelBetweenLine(MI,GJ)"
] | Value(x) | 13 | [
"parallel_property_ipsilateral_internal_angle(1,MI,GJ)",
"adjacent_complementary_angle(1,IMG,GMC)"
] | {"START": ["parallel_property_ipsilateral_internal_angle(1,MI,GJ)", "adjacent_complementary_angle(1,IMG,GMC)"]} | |
950 | XiaokaiZhang_2023-04-09 | Geometry3k-979 | 4 | 如图所示，BZ=10，∠ZXY=130°，圆X的圆心为X，BZ是圆X的直径。求弧XYZ的长度。 | As shown in the diagram, BZ=10, ∠ZXY=130°, the center of circle X is X, BZ is the diameter of circle X. Find the length of arc XYZ. | 950.png | [
"Shape(XB,XBY,YX)",
"Shape(XY,XYZ,ZX)",
"Shape(XZ,XZB,BX)",
"Collinear(BXZ)",
"Cocircular(X,BYZ)"
] | [
"Equal(LengthOfLine(BZ),10)",
"Equal(MeasureOfAngle(ZXY),130)",
"IsCentreOfCircle(X,X)",
"IsDiameterOfCircle(BZ,X)"
] | [
"Equal(LengthOfLine(BZ),10)",
"Equal(MeasureOfAngle(ZXY),130)",
"IsCentreOfCircle(X,X)",
"IsDiameterOfCircle(BZ,X)"
] | Value(LengthOfArc(XYZ)) | 65*pi/18 | [
"diameter_of_circle_property_length_equal(1,BZ,X)",
"circle_property_length_of_radius_and_diameter(1,X)",
"arc_property_center_angle(1,XYZ,X)",
"arc_length_formula(1,XYZ)"
] | {"START": ["diameter_of_circle_property_length_equal(1,BZ,X)", "circle_property_length_of_radius_and_diameter(1,X)", "arc_property_center_angle(1,XYZ,X)", "arc_length_formula(1,XYZ)"]} | |
951 | XiaokaiZhang_2023-04-09 | Geometry3k-980 | 1 | 如图所示，FL=LK，GF=x，GH=HJ，HL=15，JK=18，LH是四边形FKJG的中位线，四边形FKJG是梯形。求x的值。 | As shown in the diagram, FL=LK, GF=x, GH=HJ, HL=15, JK=18, the midsegment of FKJG is LH, quadrilateral FKJG is a trapezoid. Find the value of x. | 951.png | [
"Shape(FL,LH,HG,GF)",
"Shape(LK,KJ,JH,HL)",
"Collinear(FLK)",
"Collinear(GHJ)"
] | [
"Equal(LengthOfLine(FL),LengthOfLine(LK))",
"Equal(LengthOfLine(GF),x)",
"Equal(LengthOfLine(GH),LengthOfLine(HJ))",
"Equal(LengthOfLine(HL),15)",
"Equal(LengthOfLine(JK),18)",
"IsMidsegmentOfQuadrilateral(LH,FKJG)",
"Trapezoid(FKJG)"
] | [
"Equal(LengthOfLine(FL),LengthOfLine(LK))",
"Equal(LengthOfLine(GF),x)",
"Equal(LengthOfLine(GH),LengthOfLine(HJ))",
"Equal(LengthOfLine(HL),15)",
"Equal(LengthOfLine(JK),18)"
] | Value(x) | 12 | [
"midsegment_of_quadrilateral_property_length(1,LH,FKJG)"
] | {"START": ["midsegment_of_quadrilateral_property_length(1,LH,FKJG)"]} | |
952 | XiaokaiZhang_2023-03-19 | Geometry3k-981 | 1 | 如图所示，AC=7*sqrt(2)，BC=x，∠CBA=45°，BA⊥CA。求x的值。 | As shown in the diagram, AC=7*sqrt(2), BC=x, ∠CBA=45°, BA⊥CA. Find the value of x. | 952.png | [
"Shape(CB,BA,AC)"
] | [
"Equal(LengthOfLine(AC),7*sqrt(2))",
"Equal(LengthOfLine(BC),x)",
"Equal(MeasureOfAngle(CBA),45)",
"PerpendicularBetweenLine(BA,CA)"
] | [
"Equal(LengthOfLine(AC),7*sqrt(2))",
"Equal(LengthOfLine(BC),x)",
"Equal(MeasureOfAngle(CBA),45)",
"PerpendicularBetweenLine(BA,CA)"
] | Value(x) | 14 | [
"sine_theorem(1,CBA)"
] | {"START": ["sine_theorem(1,CBA)"]} | |
953 | XiaokaiZhang_2023-03-19 | Geometry3k-982 | 9 | 如图所示，AB=10，CE=9，AD是三角形ACB的中线，CE是三角形CBA的中线，AF⊥EF。求直线CA的长度。 | As shown in the diagram, AB=10, CE=9, AD is the median of △ ACB, CE is the median of triangle CBA, AF⊥EF. Find the length of line CA. | 953.png | [
"Shape(AC,CF,FA)",
"Shape(FC,CD,DF)",
"Shape(AF,FE,EA)",
"Shape(EF,FD,DB,BE)",
"Collinear(AEB)",
"Collinear(CDB)",
"Collinear(AFD)",
"Collinear(CFE)"
] | [
"Equal(LengthOfLine(AB),10)",
"Equal(LengthOfLine(CE),9)",
"IsMedianOfTriangle(AD,ACB)",
"IsMedianOfTriangle(CE,CBA)",
"PerpendicularBetweenLine(AF,EF)"
] | [] | Value(LengthOfLine(CA)) | 2*sqrt(13) | [
"line_addition(1,AE,EB)",
"centroid_of_triangle_judgment_intersection(1,F,BAC,E,D)",
"centroid_of_triangle_property_line_ratio(1,F,CBA,E)",
"line_addition(1,CF,FE)",
"right_triangle_judgment_angle(1,AFE)",
"right_triangle_property_pythagorean(1,AFE)",
"adjacent_complementary_angle(1,CFA,AFE)",
"right_... | {"START": ["line_addition(1,AE,EB)", "centroid_of_triangle_judgment_intersection(1,F,BAC,E,D)", "line_addition(1,CF,FE)", "right_triangle_judgment_angle(1,AFE)", "adjacent_complementary_angle(1,CFA,AFE)"], "adjacent_complementary_angle(1,CFA,AFE)": ["right_triangle_judgment_angle(1,CFA)"], "centroid_of_triangle_judgmen... | |
954 | XiaokaiZhang_2023-04-09 | Geometry3k-983 | 2 | 如图所示，∠BCA=40°，∠CAB=x°，∠CBD=115°。求x的值。 | As shown in the diagram, ∠BCA=40°, ∠CAB=x°, ∠CBD=115°. Find the value of x. | 954.png | [
"Shape(CA,AB,BC)",
"Shape(CB,BD)",
"Collinear(ABD)"
] | [
"Equal(MeasureOfAngle(BCA),40)",
"Equal(MeasureOfAngle(CAB),x)",
"Equal(MeasureOfAngle(CBD),115)"
] | [
"Equal(MeasureOfAngle(BCA),40)",
"Equal(MeasureOfAngle(CAB),x)",
"Equal(MeasureOfAngle(CBD),115)"
] | Value(x) | 75 | [
"adjacent_complementary_angle(1,ABC,CBD)",
"triangle_property_angle_sum(1,CAB)"
] | {"START": ["adjacent_complementary_angle(1,ABC,CBD)", "triangle_property_angle_sum(1,CAB)"]} | |
955 | XiaokaiZhang_2023-04-09 | Geometry3k-984 | 3 | 如图所示，FG=12，∠FGH=133°，G是⊙G的圆心。求扇形GHF的面积。 | As shown in the diagram, FG=12, ∠FGH=133°, the center of circle G is G. Find the area of the sector GHF. | 955.png | [
"Shape(GF,GFH,HG)",
"Shape(GH,GHF,FG)",
"Cocircular(G,HF)"
] | [
"Equal(LengthOfLine(FG),12)",
"Equal(MeasureOfAngle(FGH),133)",
"IsCentreOfCircle(G,G)"
] | [
"Equal(LengthOfLine(FG),12)",
"Equal(MeasureOfAngle(FGH),133)",
"IsCentreOfCircle(G,G)"
] | Value(AreaOfSector(GHF)) | 266*pi/5 | [
"arc_property_center_angle(1,GHF,G)",
"radius_of_circle_property_length_equal(1,GF,G)",
"sector_area_formula(1,GHF)"
] | {"START": ["arc_property_center_angle(1,GHF,G)", "radius_of_circle_property_length_equal(1,GF,G)", "sector_area_formula(1,GHF)"]} | |
956 | XiaokaiZhang_2023-04-09 | Geometry3k-985 | 1 | 如图所示，BA=5*x，BC=3*y-4，DA=29，DC=25，∠ADF=34°，∠DCF=54°，∠FAD=49°，BADC是平行四边形。求∠FCB的大小。 | As shown in the diagram, BA=5*x, BC=3*y-4, DA=29, DC=25, ∠ADF=34°, ∠DCF=54°, ∠FAD=49°, AB and DC are opposite sides of the parallelogram BADC. Find the measure of ∠FCB. | 956.png | [
"Shape(BA,AF,FB)",
"Shape(FA,AD,DF)",
"Shape(FD,DC,CF)",
"Shape(FC,CB,BF)",
"Collinear(BFD)",
"Collinear(AFC)"
] | [
"Equal(LengthOfLine(BA),5*x)",
"Equal(LengthOfLine(BC),3*y-4)",
"Equal(LengthOfLine(DA),29)",
"Equal(LengthOfLine(DC),25)",
"Equal(MeasureOfAngle(ADF),34)",
"Equal(MeasureOfAngle(DCF),54)",
"Equal(MeasureOfAngle(FAD),49)",
"Parallelogram(BADC)"
] | [
"Equal(LengthOfLine(BA),5*x)",
"Equal(LengthOfLine(BC),3*y-4)",
"Equal(LengthOfLine(DA),29)",
"Equal(LengthOfLine(DC),25)",
"Equal(MeasureOfAngle(ADF),34)",
"Equal(MeasureOfAngle(DCF),54)",
"Equal(MeasureOfAngle(FAD),49)"
] | Value(MeasureOfAngle(FCB)) | 49 | [
"parallel_property_alternate_interior_angle(2,BC,AD)"
] | {"START": ["parallel_property_alternate_interior_angle(2,BC,AD)"]} | |
957 | XiaokaiZhang_2023-03-19 | Geometry3k-986 | 7 | 如图所示，AD=DB，AF=FC，CA=15，CE=EB，EF=9.2，∠BDE=82°。求∠FED的大小。 | As shown in the diagram, AD=DB, AF=FC, CA=15, CE=EB, EF=9.2, ∠BDE=82°. Find the measure of ∠FED. | 957.png | [
"Shape(AF,FE,ED,DA)",
"Shape(FC,CE,EF)",
"Shape(DE,EB,BD)",
"Collinear(AFC)",
"Collinear(CEB)",
"Collinear(ADB)"
] | [
"Equal(LengthOfLine(AD),LengthOfLine(DB))",
"Equal(LengthOfLine(AF),LengthOfLine(FC))",
"Equal(LengthOfLine(CA),15)",
"Equal(LengthOfLine(CE),LengthOfLine(EB))",
"Equal(LengthOfLine(EF),9.2)",
"Equal(MeasureOfAngle(BDE),82)"
] | [
"Equal(LengthOfLine(AD),LengthOfLine(DB))",
"Equal(LengthOfLine(AF),LengthOfLine(FC))",
"Equal(LengthOfLine(CA),15)",
"Equal(LengthOfLine(CE),LengthOfLine(EB))",
"Equal(LengthOfLine(EF),9.2)",
"Equal(MeasureOfAngle(BDE),82)"
] | Value(MeasureOfAngle(FED)) | 82 | [
"line_addition(1,CF,FA)",
"line_addition(1,CE,EB)",
"similar_triangle_judgment_sas(1,CEF,CBA)",
"similar_triangle_property_angle_equal(1,FCE,ACB)",
"parallel_judgment_corresponding_angle(2,AD,FE,C)",
"adjacent_complementary_angle(1,BDE,EDA)",
"parallel_property_ipsilateral_internal_angle(1,EF,DA)"
] | {"START": ["line_addition(1,CF,FA)", "line_addition(1,CE,EB)", "adjacent_complementary_angle(1,BDE,EDA)"], "line_addition(1,CE,EB)": ["similar_triangle_judgment_sas(1,CEF,CBA)"], "line_addition(1,CF,FA)": ["similar_triangle_judgment_sas(1,CEF,CBA)"], "parallel_judgment_corresponding_angle(2,AD,FE,C)": ["parallel_proper... | |
958 | XiaokaiZhang_2023-04-09 | Geometry3k-987 | 2 | 如图所示，AB=x，AD=32，BD=40，AD⊥BD，BC⊥AC。求x的值。 | As shown in the diagram, AB=x, AD=32, BD=40, AD is perpendicular to BD, BC⊥AC. Find the value of x. | 958.png | [
"Shape(BC,CA,AB)",
"Shape(BA,AD,DB)"
] | [
"Equal(LengthOfLine(AB),x)",
"Equal(LengthOfLine(AD),32)",
"Equal(LengthOfLine(BD),40)",
"PerpendicularBetweenLine(AD,BD)",
"PerpendicularBetweenLine(BC,AC)"
] | [
"Equal(LengthOfLine(AB),x)",
"Equal(LengthOfLine(AD),32)",
"Equal(LengthOfLine(BD),40)",
"PerpendicularBetweenLine(AD,BD)",
"PerpendicularBetweenLine(BC,AC)"
] | Value(x) | 8*sqrt(41) | [
"right_triangle_judgment_angle(1,ADB)",
"right_triangle_property_pythagorean(1,ADB)"
] | {"START": ["right_triangle_judgment_angle(1,ADB)"], "right_triangle_judgment_angle(1,ADB)": ["right_triangle_property_pythagorean(1,ADB)"]} | |
959 | NaZhu_2023-03-19 | Geometry3k-988 | 6 | 如图所示，AB=10，AP=13，EP=15，∠DCP=28°，∠PAF=33°，三角形AEC的内切圆圆心为P，ED⊥PD，PB垂直于AB，PF⊥EF。求直线DE的长度。 | As shown in the diagram, AB=10, AP=13, EP=15, ∠DCP=28°, ∠PAF=33°, the incenter of △AEC is P, ED is perpendicular to PD, PB is perpendicular to AB, PF⊥EF. Find the length of line DE. | 959.png | [
"Shape(AF,FP,PA)",
"Shape(AP,PB,BA)",
"Shape(FE,EP,PF)",
"Shape(PE,ED,DP)",
"Shape(PD,DC,CP)",
"Shape(PC,CB,BP)",
"Collinear(AFE)",
"Collinear(ABC)",
"Collinear(EDC)"
] | [
"Equal(LengthOfLine(AB),10)",
"Equal(LengthOfLine(AP),13)",
"Equal(LengthOfLine(EP),15)",
"Equal(MeasureOfAngle(DCP),28)",
"Equal(MeasureOfAngle(PAF),33)",
"IsIncenterOfTriangle(P,AEC)",
"PerpendicularBetweenLine(ED,PD)",
"PerpendicularBetweenLine(PB,AB)",
"PerpendicularBetweenLine(PF,EF)"
] | [
"Equal(LengthOfLine(AB),10)",
"Equal(LengthOfLine(AP),13)",
"Equal(LengthOfLine(EP),15)",
"Equal(MeasureOfAngle(DCP),28)",
"Equal(MeasureOfAngle(PAF),33)",
"PerpendicularBetweenLine(ED,PD)",
"PerpendicularBetweenLine(PB,AB)",
"PerpendicularBetweenLine(PF,EF)"
] | Value(LengthOfLine(DE)) | 15*sin(61*pi/180) | [
"angle_addition(1,BAP,PAF)",
"angle_addition(1,FEP,PED)",
"angle_addition(1,DCP,PCB)",
"triangle_property_angle_sum(1,AEC)",
"triangle_property_angle_sum(1,PED)",
"sine_theorem(1,EDP)"
] | {"START": ["angle_addition(1,BAP,PAF)", "angle_addition(1,FEP,PED)", "angle_addition(1,DCP,PCB)", "triangle_property_angle_sum(1,AEC)", "triangle_property_angle_sum(1,PED)", "sine_theorem(1,EDP)"]} | |
960 | NaZhu_2023-03-19 | Geometry3k-989 | 5 | 如图所示，AE=6，DB=7，FC=16，EA⊥BA，FB⊥DB。求三角形DFC的面积与△ECF的面积之和。 | As shown in the diagram, AE=6, DB=7, FC=16, EA⊥BA, FB is perpendicular to DB. Find the sum of the area of △DFC and the area of triangle ECF. | 960.png | [
"Shape(DF,FB,BD)",
"Shape(DB,BA,AC,CD)",
"Shape(FE,EA,AB,BF)",
"Shape(AE,EC,CA)",
"Collinear(FBAC)"
] | [
"Equal(LengthOfLine(AE),6)",
"Equal(LengthOfLine(DB),7)",
"Equal(LengthOfLine(FC),16)",
"PerpendicularBetweenLine(EA,BA)",
"PerpendicularBetweenLine(FB,DB)"
] | [
"Equal(LengthOfLine(AE),6)",
"Equal(LengthOfLine(DB),7)",
"Equal(LengthOfLine(FC),16)",
"PerpendicularBetweenLine(EA,BA)",
"PerpendicularBetweenLine(FB,DB)"
] | Value(Add(AreaOfTriangle(DFC),AreaOfTriangle(ECF))) | 104 | [
"adjacent_complementary_angle(1,CAE,EAF)",
"altitude_of_triangle_judgment(1,DB,DFC)",
"altitude_of_triangle_judgment(1,EA,ECF)",
"triangle_area_formula_common(1,DFC)",
"triangle_area_formula_common(1,ECF)"
] | {"START": ["adjacent_complementary_angle(1,CAE,EAF)", "altitude_of_triangle_judgment(1,DB,DFC)", "triangle_area_formula_common(1,DFC)", "triangle_area_formula_common(1,ECF)"], "adjacent_complementary_angle(1,CAE,EAF)": ["altitude_of_triangle_judgment(1,EA,ECF)"]} | |
961 | NaZhu_2023-03-19 | Geometry3k-990 | 11 | 如图所示，AB=y，AD=z，BD=9，CA=x，CD=4，BD垂直于AD，CA垂直于BA。求y的值。 | As shown in the diagram, AB=y, AD=z, BD=9, CA=x, CD=4, BD⊥AD, CA is perpendicular to BA. Find the value of y. | 961.png | [
"Shape(CA,AD,DC)",
"Shape(DA,AB,BD)",
"Collinear(CDB)"
] | [
"Equal(LengthOfLine(AB),y)",
"Equal(LengthOfLine(AD),z)",
"Equal(LengthOfLine(BD),9)",
"Equal(LengthOfLine(CA),x)",
"Equal(LengthOfLine(CD),4)",
"PerpendicularBetweenLine(BD,AD)",
"PerpendicularBetweenLine(CA,BA)"
] | [
"Equal(LengthOfLine(AB),y)",
"Equal(LengthOfLine(AD),z)",
"Equal(LengthOfLine(BD),9)",
"Equal(LengthOfLine(CA),x)",
"Equal(LengthOfLine(CD),4)",
"PerpendicularBetweenLine(BD,AD)",
"PerpendicularBetweenLine(CA,BA)"
] | Value(y) | 3*sqrt(13) | [
"adjacent_complementary_angle(1,BDA,ADC)",
"line_addition(1,CD,DB)",
"angle_addition(1,CAD,DAB)",
"triangle_property_angle_sum(1,DAB)",
"mirror_similar_triangle_judgment_aa(1,ADC,BCA)",
"similar_triangle_judgment_aa(1,CAD,ABD)",
"mirror_similar_triangle_property_line_ratio(1,ADC,BCA)",
"mirror_similar... | {"START": ["adjacent_complementary_angle(1,BDA,ADC)", "line_addition(1,CD,DB)", "angle_addition(1,CAD,DAB)", "triangle_property_angle_sum(1,DAB)"], "adjacent_complementary_angle(1,BDA,ADC)": ["mirror_similar_triangle_judgment_aa(1,ADC,BCA)", "similar_triangle_judgment_aa(1,CAD,ABD)"], "angle_addition(1,CAD,DAB)": ["sim... | |
962 | NaZhu_2023-03-19 | Geometry3k-991 | 6 | 如图所示，AB=z，AC=x，AY=17，BC=y，YC=6，AY垂直于BY，BA垂直于CA。求z的值。 | As shown in the diagram, AB=z, AC=x, AY=17, BC=y, YC=6, AY is perpendicular to BY, BA is perpendicular to CA. Find the value of z. | 962.png | [
"Shape(BA,AY,YB)",
"Shape(AC,CY,YA)",
"Collinear(BYC)"
] | [
"Equal(LengthOfLine(AB),z)",
"Equal(LengthOfLine(AC),x)",
"Equal(LengthOfLine(AY),17)",
"Equal(LengthOfLine(BC),y)",
"Equal(LengthOfLine(YC),6)",
"PerpendicularBetweenLine(AY,BY)",
"PerpendicularBetweenLine(BA,CA)"
] | [
"Equal(LengthOfLine(AB),z)",
"Equal(LengthOfLine(AC),x)",
"Equal(LengthOfLine(AY),17)",
"Equal(LengthOfLine(BC),y)",
"Equal(LengthOfLine(YC),6)",
"PerpendicularBetweenLine(AY,BY)",
"PerpendicularBetweenLine(BA,CA)"
] | Value(z) | 85*sqrt(13)/6 | [
"adjacent_complementary_angle(1,CYA,AYB)",
"mirror_similar_triangle_judgment_aa(1,ACY,BAC)",
"right_triangle_judgment_angle(1,CYA)",
"right_triangle_property_pythagorean(1,CYA)",
"mirror_similar_triangle_property_line_ratio(1,ACY,BAC)",
"mirror_similar_triangle_property_line_ratio(1,CYA,CBA)"
] | {"START": ["adjacent_complementary_angle(1,CYA,AYB)"], "adjacent_complementary_angle(1,CYA,AYB)": ["mirror_similar_triangle_judgment_aa(1,ACY,BAC)", "right_triangle_judgment_angle(1,CYA)"], "mirror_similar_triangle_judgment_aa(1,ACY,BAC)": ["mirror_similar_triangle_property_line_ratio(1,ACY,BAC)", "mirror_similar_trian... | |
963 | NaZhu_2023-03-19 | Geometry3k-992 | 1 | 如图所示，AB=17，AC=12，∠ABC=x°，BC⊥AC。求x的值。 | As shown in the diagram, AB=17, AC=12, ∠ABC=x°, BC is perpendicular to AC. Find the value of x. | 963.png | [
"Shape(AB,BC,CA)"
] | [
"Equal(LengthOfLine(AB),17)",
"Equal(LengthOfLine(AC),12)",
"Equal(MeasureOfAngle(ABC),x)",
"PerpendicularBetweenLine(BC,AC)"
] | [
"Equal(LengthOfLine(AB),17)",
"Equal(LengthOfLine(AC),12)",
"Equal(MeasureOfAngle(ABC),x)",
"PerpendicularBetweenLine(BC,AC)"
] | Value(x) | 180*asin(12/17)/pi | [
"sine_theorem(1,ABC)"
] | {"START": ["sine_theorem(1,ABC)"]} | |
964 | NaZhu_2023-03-19 | Geometry3k-993 | 2 | 如图所示，AB=25，BC=15，CA=x，BC⊥AC。求x的值。 | As shown in the diagram, AB=25, BC=15, CA=x, BC is perpendicular to AC. Find the value of x. | 964.png | [
"Shape(BC,CA,AB)",
"Shape(BA,AD,DB)"
] | [
"Equal(LengthOfLine(AB),25)",
"Equal(LengthOfLine(BC),15)",
"Equal(LengthOfLine(CA),x)",
"PerpendicularBetweenLine(BC,AC)"
] | [
"Equal(LengthOfLine(AB),25)",
"Equal(LengthOfLine(BC),15)",
"Equal(LengthOfLine(CA),x)",
"PerpendicularBetweenLine(BC,AC)"
] | Value(x) | 20 | [
"right_triangle_judgment_angle(1,BCA)",
"right_triangle_property_pythagorean(1,BCA)"
] | {"START": ["right_triangle_judgment_angle(1,BCA)"], "right_triangle_judgment_angle(1,BCA)": ["right_triangle_property_pythagorean(1,BCA)"]} | |
965 | XiaokaiZhang_2023-04-09 | Geometry3k-994 | 3 | 如图所示，∠BIG=24°，∠DIB=84°，∠GIE=x°，EI垂直于DI。求x的值。 | As shown in the diagram, ∠BIG=24°, ∠DIB=84°, ∠GIE=x°, EI⊥DI. Find the value of x. | 965.png | [
"Shape(ID,IDE,EI)",
"Shape(IE,IEG,GI)",
"Shape(IG,IGB,BI)",
"Shape(IB,IBD,DI)",
"Cocircular(I,EGBD)"
] | [
"Equal(MeasureOfAngle(BIG),24)",
"Equal(MeasureOfAngle(DIB),84)",
"Equal(MeasureOfAngle(GIE),x)",
"PerpendicularBetweenLine(EI,DI)"
] | [
"Equal(MeasureOfAngle(BIG),24)",
"Equal(MeasureOfAngle(DIB),84)",
"Equal(MeasureOfAngle(GIE),x)",
"PerpendicularBetweenLine(EI,DI)"
] | Value(x) | 162 | [
"angle_addition(1,EID,DIB)",
"angle_addition(1,EIB,BIG)",
"round_angle(1,GIE,EIG)"
] | {"START": ["angle_addition(1,EID,DIB)", "angle_addition(1,EIB,BIG)", "round_angle(1,GIE,EIG)"]} | |
966 | XiaokaiZhang_2023-04-09 | Geometry3k-995 | 1 | 如图所示，∠BGC=40°，∠DGF=53°，CB垂直于GB，FG⊥CG，GF⊥DF。求∠GCB的大小。 | As shown in the diagram, ∠BGC=40°, ∠DGF=53°, CB⊥GB, FG⊥CG, GF is perpendicular to DF. Find the measure of ∠GCB. | 966.png | [
"Shape(DG,GF,FD)",
"Shape(FG,GB,BA,AF)",
"Shape(BG,GC,CB)",
"Shape(AB,BC,CA)",
"Collinear(DFA)",
"Collinear(GBA)"
] | [
"Equal(MeasureOfAngle(BGC),40)",
"Equal(MeasureOfAngle(DGF),53)",
"PerpendicularBetweenLine(CB,GB)",
"PerpendicularBetweenLine(FG,CG)",
"PerpendicularBetweenLine(GF,DF)"
] | [
"Equal(MeasureOfAngle(BGC),40)",
"Equal(MeasureOfAngle(DGF),53)",
"PerpendicularBetweenLine(CB,GB)",
"PerpendicularBetweenLine(FG,CG)",
"PerpendicularBetweenLine(GF,DF)"
] | Value(MeasureOfAngle(GCB)) | 50 | [
"triangle_property_angle_sum(1,BGC)"
] | {"START": ["triangle_property_angle_sum(1,BGC)"]} | |
967 | XiaokaiZhang_2023-04-09 | Geometry3k-996 | 1 | 如图所示，∠ACB=2*x°，∠DCA=x°。求x的值。 | As shown in the diagram, ∠ACB=2*x°, ∠DCA=x°. Find the value of x. | 967.png | [
"Shape(DC,CA)",
"Shape(AC,CB)",
"Collinear(DCB)"
] | [
"Equal(MeasureOfAngle(ACB),2*x)",
"Equal(MeasureOfAngle(DCA),x)"
] | [
"Equal(MeasureOfAngle(ACB),2*x)",
"Equal(MeasureOfAngle(DCA),x)"
] | Value(x) | 60 | [
"adjacent_complementary_angle(1,DCA,ACB)"
] | {"START": ["adjacent_complementary_angle(1,DCA,ACB)"]} | |
968 | NaZhu_2023-03-19 | Geometry3k-997 | 7 | 如图所示，PQ=25，RS=10，RT=x，SQ=5，PQ平行于TS，TR⊥SR。求x的值。 | As shown in the diagram, PQ=25, RS=10, RT=x, SQ=5, PQ is parallel to TS, TR⊥SR. Find the value of x. | 968.png | [
"Shape(TR,RS,ST)",
"Shape(PT,TS,SQ,QP)",
"Collinear(PTR)",
"Collinear(RSQ)"
] | [
"Equal(LengthOfLine(PQ),25)",
"Equal(LengthOfLine(RS),10)",
"Equal(LengthOfLine(RT),x)",
"Equal(LengthOfLine(SQ),5)",
"ParallelBetweenLine(PQ,TS)",
"PerpendicularBetweenLine(TR,SR)"
] | [
"Equal(LengthOfLine(PQ),25)",
"Equal(LengthOfLine(RS),10)",
"Equal(LengthOfLine(RT),x)",
"Equal(LengthOfLine(SQ),5)",
"ParallelBetweenLine(PQ,TS)",
"PerpendicularBetweenLine(TR,SR)"
] | Value(x) | 40/3 | [
"parallel_property_corresponding_angle(1,ST,QP,R)",
"similar_triangle_judgment_aa(1,TRS,PRQ)",
"line_addition(1,RS,SQ)",
"right_triangle_judgment_angle(1,TRS)",
"right_triangle_property_pythagorean(1,TRS)",
"similar_triangle_property_line_ratio(1,RST,RQP)",
"similar_triangle_property_line_ratio(1,TRS,PR... | {"START": ["parallel_property_corresponding_angle(1,ST,QP,R)", "line_addition(1,RS,SQ)", "right_triangle_judgment_angle(1,TRS)"], "parallel_property_corresponding_angle(1,ST,QP,R)": ["similar_triangle_judgment_aa(1,TRS,PRQ)"], "right_triangle_judgment_angle(1,TRS)": ["right_triangle_property_pythagorean(1,TRS)"], "simi... | |
969 | XiaokaiZhang_2023-04-09 | Geometry3k-998 | 1 | 如图所示，⌒BJL的角度为58，弧BMJ的角度为164，圆O的切线为KJ。求∠JKL的大小。 | As shown in the diagram, the measure of ⌒BJL is 58, the measure of arc BMJ is 164, KJ is the tangent to circle B. Find the measure of ∠JKL. | 969.png | [
"Shape(BLM,ML)",
"Shape(BMJ,BJL,LM)",
"Shape(KL,BJL,JK)",
"Collinear(KLM)",
"Cocircular(B,MJL)"
] | [
"Equal(MeasureOfArc(BJL),58)",
"Equal(MeasureOfArc(BMJ),164)",
"IsTangentOfCircle(KJ,B)"
] | [
"Equal(MeasureOfArc(BJL),58)",
"Equal(MeasureOfArc(BMJ),164)",
"IsTangentOfCircle(KJ,B)"
] | Value(MeasureOfAngle(JKL)) | 53 | [
"circle_property_circular_power_tangent_and_segment_angle(1,KJ,KLM,B)"
] | {"START": ["circle_property_circular_power_tangent_and_segment_angle(1,KJ,KLM,B)"]} | |
970 | NaZhu_2023-03-19 | Geometry3k-999 | 2 | 如图所示，AB=y，CD=9，CE=x，DE=7，XA=20，XB=14，△CED与△AXB是相似三角形。求x的值。 | As shown in the diagram, AB=y, CD=9, CE=x, DE=7, XA=20, XB=14, triangle CED is similar to triangle AXB.. Find the value of x. | 970.png | [
"Shape(CE,ED,DC)",
"Shape(AX,XB,BA)"
] | [
"Equal(LengthOfLine(AB),y)",
"Equal(LengthOfLine(CD),9)",
"Equal(LengthOfLine(CE),x)",
"Equal(LengthOfLine(DE),7)",
"Equal(LengthOfLine(XA),20)",
"Equal(LengthOfLine(XB),14)",
"SimilarBetweenTriangle(CED,AXB)"
] | [
"Equal(LengthOfLine(AB),y)",
"Equal(LengthOfLine(CD),9)",
"Equal(LengthOfLine(CE),x)",
"Equal(LengthOfLine(DE),7)",
"Equal(LengthOfLine(XA),20)",
"Equal(LengthOfLine(XB),14)",
"SimilarBetweenTriangle(CED,AXB)"
] | Value(x) | 10 | [
"similar_triangle_property_line_ratio(1,CED,AXB)",
"similar_triangle_property_line_ratio(1,DCE,BAX)"
] | {"START": ["similar_triangle_property_line_ratio(1,CED,AXB)", "similar_triangle_property_line_ratio(1,DCE,BAX)"]} | |
971 | NaZhu_2023-03-19 | Geometry3k-1000 | 0 | 如图所示，QR=3*y-1，QR=RS，QS=4*y-9，RS=y+11。求y的值。 | As shown in the diagram, QR=3*y-1, QR=RS, QS=4*y-9, RS=y+11. Find the value of y. | 971.png | [
"Shape(RQ,QS,SR)"
] | [
"Equal(LengthOfLine(QR),3*y-1)",
"Equal(LengthOfLine(QR),LengthOfLine(RS))",
"Equal(LengthOfLine(QS),4*y-9)",
"Equal(LengthOfLine(RS),y+11)"
] | [
"Equal(LengthOfLine(QR),3*y-1)",
"Equal(LengthOfLine(QR),LengthOfLine(RS))",
"Equal(LengthOfLine(QS),4*y-9)",
"Equal(LengthOfLine(RS),y+11)"
] | Value(y) | 6 | [] | {"START": []} | |
972 | XiaokaiZhang_2023-04-09 | Geometry3k-1001 | 6 | 如图所示，HW=20，XZ=39，YG=21，WH垂直于XH，YG垂直于ZG。求三角形YXZ的面积与三角形WZX的面积之和。 | As shown in the diagram, HW=20, XZ=39, YG=21, WH is perpendicular to XH, YG⊥ZG. Find the sum of the area of triangle YXZ and the area of △WZX. | 972.png | [
"Shape(YX,XH,HG,GY)",
"Shape(YG,GZ,ZY)",
"Shape(XW,WH,HX)",
"Shape(HW,WZ,ZG,GH)",
"Collinear(XHGZ)"
] | [
"Equal(LengthOfLine(HW),20)",
"Equal(LengthOfLine(XZ),39)",
"Equal(LengthOfLine(YG),21)",
"PerpendicularBetweenLine(WH,XH)",
"PerpendicularBetweenLine(YG,ZG)"
] | [
"PerpendicularBetweenLine(WH,XH)",
"PerpendicularBetweenLine(YG,ZG)"
] | Value(Add(AreaOfTriangle(YXZ),AreaOfTriangle(WZX))) | 1599/2 | [
"adjacent_complementary_angle(1,GHW,WHX)",
"adjacent_complementary_angle(1,XGY,YGZ)",
"altitude_of_triangle_judgment(1,YG,YXZ)",
"altitude_of_triangle_judgment(1,WH,WZX)",
"triangle_area_formula_common(1,YXZ)",
"triangle_area_formula_common(1,WZX)"
] | {"START": ["adjacent_complementary_angle(1,GHW,WHX)", "adjacent_complementary_angle(1,XGY,YGZ)", "triangle_area_formula_common(1,YXZ)", "triangle_area_formula_common(1,WZX)"], "adjacent_complementary_angle(1,GHW,WHX)": ["altitude_of_triangle_judgment(1,WH,WZX)"], "adjacent_complementary_angle(1,XGY,YGZ)": ["altitude_of... | |
973 | XiaokaiZhang_2023-04-09 | Geometry3k-1002 | 12 | 如图所示，AB=30，CD=30，弧XCZ的角度为40，圆X的圆心为X，AM⊥YM，DN⊥ZN。求⌒XBY的角度。 | As shown in the diagram, AB=30, CD=30, the measure of arc XCZ is 40, X is the center of ⊙X, AM⊥YM, DN is perpendicular to ZN. Find the measure of arc XBY. | 973.png | [
"Shape(XYA,AM,MY)",
"Shape(XM,MA,XAC,CN,NX)",
"Shape(NC,XCZ,ZN)",
"Shape(NZ,XZD,DN)",
"Shape(XN,ND,XDB,BM,MX)",
"Shape(YM,MB,XBY)",
"Collinear(AMB)",
"Collinear(YMX)",
"Collinear(XNZ)",
"Collinear(CND)",
"Cocircular(X,ACZDBY)"
] | [
"Equal(LengthOfLine(AB),30)",
"Equal(LengthOfLine(CD),30)",
"Equal(MeasureOfArc(XCZ),40)",
"IsCentreOfCircle(X,X)",
"PerpendicularBetweenLine(AM,YM)",
"PerpendicularBetweenLine(DN,ZN)"
] | [
"Equal(LengthOfLine(AB),30)",
"Equal(LengthOfLine(CD),30)",
"Equal(MeasureOfArc(XCZ),40)",
"IsCentreOfCircle(X,X)",
"PerpendicularBetweenLine(AM,YM)",
"PerpendicularBetweenLine(DN,ZN)"
] | Value(MeasureOfArc(XBY)) | 40 | [
"vertical_angle(1,CNX,DNZ)",
"circle_property_chord_perpendicular_bisect_arc(1,XCD,XNZ)",
"congruent_arc_judgment_length_equal(1,XCZ,XZD)",
"congruent_arc_property_measure_equal(1,XCZ,XZD)",
"arc_addition_measure(1,XCZ,XZD)",
"congruent_arc_judgment_chord_equal(1,XBA,XCD)",
"congruent_arc_property_measu... | {"START": ["vertical_angle(1,CNX,DNZ)", "arc_addition_measure(1,XCZ,XZD)", "congruent_arc_judgment_chord_equal(1,XBA,XCD)", "vertical_angle(1,AMY,BMX)", "arc_addition_measure(1,XBY,XYA)"], "circle_property_chord_perpendicular_bisect_arc(1,XBA,XMY)": ["congruent_arc_judgment_length_equal(1,XBY,XYA)"], "circle_property_c... | |
974 | XiaokaiZhang_2023-04-09 | Geometry3k-1003 | 3 | 如图所示，∠AXW=57°，A是圆A的圆心，XY是圆A的直径。求弧AXW的角度。 | As shown in the diagram, ∠AXW=57°, the center of ⊙A is A, XY is the diameter of circle A. Find the measure of ⌒AXW. | 974.png | [
"Shape(AXW,WX)",
"Shape(AX,XW,WY,YA)",
"Shape(AWY,YW)",
"Shape(XA,AY,AYX)",
"Collinear(XAY)",
"Cocircular(A,XWY)"
] | [
"Equal(MeasureOfAngle(AXW),57)",
"IsCentreOfCircle(A,A)",
"IsDiameterOfCircle(XY,A)"
] | [
"Equal(MeasureOfAngle(AXW),57)",
"IsCentreOfCircle(A,A)",
"IsDiameterOfCircle(XY,A)"
] | Value(MeasureOfArc(AXW)) | 66 | [
"diameter_of_circle_property_right_angle(1,XWY,A)",
"triangle_property_angle_sum(1,XWY)",
"arc_property_circumference_angle_external(1,AXW,Y)"
] | {"START": ["diameter_of_circle_property_right_angle(1,XWY,A)", "triangle_property_angle_sum(1,XWY)", "arc_property_circumference_angle_external(1,AXW,Y)"]} | |
975 | NaZhu_2023-03-19 | Geometry3k-1004 | 7 | 如图所示，AB=x，AD=8，BD=z，CB=y，CD=3，AD⊥BD，CB垂直于AB。求x的值。 | As shown in the diagram, AB=x, AD=8, BD=z, CB=y, CD=3, AD⊥BD, CB is perpendicular to AB. Find the value of x. | 975.png | [
"Shape(AD,DB,BA)",
"Shape(DC,CB,BD)",
"Collinear(ADC)"
] | [
"Equal(LengthOfLine(AB),x)",
"Equal(LengthOfLine(AD),8)",
"Equal(LengthOfLine(BD),z)",
"Equal(LengthOfLine(CB),y)",
"Equal(LengthOfLine(CD),3)",
"PerpendicularBetweenLine(AD,BD)",
"PerpendicularBetweenLine(CB,AB)"
] | [
"Equal(LengthOfLine(AB),x)",
"Equal(LengthOfLine(AD),8)",
"Equal(LengthOfLine(BD),z)",
"Equal(LengthOfLine(CB),y)",
"Equal(LengthOfLine(CD),3)",
"PerpendicularBetweenLine(AD,BD)",
"PerpendicularBetweenLine(CB,AB)"
] | Value(x) | 2*sqrt(22) | [
"adjacent_complementary_angle(1,ADB,BDC)",
"mirror_similar_triangle_judgment_aa(1,BDC,ACB)",
"line_addition(1,CD,DA)",
"right_triangle_judgment_angle(1,CBA)",
"right_triangle_property_pythagorean(1,CBA)",
"mirror_similar_triangle_property_line_ratio(1,BDC,ACB)",
"mirror_similar_triangle_property_line_ra... | {"START": ["adjacent_complementary_angle(1,ADB,BDC)", "line_addition(1,CD,DA)", "right_triangle_judgment_angle(1,CBA)"], "adjacent_complementary_angle(1,ADB,BDC)": ["mirror_similar_triangle_judgment_aa(1,BDC,ACB)"], "mirror_similar_triangle_judgment_aa(1,BDC,ACB)": ["mirror_similar_triangle_property_line_ratio(1,BDC,AC... | |
976 | XiaokaiZhang_2023-04-09 | Geometry3k-1005 | 1 | 如图所示，∠QRS=x°，∠RST=2*x+7°，∠STQ=x°，∠TQR=2*x+5°。求∠RST的大小。 | As shown in the diagram, ∠QRS=x°, ∠RST=2*x+7°, ∠STQ=x°, ∠TQR=2*x+5°. Find the measure of ∠RST. | 976.png | [
"Shape(QR,RS,ST,TQ)"
] | [
"Equal(MeasureOfAngle(QRS),x)",
"Equal(MeasureOfAngle(RST),2*x+7)",
"Equal(MeasureOfAngle(STQ),x)",
"Equal(MeasureOfAngle(TQR),2*x+5)"
] | [
"Equal(MeasureOfAngle(QRS),x)",
"Equal(MeasureOfAngle(RST),2*x+7)",
"Equal(MeasureOfAngle(STQ),x)",
"Equal(MeasureOfAngle(TQR),2*x+5)"
] | Value(MeasureOfAngle(RST)) | 123 | [
"quadrilateral_property_angle_sum(1,QRST)"
] | {"START": ["quadrilateral_property_angle_sum(1,QRST)"]} | |
977 | NaZhu_2023-03-19 | Geometry3k-1006 | 2 | 如图所示，AB=24，AC=3*x-1，BD=18，CD=2*x+1，∠BAD=∠DAC。求x的值。 | As shown in the diagram, AB=24, AC=3*x-1, BD=18, CD=2*x+1, ∠BAD=∠DAC. Find the value of x. | 977.png | [
"Shape(BA,AD,DB)",
"Shape(AC,CD,DA)",
"Collinear(BDC)"
] | [
"Equal(LengthOfLine(AB),24)",
"Equal(LengthOfLine(AC),3*x-1)",
"Equal(LengthOfLine(BD),18)",
"Equal(LengthOfLine(CD),2*x+1)",
"Equal(MeasureOfAngle(BAD),MeasureOfAngle(DAC))"
] | [
"Equal(LengthOfLine(AB),24)",
"Equal(LengthOfLine(AC),3*x-1)",
"Equal(LengthOfLine(BD),18)",
"Equal(LengthOfLine(CD),2*x+1)",
"Equal(MeasureOfAngle(BAD),MeasureOfAngle(DAC))"
] | Value(x) | 7 | [
"bisector_of_angle_judgment_angle_equal(1,AD,BAC)",
"bisector_of_angle_property_line_ratio(1,AD,BAC)"
] | {"START": ["bisector_of_angle_judgment_angle_equal(1,AD,BAC)"], "bisector_of_angle_judgment_angle_equal(1,AD,BAC)": ["bisector_of_angle_property_line_ratio(1,AD,BAC)"]} | |
978 | XiaokaiZhang_2023-04-09 | Geometry3k-1007 | 1 | 如图所示，∠ABC=64°，AD∥BC。求∠DAB的大小。 | As shown in the diagram, ∠ABC=64°, AD∥BC. Find the measure of ∠DAB. | 978.png | [
"Shape(AB,BC,CD,DA)"
] | [
"Equal(MeasureOfAngle(ABC),64)",
"ParallelBetweenLine(AD,BC)"
] | [
"ParallelBetweenLine(AD,BC)"
] | Value(MeasureOfAngle(DAB)) | 116 | [
"parallel_property_ipsilateral_internal_angle(1,AD,BC)"
] | {"START": ["parallel_property_ipsilateral_internal_angle(1,AD,BC)"]} | |
979 | NaZhu_2023-03-19 | Geometry3k-1008 | 8 | 如图所示，AD=12，BD=3，∠BCA=90°，AD垂直于CD。求直线AC的长度。 | As shown in the diagram, AD=12, BD=3, ∠BCA=90°, AD⊥CD. Find the length of line AC. | 979.png | [
"Shape(CA,AD,DC)",
"Shape(CD,DB,BC)",
"Collinear(ADB)"
] | [
"Equal(LengthOfLine(AD),12)",
"Equal(LengthOfLine(BD),3)",
"Equal(MeasureOfAngle(BCA),90)",
"PerpendicularBetweenLine(AD,CD)"
] | [
"Equal(LengthOfLine(AD),12)",
"Equal(LengthOfLine(BD),3)",
"PerpendicularBetweenLine(AD,CD)"
] | Value(LengthOfLine(AC)) | 6*sqrt(5) | [
"adjacent_complementary_angle(1,ADC,CDB)",
"line_addition(1,AD,DB)",
"mirror_similar_triangle_judgment_aa(1,ABC,CDB)",
"right_triangle_judgment_angle(1,ADC)",
"right_triangle_property_pythagorean(1,ADC)",
"mirror_similar_triangle_property_line_ratio(1,ABC,CDB)",
"mirror_similar_triangle_property_line_ra... | {"START": ["adjacent_complementary_angle(1,ADC,CDB)", "line_addition(1,AD,DB)", "right_triangle_judgment_angle(1,ADC)"], "adjacent_complementary_angle(1,ADC,CDB)": ["mirror_similar_triangle_judgment_aa(1,ABC,CDB)"], "mirror_similar_triangle_judgment_aa(1,ABC,CDB)": ["mirror_similar_triangle_property_line_ratio(1,ABC,CD... | |
980 | XiaokaiZhang_2023-04-09 | Geometry3k-1009 | 2 | 如图所示，XY=2，⊙W的半径为4，⊙Z的半径为7，圆W的圆心为W，Z是圆Z的圆心。求直线YZ的长度。 | As shown in the diagram, XY=2, the radius of circle W is 4, the radius of ⊙Z is 7, the center of circle W is W, the center of ⊙Z is Z. Find the length of line YZ. | 980.png | [
"Shape(WI,WIB,ZXB,XW)",
"Shape(IW,WX,ZAX,WAI)",
"Shape(ZAX,XY,WYA)",
"Shape(YX,ZXB,WBY)",
"Shape(YZ,ZC,ZCA,WAY)",
"Shape(ZY,WYB,ZBC,CZ)",
"Collinear(IWXYZC)",
"Cocircular(W,IBYA)",
"Cocircular(Z,AXBC)"
] | [
"Equal(LengthOfLine(XY),2)",
"Equal(RadiusOfCircle(W),4)",
"Equal(RadiusOfCircle(Z),7)",
"IsCentreOfCircle(W,W)",
"IsCentreOfCircle(Z,Z)"
] | [
"Equal(LengthOfLine(XY),2)",
"Equal(RadiusOfCircle(W),4)",
"Equal(RadiusOfCircle(Z),7)",
"IsCentreOfCircle(W,W)",
"IsCentreOfCircle(Z,Z)"
] | Value(LengthOfLine(YZ)) | 5 | [
"radius_of_circle_property_length_equal(1,ZX,Z)",
"line_addition(1,XY,YZ)"
] | {"START": ["radius_of_circle_property_length_equal(1,ZX,Z)", "line_addition(1,XY,YZ)"]} | |
981 | NaZhu_2023-03-19 | Geometry3k-1010 | 4 | 如图所示，AC=20，DB=2*x+1，FB=2*x-1，FC=12，∠ACF=22°，∠FBD=22°，CF⊥DF。求直线DB的长度。 | As shown in the diagram, AC=20, DB=2*x+1, FB=2*x-1, FC=12, ∠ACF=22°, ∠FBD=22°, CF⊥DF. Find the length of line DB. | 981.png | [
"Shape(AC,CF,FA)",
"Shape(DF,FB,BD)",
"Collinear(ADF)",
"Collinear(CFB)"
] | [
"Equal(LengthOfLine(AC),20)",
"Equal(LengthOfLine(DB),2*x+1)",
"Equal(LengthOfLine(FB),2*x-1)",
"Equal(LengthOfLine(FC),12)",
"Equal(MeasureOfAngle(ACF),22)",
"Equal(MeasureOfAngle(FBD),22)",
"PerpendicularBetweenLine(CF,DF)"
] | [
"Equal(LengthOfLine(AC),20)",
"Equal(LengthOfLine(DB),2*x+1)",
"Equal(LengthOfLine(FB),2*x-1)",
"Equal(LengthOfLine(FC),12)",
"Equal(MeasureOfAngle(ACF),22)",
"Equal(MeasureOfAngle(FBD),22)",
"PerpendicularBetweenLine(CF,DF)"
] | Value(LengthOfLine(DB)) | 5 | [
"adjacent_complementary_angle(1,CFA,AFB)",
"mirror_similar_triangle_judgment_aa(1,ACF,DFB)",
"mirror_similar_triangle_property_line_ratio(1,ACF,DFB)",
"mirror_similar_triangle_property_line_ratio(1,FAC,FBD)"
] | {"START": ["adjacent_complementary_angle(1,CFA,AFB)"], "adjacent_complementary_angle(1,CFA,AFB)": ["mirror_similar_triangle_judgment_aa(1,ACF,DFB)"], "mirror_similar_triangle_judgment_aa(1,ACF,DFB)": ["mirror_similar_triangle_property_line_ratio(1,ACF,DFB)", "mirror_similar_triangle_property_line_ratio(1,FAC,FBD)"]} | |
982 | NaZhu_2023-03-19 | Geometry3k-1011 | 2 | 如图所示，∠ACD=50°，∠CDA=70°，∠DBA=21°。求∠ADB的大小。 | As shown in the diagram, ∠ACD=50°, ∠CDA=70°, ∠DBA=21°. Find the measure of ∠ADB. | 982.png | [
"Shape(AC,CD,DA)",
"Shape(AD,DB,BA)",
"Collinear(CDB)"
] | [
"Equal(MeasureOfAngle(ACD),50)",
"Equal(MeasureOfAngle(CDA),70)",
"Equal(MeasureOfAngle(DBA),21)"
] | [
"Equal(MeasureOfAngle(ACD),50)",
"Equal(MeasureOfAngle(CDA),70)",
"Equal(MeasureOfAngle(DBA),21)"
] | Value(MeasureOfAngle(ADB)) | 110 | [
"flat_angle(1,CDB)",
"angle_addition(1,CDA,ADB)"
] | {"START": ["flat_angle(1,CDB)", "angle_addition(1,CDA,ADB)"]} | |
983 | XiaokaiZhang_2023-04-09 | Geometry3k-1012 | 1 | 如图所示，∠DCE=64°，BA∥CD。求∠ABC的大小。 | As shown in the diagram, ∠DCE=64°, BA is parallel to CD. Find the measure of ∠ABC. | 983.png | [
"Shape(AB,BC,CD,DA)",
"Shape(DC,CE)",
"Collinear(BCE)"
] | [
"Equal(MeasureOfAngle(DCE),64)",
"ParallelBetweenLine(BA,CD)"
] | [
"ParallelBetweenLine(BA,CD)"
] | Value(MeasureOfAngle(ABC)) | 64 | [
"parallel_property_corresponding_angle(2,BA,CD,E)"
] | {"START": ["parallel_property_corresponding_angle(2,BA,CD,E)"]} | |
984 | NaZhu_2023-03-19 | Geometry3k-1013 | 2 | 如图所示，RW=14，RZ=18，UZ=5，Z是三角形RST的重心。求直线SR的长度。 | As shown in the diagram, RW=14, RZ=18, UZ=5, the centroid of △RST is Z. Find the length of line SR. | 984.png | [
"Shape(RW,WZ,ZR)",
"Shape(RZ,ZU,UR)",
"Shape(WS,SZ,ZW)",
"Shape(UZ,ZT,TU)",
"Shape(ZS,SV,VZ)",
"Shape(ZV,VT,TZ)",
"Collinear(RWS)",
"Collinear(RUT)",
"Collinear(SVT)",
"Collinear(RZU)",
"Collinear(WZT)",
"Collinear(SZU)"
] | [
"Equal(LengthOfLine(RW),14)",
"Equal(LengthOfLine(RZ),18)",
"Equal(LengthOfLine(UZ),5)",
"IsCentroidOfTriangle(Z,RST)"
] | [
"Equal(LengthOfLine(RW),14)",
"Equal(LengthOfLine(RZ),18)",
"Equal(LengthOfLine(UZ),5)"
] | Value(LengthOfLine(SR)) | 28 | [
"centroid_of_triangle_property_intersection(1,Z,TRS,W)",
"line_addition(1,SW,WR)"
] | {"START": ["centroid_of_triangle_property_intersection(1,Z,TRS,W)", "line_addition(1,SW,WR)"]} | |
985 | NaZhu_2023-03-19 | Geometry3k-1014 | 2 | 如图所示，JH=10，KJ=x，∠JHK=45°，∠KJH=73°。求x的值。 | As shown in the diagram, JH=10, KJ=x, ∠JHK=45°, ∠KJH=73°. Find the value of x. | 985.png | [
"Shape(HK,KJ,JH)"
] | [
"Equal(LengthOfLine(JH),10)",
"Equal(LengthOfLine(KJ),x)",
"Equal(MeasureOfAngle(JHK),45)",
"Equal(MeasureOfAngle(KJH),73)"
] | [
"Equal(LengthOfLine(JH),10)",
"Equal(LengthOfLine(KJ),x)",
"Equal(MeasureOfAngle(JHK),45)",
"Equal(MeasureOfAngle(KJH),73)"
] | Value(x) | 5*sqrt(2)/sin(31*pi/90) | [
"triangle_property_angle_sum(1,HKJ)",
"sine_theorem(1,JHK)"
] | {"START": ["triangle_property_angle_sum(1,HKJ)", "sine_theorem(1,JHK)"]} | |
986 | NaZhu_2023-03-19 | Geometry3k-1016 | 0 | 如图所示，CB=CD，CD=10，CD=2*x+4，DB=x+2。求x的值。 | As shown in the diagram, CB=CD, CD=10, CD=2*x+4, DB=x+2. Find the value of x. | 986.png | [
"Shape(CB,BD,DC)"
] | [
"Equal(LengthOfLine(CB),LengthOfLine(CD))",
"Equal(LengthOfLine(CD),10)",
"Equal(LengthOfLine(CD),2*x+4)",
"Equal(LengthOfLine(DB),x+2)"
] | [
"Equal(LengthOfLine(CB),LengthOfLine(CD))",
"Equal(LengthOfLine(CD),10)",
"Equal(LengthOfLine(CD),2*x+4)",
"Equal(LengthOfLine(DB),x+2)"
] | Value(x) | 3 | [] | {"START": []} | |
987 | XiaokaiZhang_2023-04-09 | Geometry3k-1017 | 5 | 如图所示，∠JQR=131°，GT∥RQ，HR平行于TC。求∠BGT的大小。 | As shown in the diagram, ∠JQR=131°, GT∥RQ, HR is parallel to TC. Find the measure of ∠BGT. | 987.png | [
"Shape(JQ,QR)",
"Shape(QR,RH)",
"Shape(BG,GT)",
"Shape(GT,TC)",
"Shape(QT,TG,GR,RQ)",
"Collinear(JQTC)",
"Collinear(HRGB)"
] | [
"Equal(MeasureOfAngle(JQR),131)",
"ParallelBetweenLine(GT,RQ)",
"ParallelBetweenLine(HR,TC)"
] | [] | Value(MeasureOfAngle(BGT)) | 131 | [
"parallel_property_corresponding_angle(1,QR,TG,J)",
"parallel_property_collinear_extend(2,HR,TC,G)",
"parallel_property_collinear_extend(2,HG,TC,B)",
"adjacent_complementary_angle(1,QTG,GTC)",
"parallel_property_ipsilateral_internal_angle(1,GB,TC)"
] | {"START": ["parallel_property_corresponding_angle(1,QR,TG,J)", "parallel_property_collinear_extend(2,HR,TC,G)", "adjacent_complementary_angle(1,QTG,GTC)"], "parallel_property_collinear_extend(2,HG,TC,B)": ["parallel_property_ipsilateral_internal_angle(1,GB,TC)"], "parallel_property_collinear_extend(2,HR,TC,G)": ["paral... | |
988 | NaZhu_2023-03-19 | Geometry3k-1018 | 5 | 如图所示，∠ADB=9*y-2°，∠CEA=135°，∠DAE=5*y+5°，∠EDA=4*z+9°。求z的值。 | As shown in the diagram, ∠ADB=9*y-2°, ∠CEA=135°, ∠DAE=5*y+5°, ∠EDA=4*z+9°. Find the value of z. | 988.png | [
"Shape(AE,ED,DA)",
"Shape(CE,EA)",
"Shape(AD,DB)",
"Collinear(CEDB)"
] | [
"Equal(MeasureOfAngle(ADB),9*y-2)",
"Equal(MeasureOfAngle(CEA),135)",
"Equal(MeasureOfAngle(DAE),5*y+5)",
"Equal(MeasureOfAngle(EDA),4*z+9)"
] | [
"Equal(MeasureOfAngle(ADB),9*y-2)",
"Equal(MeasureOfAngle(CEA),135)",
"Equal(MeasureOfAngle(DAE),5*y+5)",
"Equal(MeasureOfAngle(EDA),4*z+9)"
] | Value(z) | 14 | [
"flat_angle(1,CED)",
"angle_addition(1,CEA,AED)",
"flat_angle(1,EDB)",
"angle_addition(1,EDA,ADB)",
"triangle_property_angle_sum(1,AED)"
] | {"START": ["flat_angle(1,CED)", "angle_addition(1,CEA,AED)", "flat_angle(1,EDB)", "angle_addition(1,EDA,ADB)", "triangle_property_angle_sum(1,AED)"]} | |
989 | NaZhu_2023-03-19 | Geometry3k-1019 | 6 | 如图所示，CB=5，CD=4，DB=3，AD⊥CD，BC垂直于AC。求三角形ABC的周长。 | As shown in the diagram, CB=5, CD=4, DB=3, AD is perpendicular to CD, BC is perpendicular to AC. Find the perimeter of triangle ABC. | 989.png | [
"Shape(CA,AD,DC)",
"Shape(CD,DB,BC)",
"Collinear(ADB)"
] | [
"Equal(LengthOfLine(CB),5)",
"Equal(LengthOfLine(CD),4)",
"Equal(LengthOfLine(DB),3)",
"PerpendicularBetweenLine(AD,CD)",
"PerpendicularBetweenLine(BC,AC)"
] | [
"Equal(LengthOfLine(CB),5)",
"Equal(LengthOfLine(CD),4)",
"Equal(LengthOfLine(DB),3)",
"PerpendicularBetweenLine(AD,CD)",
"PerpendicularBetweenLine(BC,AC)"
] | Value(PerimeterOfTriangle(ABC)) | 20 | [
"adjacent_complementary_angle(1,ADC,CDB)",
"mirror_similar_triangle_judgment_aa(1,CDB,ABC)",
"triangle_perimeter_formula(1,ABC)",
"mirror_similar_triangle_property_line_ratio(1,CDB,ABC)",
"mirror_similar_triangle_property_line_ratio(1,DBC,CAB)",
"mirror_similar_triangle_property_line_ratio(1,BCD,BCA)"
] | {"START": ["adjacent_complementary_angle(1,ADC,CDB)", "triangle_perimeter_formula(1,ABC)"], "adjacent_complementary_angle(1,ADC,CDB)": ["mirror_similar_triangle_judgment_aa(1,CDB,ABC)"], "mirror_similar_triangle_judgment_aa(1,CDB,ABC)": ["mirror_similar_triangle_property_line_ratio(1,CDB,ABC)", "mirror_similar_triangle... | |
990 | XiaokaiZhang_2023-04-09 | Geometry3k-1020 | 2 | 如图所示，AD=4，AE=2，BE=x，圆O的切线为AD。求x的值。 | As shown in the diagram, AD=4, AE=2, BE=x, AD is the tangent to ⊙C. Find the value of x. | 990.png | [
"Shape(CBD,CDE,EB)",
"Shape(CDE,DA,AE)",
"Shape(CEB,BE)",
"Collinear(BEA)",
"Cocircular(C,DEB)"
] | [
"Equal(LengthOfLine(AD),4)",
"Equal(LengthOfLine(AE),2)",
"Equal(LengthOfLine(BE),x)",
"IsTangentOfCircle(AD,C)"
] | [
"Equal(LengthOfLine(AD),4)",
"Equal(LengthOfLine(AE),2)",
"Equal(LengthOfLine(BE),x)"
] | Value(x) | 6 | [
"circle_property_circular_power_tangent_and_segment_line(1,AD,AEB,C)",
"line_addition(1,BE,EA)"
] | {"START": ["circle_property_circular_power_tangent_and_segment_line(1,AD,AEB,C)", "line_addition(1,BE,EA)"]} | |
991 | XiaokaiZhang_2023-04-09 | Geometry3k-1022 | 2 | 如图所示，∠SVT=75°，∠TVP=72°，V是圆V的圆心，RV垂直于SV。求弧VPS的角度。 | As shown in the diagram, ∠SVT=75°, ∠TVP=72°, V is the center of ⊙V, RV is perpendicular to SV. Find the measure of ⌒VPS. | 991.png | [
"Shape(VR,VRQ,QV)",
"Shape(VQ,VQP,PV)",
"Shape(VP,VPT,TV)",
"Shape(VT,VTS,SV)",
"Shape(VS,VSR,RV)",
"Collinear(QVS)",
"Cocircular(V,RQPTS)"
] | [
"Equal(MeasureOfAngle(SVT),75)",
"Equal(MeasureOfAngle(TVP),72)",
"IsCentreOfCircle(V,V)",
"PerpendicularBetweenLine(RV,SV)"
] | [
"Equal(MeasureOfAngle(SVT),75)",
"Equal(MeasureOfAngle(TVP),72)",
"IsCentreOfCircle(V,V)",
"PerpendicularBetweenLine(RV,SV)"
] | Value(MeasureOfArc(VPS)) | 147 | [
"angle_addition(1,SVT,TVP)",
"arc_property_center_angle(1,VPS,V)"
] | {"START": ["angle_addition(1,SVT,TVP)", "arc_property_center_angle(1,VPS,V)"]} | |
992 | XiaokaiZhang_2023-04-09 | Geometry3k-1023 | 1 | 如图所示，∠ABF=6*x+12°，∠FDA=4*x+8°，ABCD是长方形。求x的值。 | As shown in the diagram, ∠ABF=6*x+12°, ∠FDA=4*x+8°, quadrilateral ABCD is a rectangle. Find the value of x. | 992.png | [
"Shape(AB,BF,FA)",
"Shape(FB,BC,CF)",
"Shape(FC,CD,DF)",
"Shape(AF,FD,DA)",
"Collinear(AFC)",
"Collinear(BFD)"
] | [
"Equal(MeasureOfAngle(ABF),6*x+12)",
"Equal(MeasureOfAngle(FDA),4*x+8)",
"Rectangle(ABCD)"
] | [
"Equal(MeasureOfAngle(ABF),6*x+12)",
"Equal(MeasureOfAngle(FDA),4*x+8)"
] | Value(x) | 7 | [
"triangle_property_angle_sum(1,DAB)"
] | {"START": ["triangle_property_angle_sum(1,DAB)"]} | |
993 | XiaokaiZhang_2023-04-09 | Geometry3k-1024 | 2 | 如图所示，BC=x，BD=7，DE=13，圆O的切线为DE。求x的值。 | As shown in the diagram, BC=x, BD=7, DE=13, DE is the tangent to ⊙A. Find the value of x. | 993.png | [
"Shape(BD,DE,ABE)",
"Shape(ABE,AEC,CB)",
"Shape(ACB,BC)",
"Collinear(DBC)",
"Cocircular(A,BEC)"
] | [
"Equal(LengthOfLine(BC),x)",
"Equal(LengthOfLine(BD),7)",
"Equal(LengthOfLine(DE),13)",
"IsTangentOfCircle(DE,A)"
] | [
"Equal(LengthOfLine(BC),x)",
"Equal(LengthOfLine(BD),7)",
"Equal(LengthOfLine(DE),13)"
] | Value(x) | 120/7 | [
"circle_property_circular_power_tangent_and_segment_line(1,DE,DBC,A)",
"line_addition(1,DB,BC)"
] | {"START": ["circle_property_circular_power_tangent_and_segment_line(1,DE,DBC,A)", "line_addition(1,DB,BC)"]} | |
994 | NaZhu_2023-03-19 | Geometry3k-1025 | 0 | 如图所示，RQ=4*x，RS=2*x+1，SQ=6*x-1，三角形RQS为等边三角形。求直线RQ的长度。 | As shown in the diagram, RQ=4*x, RS=2*x+1, SQ=6*x-1, triangle RQS is an equilateral triangle. Find the length of line RQ. | 994.png | [
"Shape(RQ,QS,SR)"
] | [
"Equal(LengthOfLine(RQ),4*x)",
"Equal(LengthOfLine(RS),2*x+1)",
"Equal(LengthOfLine(SQ),6*x-1)",
"EquilateralTriangle(RQS)"
] | [
"Equal(LengthOfLine(RQ),4*x)",
"Equal(LengthOfLine(RS),2*x+1)",
"Equal(LengthOfLine(SQ),6*x-1)"
] | Value(LengthOfLine(RQ)) | 2 | [] | {"START": []} | |
995 | XiaokaiZhang_2023-04-09 | Geometry3k-1026 | 4 | 如图所示，BN=EN，CB=BN，CN=2*sqrt(2)，EN=CE，CB垂直于NB，NE垂直于CE。求CBNE的面积。 | As shown in the diagram, BN=EN, CB=BN, CN=2*sqrt(2), EN=CE, CB is perpendicular to NB, NE⊥CE. Find the area of CBNE. | 995.png | [
"Shape(CB,BN,NC)",
"Shape(CN,NE,EC)"
] | [
"Equal(LengthOfLine(BN),LengthOfLine(EN))",
"Equal(LengthOfLine(CB),LengthOfLine(BN))",
"Equal(LengthOfLine(CN),2*sqrt(2))",
"Equal(LengthOfLine(EN),LengthOfLine(CE))",
"PerpendicularBetweenLine(CB,NB)",
"PerpendicularBetweenLine(NE,CE)"
] | [
"Equal(LengthOfLine(BN),LengthOfLine(EN))",
"Equal(LengthOfLine(CB),LengthOfLine(BN))",
"Equal(LengthOfLine(CN),2*sqrt(2))",
"Equal(LengthOfLine(EN),LengthOfLine(CE))",
"PerpendicularBetweenLine(CB,NB)",
"PerpendicularBetweenLine(NE,CE)"
] | Value(AreaOfQuadrilateral(CBNE)) | 4 | [
"right_triangle_judgment_angle(1,CBN)",
"right_triangle_property_pythagorean(1,CBN)",
"parallelogram_judgment_equal_and_equal(1,CBNE)",
"parallelogram_area_formula_sine(1,CBNE)"
] | {"START": ["right_triangle_judgment_angle(1,CBN)"], "parallelogram_judgment_equal_and_equal(1,CBNE)": ["parallelogram_area_formula_sine(1,CBNE)"], "right_triangle_judgment_angle(1,CBN)": ["right_triangle_property_pythagorean(1,CBN)"], "right_triangle_property_pythagorean(1,CBN)": ["parallelogram_judgment_equal_and_equa... | |
996 | XiaokaiZhang_2023-04-09 | Geometry3k-1027 | 2 | 如图所示，AN=5，N是圆N的圆心。求圆N的周长。 | As shown in the diagram, AN=5, the center of ⊙N is N. Find the circumference of the ⊙N. | 996.png | [
"Shape(NB,NBA,AN)",
"Shape(DN,NA,NAE,ED)",
"Shape(NED,DE)",
"Shape(ND,NDC,CN)",
"Shape(NC,CB,BN)",
"Shape(NCB,BC)",
"Collinear(AND)",
"Cocircular(N,AEDCB)"
] | [
"Equal(LengthOfLine(AN),5)",
"IsCentreOfCircle(N,N)"
] | [
"IsCentreOfCircle(N,N)"
] | Value(PerimeterOfCircle(N)) | 10*pi | [
"radius_of_circle_property_length_equal(1,NA,N)",
"circle_perimeter_formula(1,N)"
] | {"START": ["radius_of_circle_property_length_equal(1,NA,N)", "circle_perimeter_formula(1,N)"]} | |
997 | NaZhu_2023-03-19 | Geometry3k-1028 | 0 | 如图所示，RS=3*x+2，RS=RT，TR=2*x+4。求直线RS的长度。 | As shown in the diagram, RS=3*x+2, RS=RT, TR=2*x+4. Find the length of line RS. | 997.png | [
"Shape(RT,TS,SR)"
] | [
"Equal(LengthOfLine(RS),3*x+2)",
"Equal(LengthOfLine(RS),LengthOfLine(RT))",
"Equal(LengthOfLine(TR),2*x+4)"
] | [
"Equal(LengthOfLine(RS),3*x+2)",
"Equal(LengthOfLine(RS),LengthOfLine(RT))",
"Equal(LengthOfLine(TR),2*x+4)"
] | Value(LengthOfLine(RS)) | 8 | [] | {"START": []} | |
998 | NaZhu_2023-03-19 | Geometry3k-1029 | 2 | 如图所示，AC=x，BC=4，∠ACB=73°，∠CBA=29°。求x的值。 | As shown in the diagram, AC=x, BC=4, ∠ACB=73°, ∠CBA=29°. Find the value of x. | 998.png | [
"Shape(BA,AC,CB)"
] | [
"Equal(LengthOfLine(AC),x)",
"Equal(LengthOfLine(BC),4)",
"Equal(MeasureOfAngle(ACB),73)",
"Equal(MeasureOfAngle(CBA),29)"
] | [
"Equal(LengthOfLine(AC),x)",
"Equal(LengthOfLine(BC),4)",
"Equal(MeasureOfAngle(ACB),73)",
"Equal(MeasureOfAngle(CBA),29)"
] | Value(x) | 32*sqrt(2)*sin(29*pi/180)/(-sqrt(2)+sqrt(10)+2*sqrt(3)*sqrt(sqrt(5)+5)) | [
"triangle_property_angle_sum(1,BAC)",
"sine_theorem(1,CBA)"
] | {"START": ["triangle_property_angle_sum(1,BAC)", "sine_theorem(1,CBA)"]} | |
999 | XiaokaiZhang_2023-04-09 | Geometry3k-1030 | 2 | 如图所示，∠ZYX=120°，四边形YXWZ是风筝形，XW垂直于ZW。求∠WZY的大小。 | As shown in the diagram, ∠ZYX=120°, quadrilateral YXWZ is a kite, XW⊥ZW. Find the measure of ∠WZY. | 999.png | [
"Shape(YX,XW,WZ,ZY)"
] | [
"Equal(MeasureOfAngle(ZYX),120)",
"Kite(YXWZ)",
"PerpendicularBetweenLine(XW,ZW)"
] | [
"Equal(MeasureOfAngle(ZYX),120)",
"PerpendicularBetweenLine(XW,ZW)"
] | Value(MeasureOfAngle(WZY)) | 75 | [
"kite_property_opposite_angle_equal(1,YXWZ)",
"quadrilateral_property_angle_sum(1,YXWZ)"
] | {"START": ["kite_property_opposite_angle_equal(1,YXWZ)", "quadrilateral_property_angle_sum(1,YXWZ)"]} | |
1,000 | XiaokaiZhang_2023-04-09 | Geometry3k-1031 | 2 | 如图所示，AD=BA，CD=BC，∠ADC=85°，∠BAD=120°，CD和CB是风筝形ADCB的一组临边。求∠DCB的大小。 | As shown in the diagram, AD=BA, CD=BC, ∠ADC=85°, ∠BAD=120°, quadrilateral ADCB is a kite. Find the measure of ∠DCB. | 1000.png | [
"Shape(AD,DC,CB,BA)"
] | [
"Equal(LengthOfLine(AD),LengthOfLine(BA))",
"Equal(LengthOfLine(CD),LengthOfLine(BC))",
"Equal(MeasureOfAngle(ADC),85)",
"Equal(MeasureOfAngle(BAD),120)",
"Kite(ADCB)"
] | [
"Equal(LengthOfLine(AD),LengthOfLine(BA))",
"Equal(LengthOfLine(CD),LengthOfLine(BC))",
"Equal(MeasureOfAngle(ADC),85)",
"Equal(MeasureOfAngle(BAD),120)"
] | Value(MeasureOfAngle(DCB)) | 70 | [
"kite_property_opposite_angle_equal(1,ADCB)",
"quadrilateral_property_angle_sum(1,ADCB)"
] | {"START": ["kite_property_opposite_angle_equal(1,ADCB)", "quadrilateral_property_angle_sum(1,ADCB)"]} |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.