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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
601 | JiaZou_2023-03-12 | Geometry3k-616 | 0 | 如图所示，BD=4*x+9，CD=7*x-6，∠CDA=2*y-6°，AD是△ACB的高。求y的值。 | As shown in the diagram, BD=4*x+9, CD=7*x-6, ∠CDA=2*y-6°, AD is the altitude of triangle ACB. Find the value of y. | 601.png | [
"Shape(BA,AD,DB)",
"Shape(DA,AC,CD)",
"Collinear(BDC)"
] | [
"Equal(LengthOfLine(BD),4*x+9)",
"Equal(LengthOfLine(CD),7*x-6)",
"Equal(MeasureOfAngle(CDA),2*y-6)",
"IsAltitudeOfTriangle(AD,ACB)"
] | [
"Equal(LengthOfLine(BD),4*x+9)",
"Equal(LengthOfLine(CD),7*x-6)",
"Equal(MeasureOfAngle(CDA),2*y-6)"
] | Value(y) | 48 | [] | {"START": []} | |
602 | JiaZou_2023-03-12 | Geometry3k-618 | 6 | 如图所示，AB=6，AE=9，BC=4，CD∥BE。求直线ED的长度。 | As shown in the diagram, AB=6, AE=9, BC=4, CD∥BE. Find the length of line ED. | 602.png | [
"Shape(AE,EB,BA)",
"Shape(BE,ED,DC,CB)",
"Collinear(ABC)",
"Collinear(AED)"
] | [
"Equal(LengthOfLine(AB),6)",
"Equal(LengthOfLine(AE),9)",
"Equal(LengthOfLine(BC),4)",
"ParallelBetweenLine(CD,BE)"
] | [
"Equal(LengthOfLine(AB),6)",
"Equal(LengthOfLine(AE),9)",
"Equal(LengthOfLine(BC),4)",
"ParallelBetweenLine(CD,BE)"
] | Value(LengthOfLine(ED)) | 6 | [
"parallel_property_corresponding_angle(1,EB,DC,A)",
"similar_triangle_judgment_aa(1,BAE,CAD)",
"line_addition(1,AE,ED)",
"line_addition(1,AB,BC)",
"similar_triangle_property_line_ratio(1,BAE,CAD)",
"similar_triangle_property_line_ratio(1,EBA,DCA)"
] | {"START": ["parallel_property_corresponding_angle(1,EB,DC,A)", "line_addition(1,AE,ED)", "line_addition(1,AB,BC)"], "parallel_property_corresponding_angle(1,EB,DC,A)": ["similar_triangle_judgment_aa(1,BAE,CAD)"], "similar_triangle_judgment_aa(1,BAE,CAD)": ["similar_triangle_property_line_ratio(1,BAE,CAD)", "similar_tri... | |
603 | JiaZou_2023-03-12 | Geometry3k-619 | 2 | 如图所示，AB=72，AC=78，BC=x，AB⊥CB。求x的值。 | As shown in the diagram, AB=72, AC=78, BC=x, AB⊥CB. Find the value of x. | 603.png | [
"Shape(AB,BC,CA)"
] | [
"Equal(LengthOfLine(AB),72)",
"Equal(LengthOfLine(AC),78)",
"Equal(LengthOfLine(BC),x)",
"PerpendicularBetweenLine(AB,CB)"
] | [
"Equal(LengthOfLine(AB),72)",
"Equal(LengthOfLine(AC),78)",
"Equal(LengthOfLine(BC),x)",
"PerpendicularBetweenLine(AB,CB)"
] | Value(x) | 30 | [
"right_triangle_judgment_angle(1,ABC)",
"right_triangle_property_pythagorean(1,ABC)"
] | {"START": ["right_triangle_judgment_angle(1,ABC)"], "right_triangle_judgment_angle(1,ABC)": ["right_triangle_property_pythagorean(1,ABC)"]} | |
604 | YimingHe_2023-04-09 | Geometry3k-621 | 3 | 如图所示，∠UEN=64°，IW平行于KA，JL平行于BN。求∠AUL的大小。 | As shown in the diagram, ∠UEN=64°, IW∥KA, JL∥BN. Find the measure of ∠AUL. | 604.png | [
"Shape(JD,DW)",
"Shape(WD,DU)",
"Shape(DU,UA)",
"Shape(AU,UL)",
"Shape(HD,DJ)",
"Shape(BH,HD)",
"Shape(IH,HB)",
"Shape(DH,HE,EU,UD)",
"Shape(EH,HI)",
"Shape(KE,EH)",
"Shape(LU,UE)",
"Shape(UE,EN)",
"Shape(NE,EK)",
"Collinear(WDHI)",
"Collinear(AUEK)",
"Collinear(JDUL)",
"Collinear(BH... | [
"Equal(MeasureOfAngle(UEN),64)",
"ParallelBetweenLine(IW,KA)",
"ParallelBetweenLine(JL,BN)"
] | [
"ParallelBetweenLine(IW,KA)",
"ParallelBetweenLine(JL,BN)"
] | Value(MeasureOfAngle(AUL)) | 64 | [
"parallel_property_collinear_extend(3,JL,BN,U)",
"parallel_property_collinear_extend(3,NB,LU,E)",
"parallel_property_corresponding_angle(1,UL,EN,A)"
] | {"START": ["parallel_property_collinear_extend(3,JL,BN,U)"], "parallel_property_collinear_extend(3,JL,BN,U)": ["parallel_property_collinear_extend(3,NB,LU,E)"], "parallel_property_collinear_extend(3,NB,LU,E)": ["parallel_property_corresponding_angle(1,UL,EN,A)"]} | |
605 | YimingHe_2023-04-09 | Geometry3k-622 | 5 | 如图所示，R是圆R的圆心，RS垂直于XS，WZYX是正方形。求∠XRY的大小。 | As shown in the diagram, R is the center of ⊙R, RS⊥XS, quadrilateral WZYX is a square. Find the measure of ∠XRY. | 605.png | [
"Shape(WZ,ZY,YR,RW)",
"Shape(WR,RX,XW)",
"Shape(XR,RS,SX)",
"Shape(SR,RY,YS)",
"Shape(WX,RXW)",
"Shape(RWZ,ZW)",
"Shape(RZY,YZ)",
"Shape(RYX,XY)",
"Collinear(XSY)",
"Collinear(YRW)",
"Cocircular(R,WZYX)"
] | [
"IsCentreOfCircle(R,R)",
"PerpendicularBetweenLine(RS,XS)",
"Square(WZYX)"
] | [
"IsCentreOfCircle(R,R)",
"PerpendicularBetweenLine(RS,XS)"
] | Value(MeasureOfAngle(XRY)) | 90 | [
"isosceles_triangle_judgment_line_equal(1,XWY)",
"isosceles_triangle_property_angle_equal(1,XWY)",
"triangle_property_angle_sum(1,XWY)",
"arc_property_circumference_angle_external(1,RYX,W)",
"arc_property_center_angle(1,RYX,R)"
] | {"START": ["isosceles_triangle_judgment_line_equal(1,XWY)", "triangle_property_angle_sum(1,XWY)", "arc_property_circumference_angle_external(1,RYX,W)", "arc_property_center_angle(1,RYX,R)"], "isosceles_triangle_judgment_line_equal(1,XWY)": ["isosceles_triangle_property_angle_equal(1,XWY)"]} | |
606 | JiaZou_2023-03-12 | Geometry3k-623 | 1 | 如图所示，BA=2*x+4，BC=4*x-8，CA=3*x-1，三角形ABC为等腰三角形。求三角形ABC的周长。 | As shown in the diagram, BA=2*x+4, BC=4*x-8, CA=3*x-1, △ABC is an isosceles △. Find the perimeter of triangle ABC. | 606.png | [
"Shape(AB,BC,CA)"
] | [
"Equal(LengthOfLine(BA),2*x+4)",
"Equal(LengthOfLine(BC),4*x-8)",
"Equal(LengthOfLine(CA),3*x-1)",
"IsoscelesTriangle(ABC)"
] | [
"Equal(LengthOfLine(BA),2*x+4)",
"Equal(LengthOfLine(BC),4*x-8)",
"Equal(LengthOfLine(CA),3*x-1)"
] | Value(PerimeterOfTriangle(ABC)) | 40 | [
"triangle_perimeter_formula(1,ABC)"
] | {"START": ["triangle_perimeter_formula(1,ABC)"]} | |
607 | YimingHe_2023-04-09 | Geometry3k-624 | 2 | 如图所示，∠BAD=58°，∠CBE=26°，∠EBA=47°，AB∥EC。求∠ECB的大小。 | As shown in the diagram, ∠BAD=58°, ∠CBE=26°, ∠EBA=47°, AB∥EC. Find the measure of ∠ECB. | 607.png | [
"Shape(AE,EB,BA)",
"Shape(BE,EC,CB)",
"Shape(CE,ED,DC)",
"Collinear(AED)",
"Collinear(BCD)"
] | [
"Equal(MeasureOfAngle(BAD),58)",
"Equal(MeasureOfAngle(CBE),26)",
"Equal(MeasureOfAngle(EBA),47)",
"ParallelBetweenLine(AB,EC)"
] | [
"Equal(MeasureOfAngle(BAD),58)",
"Equal(MeasureOfAngle(CBE),26)",
"Equal(MeasureOfAngle(EBA),47)",
"ParallelBetweenLine(AB,EC)"
] | Value(MeasureOfAngle(ECB)) | 107 | [
"angle_addition(1,CBE,EBA)",
"parallel_property_ipsilateral_internal_angle(1,CE,BA)"
] | {"START": ["angle_addition(1,CBE,EBA)", "parallel_property_ipsilateral_internal_angle(1,CE,BA)"]} | |
608 | YimingHe_2023-04-09 | Geometry3k-625 | 6 | 如图所示，RT=11，∠RPS=130°，∠TPQ=112°，圆P的圆心为P，⊙P的直径为RT。求⌒PQR的长度。 | As shown in the diagram, RT=11, ∠RPS=130°, ∠TPQ=112°, P is the center of circle P, the diameter of ⊙P is RT. Find the length of ⌒PQR. | 608.png | [
"Shape(QP,PR,PRQ)",
"Shape(TP,PQ,PQT)",
"Shape(SP,PT,PTS)",
"Shape(RP,PS,PSR)",
"Collinear(RPT)",
"Cocircular(P,RQTS)"
] | [
"Equal(LengthOfLine(RT),11)",
"Equal(MeasureOfAngle(RPS),130)",
"Equal(MeasureOfAngle(TPQ),112)",
"IsCentreOfCircle(P,P)",
"IsDiameterOfCircle(RT,P)"
] | [
"Equal(LengthOfLine(RT),11)",
"Equal(MeasureOfAngle(RPS),130)",
"Equal(MeasureOfAngle(TPQ),112)",
"IsCentreOfCircle(P,P)",
"IsDiameterOfCircle(RT,P)"
] | Value(LengthOfArc(PQR)) | 803*pi/90 | [
"flat_angle(1,RPT)",
"angle_addition(1,RPT,TPQ)",
"arc_length_formula(1,PQR)",
"arc_property_center_angle(1,PQR,P)",
"diameter_of_circle_property_length_equal(1,RT,P)",
"circle_property_length_of_radius_and_diameter(1,P)"
] | {"START": ["flat_angle(1,RPT)", "angle_addition(1,RPT,TPQ)", "arc_length_formula(1,PQR)", "arc_property_center_angle(1,PQR,P)", "diameter_of_circle_property_length_equal(1,RT,P)", "circle_property_length_of_radius_and_diameter(1,P)"]} | |
609 | JiaZou_2023-03-12 | Geometry3k-626 | 4 | 如图所示，JK=8，JS=10，∠SLK=25°，∠SPM=28°，三角形JPL的内切圆圆心为S，PM⊥SM，SK垂直于JK，SQ垂直于PQ。求∠SJP的大小。 | As shown in the diagram, JK=8, JS=10, ∠SLK=25°, ∠SPM=28°, S is the incenter of triangle JPL, PM is perpendicular to SM, SK⊥JK, SQ⊥PQ. Find the measure of ∠SJP. | 609.png | [
"Shape(JQ,QS,SJ)",
"Shape(QP,PS,SQ)",
"Shape(PM,MS,SP)",
"Shape(SM,ML,LS)",
"Shape(SL,LK,KS)",
"Shape(SK,KJ,JS)",
"Collinear(JQP)",
"Collinear(PML)",
"Collinear(LKJ)"
] | [
"Equal(LengthOfLine(JK),8)",
"Equal(LengthOfLine(JS),10)",
"Equal(MeasureOfAngle(SLK),25)",
"Equal(MeasureOfAngle(SPM),28)",
"IsIncenterOfTriangle(S,JPL)",
"PerpendicularBetweenLine(PM,SM)",
"PerpendicularBetweenLine(SK,JK)",
"PerpendicularBetweenLine(SQ,PQ)"
] | [
"Equal(LengthOfLine(JK),8)",
"Equal(LengthOfLine(JS),10)",
"Equal(MeasureOfAngle(SLK),25)",
"Equal(MeasureOfAngle(SPM),28)",
"PerpendicularBetweenLine(PM,SM)",
"PerpendicularBetweenLine(SK,JK)",
"PerpendicularBetweenLine(SQ,PQ)"
] | Value(MeasureOfAngle(SJP)) | 37 | [
"angle_addition(1,MLS,SLK)",
"angle_addition(1,KJS,SJQ)",
"angle_addition(1,QPS,SPM)",
"triangle_property_angle_sum(1,JPL)"
] | {"START": ["angle_addition(1,MLS,SLK)", "angle_addition(1,KJS,SJQ)", "angle_addition(1,QPS,SPM)", "triangle_property_angle_sum(1,JPL)"]} | |
610 | JiaZou_2023-03-12 | Geometry3k-627 | 1 | 如图所示，∠WZX=24°，∠XWZ=23°，∠YXZ=105°，∠ZYX=∠XZY。求∠ZXW的大小。 | As shown in the diagram, ∠WZX=24°, ∠XWZ=23°, ∠YXZ=105°, ∠ZYX=∠XZY. Find the measure of ∠ZXW. | 610.png | [
"Shape(WZ,ZX,XW)",
"Shape(XZ,ZY,YX)"
] | [
"Equal(MeasureOfAngle(WZX),24)",
"Equal(MeasureOfAngle(XWZ),23)",
"Equal(MeasureOfAngle(YXZ),105)",
"Equal(MeasureOfAngle(ZYX),MeasureOfAngle(XZY))"
] | [
"Equal(MeasureOfAngle(WZX),24)",
"Equal(MeasureOfAngle(XWZ),23)",
"Equal(MeasureOfAngle(YXZ),105)",
"Equal(MeasureOfAngle(ZYX),MeasureOfAngle(XZY))"
] | Value(MeasureOfAngle(ZXW)) | 133 | [
"triangle_property_angle_sum(1,WZX)"
] | {"START": ["triangle_property_angle_sum(1,WZX)"]} | |
611 | YimingHe_2023-04-09 | Geometry3k-628 | 3 | 如图所示，CD=22，圆A的半径为14，A是⊙A的圆心，AE⊥DE。求直线CE的长度。 | As shown in the diagram, CD=22, the radius of circle A is 14, the center of ⊙A is A, AE⊥DE. Find the length of line CE. | 611.png | [
"Shape(ADC,CE,ED)",
"Shape(EC,ACB,BE)",
"Shape(ABD,DE,EB)",
"Shape(AE,ED)",
"Shape(CE,EA)",
"Collinear(AEB)",
"Collinear(CED)",
"Cocircular(A,CBD)"
] | [
"Equal(LengthOfLine(CD),22)",
"Equal(RadiusOfCircle(A),14)",
"IsCentreOfCircle(A,A)",
"PerpendicularBetweenLine(AE,DE)"
] | [
"IsCentreOfCircle(A,A)",
"PerpendicularBetweenLine(AE,DE)"
] | Value(LengthOfLine(CE)) | 11 | [
"adjacent_complementary_angle(1,CEA,AED)",
"circle_property_chord_perpendicular_bisect_chord(1,A,AE,CD)",
"line_addition(1,CE,ED)"
] | {"START": ["adjacent_complementary_angle(1,CEA,AED)", "line_addition(1,CE,ED)"], "adjacent_complementary_angle(1,CEA,AED)": ["circle_property_chord_perpendicular_bisect_chord(1,A,AE,CD)"]} | |
612 | YimingHe_2023-04-09 | Geometry3k-629 | 5 | 如图所示，∠ABP=3*x-60°，∠MCL=2*x+15°，∠PBC=y°，OB∥NC，OP平行于NM。求∠BCM的大小。 | As shown in the diagram, ∠ABP=3*x-60°, ∠MCL=2*x+15°, ∠PBC=y°, OB∥NC, OP∥NM. Find the measure of ∠BCM. | 612.png | [
"Shape(OR,RA)",
"Shape(AR,RP)",
"Shape(CB,BO)",
"Shape(PB,BC)",
"Shape(NC,CB)",
"Shape(LC,CN)",
"Shape(BC,CM)",
"Shape(MC,CL)",
"Collinear(OBP)",
"Collinear(ABCL)",
"Collinear(NCM)"
] | [
"Equal(MeasureOfAngle(ABP),3*x-60)",
"Equal(MeasureOfAngle(MCL),2*x+15)",
"Equal(MeasureOfAngle(PBC),y)",
"ParallelBetweenLine(OB,NC)",
"ParallelBetweenLine(OP,NM)"
] | [
"Equal(MeasureOfAngle(ABP),3*x-60)",
"Equal(MeasureOfAngle(MCL),2*x+15)",
"Equal(MeasureOfAngle(PBC),y)",
"ParallelBetweenLine(OB,NC)"
] | Value(MeasureOfAngle(BCM)) | 75 | [
"parallel_property_collinear_extend(2,OB,NC,P)",
"parallel_property_collinear_extend(1,CN,PB,M)",
"parallel_property_corresponding_angle(2,BP,CM,L)",
"adjacent_complementary_angle(1,ABP,PBC)",
"adjacent_complementary_angle(1,BCM,MCL)"
] | {"START": ["parallel_property_collinear_extend(2,OB,NC,P)", "adjacent_complementary_angle(1,ABP,PBC)", "adjacent_complementary_angle(1,BCM,MCL)"], "parallel_property_collinear_extend(1,CN,PB,M)": ["parallel_property_corresponding_angle(2,BP,CM,L)"], "parallel_property_collinear_extend(2,OB,NC,P)": ["parallel_property_c... | |
613 | JiaZou_2023-03-12 | Geometry3k-630 | 2 | 如图所示，AC=24，CB=x，∠ACB=86°，∠BAC=33°。求x的值。 | As shown in the diagram, AC=24, CB=x, ∠ACB=86°, ∠BAC=33°. Find the value of x. | 613.png | [
"Shape(AC,CB,BA)"
] | [
"Equal(LengthOfLine(AC),24)",
"Equal(LengthOfLine(CB),x)",
"Equal(MeasureOfAngle(ACB),86)",
"Equal(MeasureOfAngle(BAC),33)"
] | [
"Equal(LengthOfLine(AC),24)",
"Equal(LengthOfLine(CB),x)",
"Equal(MeasureOfAngle(ACB),86)",
"Equal(MeasureOfAngle(BAC),33)"
] | Value(x) | (-3*sqrt(5)*sqrt(5-sqrt(5))-3*sqrt(6)-3*sqrt(5-sqrt(5))-3*sqrt(2)+3*sqrt(3)*sqrt(5-sqrt(5))+3*sqrt(10)+3*sqrt(30)+3*sqrt(15)*sqrt(5-sqrt(5)))/(2*sin(61*pi/180)) | [
"triangle_property_angle_sum(1,ACB)",
"sine_theorem(1,CBA)"
] | {"START": ["triangle_property_angle_sum(1,ACB)", "sine_theorem(1,CBA)"]} | |
614 | YimingHe_2023-04-09 | Geometry3k-631 | 2 | 如图所示，∠GCH=2*x°，∠HCD=6*x+28°，⊙C的圆心为C，FC垂直于GC。求弧CDH的角度。 | As shown in the diagram, ∠GCH=2*x°, ∠HCD=6*x+28°, C is the center of circle C, FC⊥GC. Find the measure of arc CDH. | 614.png | [
"Shape(GC,CH,CHG)",
"Shape(FC,CG,CGF)",
"Shape(EC,CF,CFE)",
"Shape(DC,CE,CED)",
"Shape(HC,CD,CDH)",
"Collinear(HCE)",
"Collinear(GCD)",
"Cocircular(C,HGFED)"
] | [
"Equal(MeasureOfAngle(GCH),2*x)",
"Equal(MeasureOfAngle(HCD),6*x+28)",
"IsCentreOfCircle(C,C)",
"PerpendicularBetweenLine(FC,GC)"
] | [
"IsCentreOfCircle(C,C)",
"PerpendicularBetweenLine(FC,GC)"
] | Value(MeasureOfArc(CDH)) | 142 | [
"adjacent_complementary_angle(1,GCH,HCD)",
"arc_property_center_angle(1,CDH,C)"
] | {"START": ["adjacent_complementary_angle(1,GCH,HCD)", "arc_property_center_angle(1,CDH,C)"]} | |
615 | JiaZou_2023-03-12 | Geometry3k-632 | 1 | 如图所示，AB=11，AC=x，BC=12，∠CBA=67°。求x的值。 | As shown in the diagram, AB=11, AC=x, BC=12, ∠CBA=67°. Find the value of x. | 615.png | [
"Shape(CB,BA,AC)"
] | [
"Equal(LengthOfLine(AB),11)",
"Equal(LengthOfLine(AC),x)",
"Equal(LengthOfLine(BC),12)",
"Equal(MeasureOfAngle(CBA),67)"
] | [
"Equal(LengthOfLine(AB),11)",
"Equal(LengthOfLine(AC),x)",
"Equal(LengthOfLine(BC),12)",
"Equal(MeasureOfAngle(CBA),67)"
] | Value(x) | sqrt(265-264*cos(67*pi/180)) | [
"cosine_theorem(1,BAC)"
] | {"START": ["cosine_theorem(1,BAC)"]} | |
616 | YimingHe_2023-04-09 | Geometry3k-633 | 1 | 如图所示，∠ADC=x+34°，∠BAD=82°，∠DCB=83°，∠PRS=3*y-13°，∠QPR=97°，∠RSQ=98°，四边形ADCB相似于四边形RSQP。求y的值。 | As shown in the diagram, ∠ADC=x+34°, ∠BAD=82°, ∠DCB=83°, ∠PRS=3*y-13°, ∠QPR=97°, ∠RSQ=98°, quadrilateral ADCB is similar to quadrilateral RSQP. Find the value of y. | 616.png | [
"Shape(AD,DC,CB,BA)",
"Shape(PR,RS,SQ,QP)"
] | [
"Equal(MeasureOfAngle(ADC),x+34)",
"Equal(MeasureOfAngle(BAD),82)",
"Equal(MeasureOfAngle(DCB),83)",
"Equal(MeasureOfAngle(PRS),3*y-13)",
"Equal(MeasureOfAngle(QPR),97)",
"Equal(MeasureOfAngle(RSQ),98)",
"SimilarBetweenQuadrilateral(ADCB,RSQP)"
] | [
"Equal(MeasureOfAngle(ADC),x+34)",
"Equal(MeasureOfAngle(BAD),82)",
"Equal(MeasureOfAngle(DCB),83)",
"Equal(MeasureOfAngle(PRS),3*y-13)",
"Equal(MeasureOfAngle(QPR),97)",
"Equal(MeasureOfAngle(RSQ),98)"
] | Value(y) | 95/3 | [
"similar_quadrilateral_property_angle_equal(1,ADCB,RSQP)"
] | {"START": ["similar_quadrilateral_property_angle_equal(1,ADCB,RSQP)"]} | |
617 | JiaZou_2023-03-12 | Geometry3k-634 | 0 | 如图所示，RS=x+9，RT=3*x-9，ST=2*x，△SRT为等边△。求直线RS的长度。 | As shown in the diagram, RS=x+9, RT=3*x-9, ST=2*x, triangle SRT is an equilateral triangle. Find the length of line RS. | 617.png | [
"Shape(SR,RT,TS)"
] | [
"Equal(LengthOfLine(RS),x+9)",
"Equal(LengthOfLine(RT),3*x-9)",
"Equal(LengthOfLine(ST),2*x)",
"EquilateralTriangle(SRT)"
] | [
"Equal(LengthOfLine(RS),x+9)",
"Equal(LengthOfLine(RT),3*x-9)",
"Equal(LengthOfLine(ST),2*x)"
] | Value(LengthOfLine(RS)) | 18 | [] | {"START": []} | |
618 | YimingHe_2023-04-09 | Geometry3k-635 | 0 | 如图所示，圆A的直径为10，圆B的直径为30，⊙C的直径为10，AZ=CW，CW=2。求直线AZ的长度。 | As shown in the diagram, the diameter of ⊙A is 10, the diameter of ⊙B is 30, the diameter of circle C is 10, AZ=CW, CW=2. Find the length of line AZ. | 618.png | [
"Shape(GA,AZ,BJZ,AJG)",
"Shape(ZA,AG,AGK,BZK)",
"Shape(AXJ,BJZ,ZX)",
"Shape(AKX,XZ,BZK)",
"Shape(XB,BY,CMY,BMJ,AXJ)",
"Shape(YB,BX,AKX,BKN,CYN)",
"Shape(CMY,YW,BWM)",
"Shape(BNW,WY,CYN)",
"Shape(WC,CF,CFM,BWM)",
"Shape(FC,CW,BNW,CNF)",
"Collinear(GAZXBYWCF)",
"Cocircular(A,JGKX)",
"Cocircula... | [
"Equal(DiameterOfCircle(A),10)",
"Equal(DiameterOfCircle(B),30)",
"Equal(DiameterOfCircle(C),10)",
"Equal(LengthOfLine(AZ),LengthOfLine(CW))",
"Equal(LengthOfLine(CW),2)"
] | [] | Value(LengthOfLine(AZ)) | 2 | [] | {"START": []} | |
619 | YimingHe_2023-04-09 | Geometry3k-636 | 3 | 如图所示，∠XZW=5*x-12°，∠YZX=3*x+6°，ZWXY是▱，ZW垂直于XW。求∠ZXY的大小。 | As shown in the diagram, ∠XZW=5*x-12°, ∠YZX=3*x+6°, ZY and WX are opposite sides of the parallelogram ZWXY, ZW is perpendicular to XW. Find the measure of ∠ZXY. | 619.png | [
"Shape(ZW,WP,PZ)",
"Shape(PW,WX,XP)",
"Shape(YP,PX,XY)",
"Shape(ZP,PY,YZ)",
"Collinear(ZPX)",
"Collinear(WPY)"
] | [
"Equal(MeasureOfAngle(XZW),5*x-12)",
"Equal(MeasureOfAngle(YZX),3*x+6)",
"Parallelogram(ZWXY)",
"PerpendicularBetweenLine(ZW,XW)"
] | [
"Parallelogram(ZWXY)",
"PerpendicularBetweenLine(ZW,XW)"
] | Value(MeasureOfAngle(ZXY)) | 48 | [
"parallel_property_ipsilateral_internal_angle(1,ZY,WX)",
"angle_addition(1,YZX,XZW)",
"parallel_property_alternate_interior_angle(2,YX,ZW)"
] | {"START": ["parallel_property_ipsilateral_internal_angle(1,ZY,WX)", "angle_addition(1,YZX,XZW)", "parallel_property_alternate_interior_angle(2,YX,ZW)"]} | |
620 | JiaZou_2023-03-12 | Geometry3k-637 | 0 | 如图所示，BA=9*x-1，CA=4*x+1，CA=BC，CB=5*x-1/2，三角形CBA为等腰三角形。求直线CB的长度。 | As shown in the diagram, BA=9*x-1, CA=4*x+1, CA=BC, CB=5*x-1/2, △CBA is an isosceles △. Find the length of line CB. | 620.png | [
"Shape(AC,CB,BA)"
] | [
"Equal(LengthOfLine(BA),9*x-1)",
"Equal(LengthOfLine(CA),4*x+1)",
"Equal(LengthOfLine(CA),LengthOfLine(BC))",
"Equal(LengthOfLine(CB),5*x-1/2)",
"IsoscelesTriangle(CBA)"
] | [
"Equal(LengthOfLine(BA),9*x-1)",
"Equal(LengthOfLine(CA),4*x+1)",
"Equal(LengthOfLine(CA),LengthOfLine(BC))",
"Equal(LengthOfLine(CB),5*x-1/2)"
] | Value(LengthOfLine(CB)) | 7 | [] | {"START": []} | |
621 | JiaZou_2023-03-12 | Geometry3k-638 | 2 | 如图所示，XY=7，ZX=14，ZY=x，XY垂直于ZY。求x的值。 | As shown in the diagram, XY=7, ZX=14, ZY=x, XY is perpendicular to ZY. Find the value of x. | 621.png | [
"Shape(XY,YZ,ZX)"
] | [
"Equal(LengthOfLine(XY),7)",
"Equal(LengthOfLine(ZX),14)",
"Equal(LengthOfLine(ZY),x)",
"PerpendicularBetweenLine(XY,ZY)"
] | [
"Equal(LengthOfLine(XY),7)",
"Equal(LengthOfLine(ZX),14)",
"Equal(LengthOfLine(ZY),x)",
"PerpendicularBetweenLine(XY,ZY)"
] | Value(x) | 7*sqrt(3) | [
"right_triangle_judgment_angle(1,XYZ)",
"right_triangle_property_pythagorean(1,XYZ)"
] | {"START": ["right_triangle_judgment_angle(1,XYZ)"], "right_triangle_judgment_angle(1,XYZ)": ["right_triangle_property_pythagorean(1,XYZ)"]} | |
622 | JiaZou_2023-03-12 | Geometry3k-639 | 0 | 如图所示，QR=5，QS=RS，RS=5*x+3，SQ=10*x-7，∠PSR=15*x+42°，PS是△PQR的中线。求x的值。 | As shown in the diagram, QR=5, QS=RS, RS=5*x+3, SQ=10*x-7, ∠PSR=15*x+42°, PS is the median of triangle PQR. Find the value of x. | 622.png | [
"Shape(PQ,QS,SP)",
"Shape(PS,SR,RP)",
"Collinear(QSR)"
] | [
"Equal(LengthOfLine(QR),5)",
"Equal(LengthOfLine(QS),LengthOfLine(RS))",
"Equal(LengthOfLine(RS),5*x+3)",
"Equal(LengthOfLine(SQ),10*x-7)",
"Equal(MeasureOfAngle(PSR),15*x+42)",
"IsMedianOfTriangle(PS,PQR)"
] | [
"Equal(LengthOfLine(QR),5)",
"Equal(LengthOfLine(QS),LengthOfLine(RS))",
"Equal(LengthOfLine(RS),5*x+3)",
"Equal(LengthOfLine(SQ),10*x-7)",
"Equal(MeasureOfAngle(PSR),15*x+42)"
] | Value(x) | 2 | [] | {"START": []} | |
623 | YimingHe_2023-04-09 | Geometry3k-640 | 6 | 如图所示，TW=13，ZV=1，T是圆T的圆心，TV垂直于XV。求直线XV的长度。 | As shown in the diagram, TW=13, ZV=1, the center of circle T is T, TV is perpendicular to XV. Find the length of line XV. | 623.png | [
"Shape(TZX,XV,VZ)",
"Shape(TYZ,ZV,VY)",
"Shape(TV,VX,XT)",
"Shape(WT,TX,TXW)",
"Shape(VT,TW,TWY,YV)",
"Collinear(ZVTW)",
"Collinear(XVY)",
"Cocircular(T,ZXWY)"
] | [
"Equal(LengthOfLine(TW),13)",
"Equal(LengthOfLine(ZV),1)",
"IsCentreOfCircle(T,T)",
"PerpendicularBetweenLine(TV,XV)"
] | [
"IsCentreOfCircle(T,T)",
"PerpendicularBetweenLine(TV,XV)"
] | Value(LengthOfLine(XV)) | 5 | [
"radius_of_circle_property_length_equal(1,TW,T)",
"radius_of_circle_property_length_equal(1,TX,T)",
"radius_of_circle_property_length_equal(1,TZ,T)",
"line_addition(1,ZV,VT)",
"right_triangle_judgment_angle(1,TVX)",
"right_triangle_property_pythagorean(1,TVX)"
] | {"START": ["radius_of_circle_property_length_equal(1,TW,T)", "radius_of_circle_property_length_equal(1,TX,T)", "radius_of_circle_property_length_equal(1,TZ,T)", "line_addition(1,ZV,VT)", "right_triangle_judgment_angle(1,TVX)"], "right_triangle_judgment_angle(1,TVX)": ["right_triangle_property_pythagorean(1,TVX)"]} | |
624 | JiaZou_2023-03-12 | Geometry3k-641 | 2 | 如图所示，∠CDB=20°，∠DBC=25°，∠ECB=x°。求x的值。 | As shown in the diagram, ∠CDB=20°, ∠DBC=25°, ∠ECB=x°. Find the value of x. | 624.png | [
"Shape(BE,EC,CB)",
"Shape(BC,CD,DB)",
"Collinear(ECD)"
] | [
"Equal(MeasureOfAngle(CDB),20)",
"Equal(MeasureOfAngle(DBC),25)",
"Equal(MeasureOfAngle(ECB),x)"
] | [
"Equal(MeasureOfAngle(CDB),20)",
"Equal(MeasureOfAngle(DBC),25)",
"Equal(MeasureOfAngle(ECB),x)"
] | Value(x) | 45 | [
"triangle_property_angle_sum(1,BCD)",
"adjacent_complementary_angle(1,ECB,BCD)"
] | {"START": ["triangle_property_angle_sum(1,BCD)", "adjacent_complementary_angle(1,ECB,BCD)"]} | |
625 | JiaZou_2023-03-12 | Geometry3k-642 | 7 | 如图所示，AB=x，AC=19，AD=15，BC=z，BD=y，CA垂直于BA，DB垂直于CB。求x的值。 | As shown in the diagram, AB=x, AC=19, AD=15, BC=z, BD=y, CA⊥BA, DB⊥CB. Find the value of x. | 625.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(x) | sqrt(285) | [
"adjacent_complementary_angle(1,CAB,BAD)",
"mirror_similar_triangle_judgment_aa(1,BAD,CDB)",
"mirror_similar_triangle_judgment_aa(1,BCA,DBC)",
"mirror_similar_triangle_property_line_ratio(1,BAD,CDB)",
"mirror_similar_triangle_property_line_ratio(1,DBA,DBC)",
"mirror_similar_triangle_property_line_ratio(1,... | {"START": ["adjacent_complementary_angle(1,CAB,BAD)", "mirror_similar_triangle_judgment_aa(1,BCA,DBC)"], "adjacent_complementary_angle(1,CAB,BAD)": ["mirror_similar_triangle_judgment_aa(1,BAD,CDB)"], "mirror_similar_triangle_judgment_aa(1,BAD,CDB)": ["mirror_similar_triangle_property_line_ratio(1,BAD,CDB)", "mirror_sim... | |
626 | YimingHe_2023-04-09 | Geometry3k-643 | 1 | 如图所示，四边形NMQP的面积为375，MP=25，MQPN是菱形。求直线NQ的长度。 | As shown in the diagram, the area of quadrilateral NMQP is 375, MP=25, MQPN is a rhombus. Find the length of line NQ. | 626.png | [
"Shape(MA,AN,NM)",
"Shape(NA,AP,PN)",
"Shape(MQ,QA,AM)",
"Shape(AQ,QP,PA)",
"Collinear(MAP)",
"Collinear(NAQ)"
] | [
"Equal(AreaOfQuadrilateral(NMQP),375)",
"Equal(LengthOfLine(MP),25)",
"Rhombus(MQPN)"
] | [] | Value(LengthOfLine(NQ)) | 30 | [
"kite_area_formula_diagonal(1,NMQP)"
] | {"START": ["kite_area_formula_diagonal(1,NMQP)"]} | |
627 | YimingHe_2023-04-09 | Geometry3k-644 | 2 | 如图所示，GH=10，⊙G的圆心为G，J是圆J的圆心，K是圆K的圆心。求直线GL的长度。 | As shown in the diagram, GH=10, G is the center of ⊙G, J is the center of ⊙J, the center of circle K is K. Find the length of line GL. | 627.png | [
"Shape(BG,GH,GHB)",
"Shape(FG,GB,GBF)",
"Shape(GF,GFL,JGL)",
"Shape(JGL,KJL,JG)",
"Shape(KJL,LK,KJ)",
"Shape(JK,KL,KLJ)",
"Shape(KLJ,JLG,GJ)",
"Shape(JLG,GKH,HG)",
"Collinear(BGJKL)",
"Collinear(HGF)",
"Cocircular(G,HBFL)",
"Cocircular(J,GL)",
"Cocircular(K,JL)"
] | [
"Equal(LengthOfLine(GH),10)",
"IsCentreOfCircle(G,G)",
"IsCentreOfCircle(J,J)",
"IsCentreOfCircle(K,K)"
] | [
"IsCentreOfCircle(G,G)",
"IsCentreOfCircle(J,J)",
"IsCentreOfCircle(K,K)"
] | Value(LengthOfLine(GL)) | 10 | [
"radius_of_circle_property_length_equal(1,GH,G)",
"radius_of_circle_property_length_equal(1,GL,G)"
] | {"START": ["radius_of_circle_property_length_equal(1,GH,G)", "radius_of_circle_property_length_equal(1,GL,G)"]} | |
628 | YimingHe_2023-04-09 | Geometry3k-645 | 1 | 如图所示，∠PNO=56°，弧BMN的角度为70。求∠NPM的大小。 | As shown in the diagram, ∠PNO=56°, the measure of ⌒BMN is 70. Find the measure of ∠NPM. | 628.png | [
"Shape(MP,BPM)",
"Shape(NP,PM,BMN)",
"Shape(ON,BNO)",
"Shape(PN,NO,BOP)",
"Cocircular(B,NOPM)"
] | [
"Equal(MeasureOfAngle(PNO),56)",
"Equal(MeasureOfArc(BMN),70)"
] | [
"Equal(MeasureOfAngle(PNO),56)",
"Equal(MeasureOfArc(BMN),70)"
] | Value(MeasureOfAngle(NPM)) | 35 | [
"arc_property_circumference_angle_external(1,BMN,P)"
] | {"START": ["arc_property_circumference_angle_external(1,BMN,P)"]} | |
629 | YimingHe_2023-04-09 | Geometry3k-646 | 2 | 如图所示，∠BCH=8*y-12°，∠BHD=1/4*x°，∠HBC=y-8°，∠HDB=4*x-8°，DBCH是平行四边形。求y的值。 | As shown in the diagram, ∠BCH=8*y-12°, ∠BHD=1/4*x°, ∠HBC=y-8°, ∠HDB=4*x-8°, BD and CH are opposite sides of the ▱ DBCH. Find the value of y. | 629.png | [
"Shape(DB,BH,HD)",
"Shape(HB,BC,CH)"
] | [
"Equal(MeasureOfAngle(BCH),8*y-12)",
"Equal(MeasureOfAngle(BHD),1/4*x)",
"Equal(MeasureOfAngle(HBC),y-8)",
"Equal(MeasureOfAngle(HDB),4*x-8)",
"Parallelogram(DBCH)"
] | [
"Equal(MeasureOfAngle(BCH),8*y-12)",
"Equal(MeasureOfAngle(BHD),1/4*x)",
"Equal(MeasureOfAngle(HBC),y-8)",
"Equal(MeasureOfAngle(HDB),4*x-8)"
] | Value(y) | 31/2 | [
"parallel_property_alternate_interior_angle(2,DH,BC)",
"parallelogram_property_opposite_angle_equal(1,DBCH)"
] | {"START": ["parallel_property_alternate_interior_angle(2,DH,BC)", "parallelogram_property_opposite_angle_equal(1,DBCH)"]} | |
630 | JiaZou_2023-03-12 | Geometry3k-647 | 1 | 如图所示，CA=x，CB=8，∠ABC=60°，∠CAB=78°。求x的值。 | As shown in the diagram, CA=x, CB=8, ∠ABC=60°, ∠CAB=78°. Find the value of x. | 630.png | [
"Shape(AB,BC,CA)"
] | [
"Equal(LengthOfLine(CA),x)",
"Equal(LengthOfLine(CB),8)",
"Equal(MeasureOfAngle(ABC),60)",
"Equal(MeasureOfAngle(CAB),78)"
] | [
"Equal(LengthOfLine(CA),x)",
"Equal(LengthOfLine(CB),8)",
"Equal(MeasureOfAngle(ABC),60)",
"Equal(MeasureOfAngle(CAB),78)"
] | Value(x) | 32*sqrt(6)/(-sqrt(2)+sqrt(10)+2*sqrt(3)*sqrt(sqrt(5)+5)) | [
"sine_theorem(1,CAB)"
] | {"START": ["sine_theorem(1,CAB)"]} | |
631 | JiaZou_2023-03-12 | Geometry3k-648 | 7 | 如图所示，AB=6，AF=8，BC=x，CD=y，DE=2*y-3，FE=x+10/3，BC∥FD，BF平行于CD。求直线FE的长度。 | As shown in the diagram, AB=6, AF=8, BC=x, CD=y, DE=2*y-3, FE=x+10/3, BC∥FD, BF is parallel to CD. Find the length of line FE. | 631.png | [
"Shape(AB,BF,FA)",
"Shape(BC,CD,DF,FB)",
"Shape(FD,DE,EF)",
"Collinear(ABC)",
"Collinear(AFE)",
"Collinear(CDE)"
] | [
"Equal(LengthOfLine(AB),6)",
"Equal(LengthOfLine(AF),8)",
"Equal(LengthOfLine(BC),x)",
"Equal(LengthOfLine(CD),y)",
"Equal(LengthOfLine(DE),2*y-3)",
"Equal(LengthOfLine(FE),x+10/3)",
"ParallelBetweenLine(BC,FD)",
"ParallelBetweenLine(BF,CD)"
] | [
"Equal(LengthOfLine(AB),6)",
"Equal(LengthOfLine(AF),8)",
"Equal(LengthOfLine(BC),x)",
"Equal(LengthOfLine(CD),y)",
"Equal(LengthOfLine(DE),2*y-3)",
"Equal(LengthOfLine(FE),x+10/3)",
"ParallelBetweenLine(BC,FD)",
"ParallelBetweenLine(BF,CD)"
] | Value(LengthOfLine(FE)) | 40/3 | [
"line_addition(1,AB,BC)",
"line_addition(1,AF,FE)",
"parallel_property_collinear_extend(1,DC,FB,E)",
"parallel_property_corresponding_angle(1,BF,CE,A)",
"similar_triangle_judgment_aa(1,FAB,EAC)",
"similar_triangle_property_line_ratio(1,FAB,EAC)",
"similar_triangle_property_line_ratio(1,BFA,CEA)"
] | {"START": ["line_addition(1,AB,BC)", "line_addition(1,AF,FE)", "parallel_property_collinear_extend(1,DC,FB,E)"], "parallel_property_collinear_extend(1,DC,FB,E)": ["parallel_property_corresponding_angle(1,BF,CE,A)"], "parallel_property_corresponding_angle(1,BF,CE,A)": ["similar_triangle_judgment_aa(1,FAB,EAC)"], "simila... | |
632 | JiaZou_2023-03-12 | Geometry3k-649 | 2 | 如图所示，BC=30，BC=AB，BD=x，∠BCA=42°，BD⊥AD。求x的值。 | As shown in the diagram, BC=30, BC=AB, BD=x, ∠BCA=42°, BD is perpendicular to AD. Find the value of x. | 632.png | [
"Shape(BC,CD,DB)",
"Shape(BD,DA,AB)",
"Collinear(CDA)"
] | [
"Equal(LengthOfLine(BC),30)",
"Equal(LengthOfLine(BC),LengthOfLine(AB))",
"Equal(LengthOfLine(BD),x)",
"Equal(MeasureOfAngle(BCA),42)",
"PerpendicularBetweenLine(BD,AD)"
] | [
"Equal(LengthOfLine(BC),30)",
"Equal(LengthOfLine(BC),LengthOfLine(AB))",
"Equal(LengthOfLine(BD),x)",
"Equal(MeasureOfAngle(BCA),42)",
"PerpendicularBetweenLine(BD,AD)"
] | Value(x) | -15*sqrt(5)/4+15/4+15*sqrt(6*sqrt(5)+30)/4 | [
"sine_theorem(1,BDA)",
"sine_theorem(1,BCA)"
] | {"START": ["sine_theorem(1,BDA)", "sine_theorem(1,BCA)"]} | |
633 | YimingHe_2023-04-09 | Geometry3k-650 | 2 | 如图所示，AC=4*x-2，EB=6*x-10，⌒DCA的角度为133，弧DEB的角度为133。求x的值。 | As shown in the diagram, AC=4*x-2, EB=6*x-10, the measure of arc DCA is 133, the measure of arc DEB is 133. Find the value of x. | 633.png | [
"Shape(AC,DCA)",
"Shape(CA,DAE,EB,DBC)",
"Shape(BE,DEB)",
"Cocircular(D,AEBC)"
] | [
"Equal(LengthOfLine(AC),4*x-2)",
"Equal(LengthOfLine(EB),6*x-10)",
"Equal(MeasureOfArc(DCA),133)",
"Equal(MeasureOfArc(DEB),133)"
] | [
"Equal(LengthOfLine(AC),4*x-2)",
"Equal(LengthOfLine(EB),6*x-10)",
"Equal(MeasureOfArc(DCA),133)",
"Equal(MeasureOfArc(DEB),133)"
] | Value(x) | 4 | [
"congruent_arc_judgment_measure_equal(1,DEB,DCA)",
"congruent_arc_property_chord_equal(1,DEB,DCA)"
] | {"START": ["congruent_arc_judgment_measure_equal(1,DEB,DCA)"], "congruent_arc_judgment_measure_equal(1,DEB,DCA)": ["congruent_arc_property_chord_equal(1,DEB,DCA)"]} | |
634 | YimingHe_2023-04-09 | Geometry3k-651 | 4 | 如图所示，OLAB的面积为96，LE=7，OE=EA，OE=x，OL=LA，四边形LABO是菱形。求x的值。 | As shown in the diagram, the area of quadrilateral OLAB is 96, LE=7, OE=EA, OE=x, OL=LA, quadrilateral LABO is a rhombus. Find the value of x. | 634.png | [
"Shape(OL,LE,EO)",
"Shape(EL,LA,AE)",
"Shape(EA,AB,BE)",
"Shape(OE,EB,BO)",
"Collinear(OEA)",
"Collinear(LEB)"
] | [
"Equal(AreaOfQuadrilateral(OLAB),96)",
"Equal(LengthOfLine(LE),7)",
"Equal(LengthOfLine(OE),LengthOfLine(EA))",
"Equal(LengthOfLine(OE),x)",
"Equal(LengthOfLine(OL),LengthOfLine(LA))",
"Rhombus(LABO)"
] | [
"Equal(AreaOfQuadrilateral(OLAB),96)",
"Equal(LengthOfLine(LE),7)",
"Equal(LengthOfLine(OE),LengthOfLine(EA))",
"Equal(LengthOfLine(OE),x)",
"Equal(LengthOfLine(OL),LengthOfLine(LA))",
"Rhombus(LABO)"
] | Value(x) | 48/7 | [
"parallelogram_property_diagonal_bisection(1,LABO,E)",
"kite_area_formula_diagonal(1,LABO)",
"line_addition(1,LE,EB)",
"line_addition(1,OE,EA)"
] | {"START": ["parallelogram_property_diagonal_bisection(1,LABO,E)", "kite_area_formula_diagonal(1,LABO)", "line_addition(1,LE,EB)", "line_addition(1,OE,EA)"]} | |
635 | YimingHe_2023-03-12 | Geometry3k-652 | 5 | 如图所示，BA=c，BC=a，BE=x，CA=b，EA=y，∠ABC=60°，∠CAB=30°，a=10*sqrt(3)，AE垂直于CE，BC垂直于AC。求y的值。 | As shown in the diagram, BA=c, BC=a, BE=x, CA=b, EA=y, ∠ABC=60°, ∠CAB=30°, a=10*sqrt(3), AE is perpendicular to CE, BC is perpendicular to AC. Find the value of y. | 635.png | [
"Shape(BC,CE,EB)",
"Shape(EC,CA,AE)",
"Collinear(BEA)"
] | [
"Equal(LengthOfLine(BA),c)",
"Equal(LengthOfLine(BC),a)",
"Equal(LengthOfLine(BE),x)",
"Equal(LengthOfLine(CA),b)",
"Equal(LengthOfLine(EA),y)",
"Equal(MeasureOfAngle(ABC),60)",
"Equal(MeasureOfAngle(CAB),30)",
"Equal(a,10*sqrt(3))",
"PerpendicularBetweenLine(AE,CE)",
"PerpendicularBetweenLine(BC,... | [
"Equal(LengthOfLine(BA),c)",
"Equal(LengthOfLine(BC),a)",
"Equal(LengthOfLine(BE),x)",
"Equal(LengthOfLine(CA),b)",
"Equal(LengthOfLine(EA),y)",
"Equal(MeasureOfAngle(ABC),60)",
"Equal(MeasureOfAngle(CAB),30)",
"PerpendicularBetweenLine(AE,CE)",
"PerpendicularBetweenLine(BC,AC)"
] | Value(y) | 15*sqrt(3) | [
"adjacent_complementary_angle(1,AEC,CEB)",
"triangle_property_angle_sum(1,AEC)",
"sine_theorem(1,AEC)",
"sine_theorem(1,CAE)",
"sine_theorem(1,CEB)"
] | {"START": ["adjacent_complementary_angle(1,AEC,CEB)", "triangle_property_angle_sum(1,AEC)", "sine_theorem(1,AEC)", "sine_theorem(1,CAE)", "sine_theorem(1,CEB)"]} | |
636 | YimingHe_2023-03-12 | Geometry3k-653 | 1 | 如图所示，三角形ACB全等于三角形FHG，AB=13，AC=2*x+5，BC=7，FG=4*x+1，FH=11，HG=3*x-2。求x的值。 | As shown in the diagram, triangle ACB is congruent to triangle FHG, AB=13, AC=2*x+5, BC=7, FG=4*x+1, FH=11, HG=3*x-2. Find the value of x. | 636.png | [
"Shape(BA,AC,CB)",
"Shape(FH,HG,GF)"
] | [
"CongruentBetweenTriangle(ACB,FHG)",
"Equal(LengthOfLine(AB),13)",
"Equal(LengthOfLine(AC),2*x+5)",
"Equal(LengthOfLine(BC),7)",
"Equal(LengthOfLine(FG),4*x+1)",
"Equal(LengthOfLine(FH),11)",
"Equal(LengthOfLine(HG),3*x-2)"
] | [
"CongruentBetweenTriangle(ACB,FHG)",
"Equal(LengthOfLine(AB),13)",
"Equal(LengthOfLine(AC),2*x+5)",
"Equal(LengthOfLine(BC),7)",
"Equal(LengthOfLine(FG),4*x+1)",
"Equal(LengthOfLine(FH),11)",
"Equal(LengthOfLine(HG),3*x-2)"
] | Value(x) | 3 | [
"congruent_triangle_property_line_equal(1,CBA,HGF)"
] | {"START": ["congruent_triangle_property_line_equal(1,CBA,HGF)"]} | |
637 | YimingHe_2023-03-12 | Geometry3k-654 | 8 | 如图所示，AC=y，AN=x，BA=z，NB=12，NC=8，BA⊥NA，NC垂直于AC。求z的值。 | As shown in the diagram, AC=y, AN=x, BA=z, NB=12, NC=8, BA is perpendicular to NA, NC is perpendicular to AC. Find the value of z. | 637.png | [
"Shape(BA,AC,CB)",
"Shape(CA,AN,NC)",
"Collinear(NCB)"
] | [
"Equal(LengthOfLine(AC),y)",
"Equal(LengthOfLine(AN),x)",
"Equal(LengthOfLine(BA),z)",
"Equal(LengthOfLine(NB),12)",
"Equal(LengthOfLine(NC),8)",
"PerpendicularBetweenLine(BA,NA)",
"PerpendicularBetweenLine(NC,AC)"
] | [
"Equal(LengthOfLine(AC),y)",
"Equal(LengthOfLine(AN),x)",
"Equal(LengthOfLine(BA),z)",
"Equal(LengthOfLine(NB),12)",
"Equal(LengthOfLine(NC),8)",
"PerpendicularBetweenLine(BA,NA)",
"PerpendicularBetweenLine(NC,AC)"
] | Value(z) | 4*sqrt(3) | [
"adjacent_complementary_angle(1,NCA,ACB)",
"right_triangle_judgment_angle(1,ACB)",
"right_triangle_judgment_angle(1,NCA)",
"right_triangle_judgment_angle(1,BAN)",
"right_triangle_property_pythagorean(1,ACB)",
"right_triangle_property_pythagorean(1,NCA)",
"right_triangle_property_pythagorean(1,BAN)",
"... | {"START": ["adjacent_complementary_angle(1,NCA,ACB)", "right_triangle_judgment_angle(1,NCA)", "right_triangle_judgment_angle(1,BAN)", "line_addition(1,NC,CB)"], "adjacent_complementary_angle(1,NCA,ACB)": ["right_triangle_judgment_angle(1,ACB)"], "right_triangle_judgment_angle(1,ACB)": ["right_triangle_property_pythagor... | |
638 | YimingHe_2023-04-09 | Geometry3k-655 | 2 | 如图所示，AB=3*y-8，CB=2*x+7，DA=13，DC=10，∠ADF=59°，∠BFC=49°，∠FBA=20°，DA和CB是▱ADCB的一组对边。求∠CAD的大小。 | As shown in the diagram, AB=3*y-8, CB=2*x+7, DA=13, DC=10, ∠ADF=59°, ∠BFC=49°, ∠FBA=20°, ADCB is a ▱. Find the measure of ∠CAD. | 638.png | [
"Shape(AD,DF,FA)",
"Shape(FD,DC,CF)",
"Shape(FC,CB,BF)",
"Shape(AF,FB,BA)",
"Collinear(AFC)",
"Collinear(DFB)"
] | [
"Equal(LengthOfLine(AB),3*y-8)",
"Equal(LengthOfLine(CB),2*x+7)",
"Equal(LengthOfLine(DA),13)",
"Equal(LengthOfLine(DC),10)",
"Equal(MeasureOfAngle(ADF),59)",
"Equal(MeasureOfAngle(BFC),49)",
"Equal(MeasureOfAngle(FBA),20)",
"Parallelogram(ADCB)"
] | [
"Equal(LengthOfLine(AB),3*y-8)",
"Equal(LengthOfLine(CB),2*x+7)",
"Equal(LengthOfLine(DA),13)",
"Equal(LengthOfLine(DC),10)",
"Equal(MeasureOfAngle(ADF),59)",
"Equal(MeasureOfAngle(BFC),49)",
"Equal(MeasureOfAngle(FBA),20)"
] | Value(MeasureOfAngle(CAD)) | 72 | [
"vertical_angle(1,DFA,BFC)",
"triangle_property_angle_sum(1,ADF)"
] | {"START": ["vertical_angle(1,DFA,BFC)", "triangle_property_angle_sum(1,ADF)"]} | |
639 | YimingHe_2023-04-09 | Geometry3k-656 | 3 | 如图所示，AX=5，YA=8，YZ和YX是风筝形WZYX的一组临边。求直线YZ的长度。 | As shown in the diagram, AX=5, YA=8, quadrilateral WZYX is a kite. Find the length of line YZ. | 639.png | [
"Shape(WZ,ZA,AW)",
"Shape(AZ,ZY,YA)",
"Shape(AY,YX,XA)",
"Shape(WA,AX,XW)",
"Collinear(WAY)",
"Collinear(ZAX)"
] | [
"Equal(LengthOfLine(AX),5)",
"Equal(LengthOfLine(YA),8)",
"Kite(WZYX)"
] | [
"Equal(LengthOfLine(AX),5)",
"Equal(LengthOfLine(YA),8)",
"Kite(WZYX)"
] | Value(LengthOfLine(YZ)) | sqrt(89) | [
"kite_property_diagonal_perpendicular_bisection(1,YXWZ,A)",
"right_triangle_judgment_angle(1,YAZ)",
"right_triangle_property_pythagorean(1,YAZ)"
] | {"START": ["kite_property_diagonal_perpendicular_bisection(1,YXWZ,A)"], "kite_property_diagonal_perpendicular_bisection(1,YXWZ,A)": ["right_triangle_judgment_angle(1,YAZ)"], "right_triangle_judgment_angle(1,YAZ)": ["right_triangle_property_pythagorean(1,YAZ)"]} | |
640 | YimingHe_2023-03-12 | Geometry3k-657 | 2 | 如图所示，AB=19，AC=x，∠ABC=24°，CA⊥BA。求x的值。 | As shown in the diagram, AB=19, AC=x, ∠ABC=24°, CA⊥BA. Find the value of x. | 640.png | [
"Shape(CA,AB,BC)"
] | [
"Equal(LengthOfLine(AB),19)",
"Equal(LengthOfLine(AC),x)",
"Equal(MeasureOfAngle(ABC),24)",
"PerpendicularBetweenLine(CA,BA)"
] | [
"Equal(LengthOfLine(AB),19)",
"Equal(LengthOfLine(AC),x)",
"Equal(MeasureOfAngle(ABC),24)",
"PerpendicularBetweenLine(CA,BA)"
] | Value(x) | 19*(-2*sqrt(5-sqrt(5))+sqrt(6)+sqrt(30))/(sqrt(2)+sqrt(10)+2*sqrt(3)*sqrt(5-sqrt(5))) | [
"triangle_property_angle_sum(1,CAB)",
"sine_theorem(1,ABC)"
] | {"START": ["triangle_property_angle_sum(1,CAB)", "sine_theorem(1,ABC)"]} | |
641 | YimingHe_2023-03-12 | Geometry3k-658 | 2 | 如图所示，BM=16，GC=x，MH=22，VG=12，∠CVG=∠HBM，∠VGC=∠BMH，三角形VGC相似于三角形BMH。求x的值。 | As shown in the diagram, BM=16, GC=x, MH=22, VG=12, ∠CVG=∠HBM, ∠VGC=∠BMH, △VGC is similar to △BMH.. Find the value of x. | 641.png | [
"Shape(VG,GC,CV)",
"Shape(BM,MH,HB)"
] | [
"Equal(LengthOfLine(BM),16)",
"Equal(LengthOfLine(GC),x)",
"Equal(LengthOfLine(MH),22)",
"Equal(LengthOfLine(VG),12)",
"Equal(MeasureOfAngle(CVG),MeasureOfAngle(HBM))",
"Equal(MeasureOfAngle(VGC),MeasureOfAngle(BMH))",
"SimilarBetweenTriangle(VGC,BMH)"
] | [
"Equal(LengthOfLine(BM),16)",
"Equal(LengthOfLine(GC),x)",
"Equal(LengthOfLine(MH),22)",
"Equal(LengthOfLine(VG),12)",
"Equal(MeasureOfAngle(CVG),MeasureOfAngle(HBM))",
"Equal(MeasureOfAngle(VGC),MeasureOfAngle(BMH))",
"SimilarBetweenTriangle(VGC,BMH)"
] | Value(x) | 33/2 | [
"similar_triangle_property_line_ratio(1,VGC,BMH)",
"similar_triangle_property_line_ratio(1,CVG,HBM)"
] | {"START": ["similar_triangle_property_line_ratio(1,VGC,BMH)", "similar_triangle_property_line_ratio(1,CVG,HBM)"]} | |
642 | YimingHe_2023-03-12 | Geometry3k-659 | 2 | 如图所示，AB=x，AC=x-4，BC=8，BC⊥AC。求x的值。 | As shown in the diagram, AB=x, AC=x-4, BC=8, BC⊥AC. Find the value of x. | 642.png | [
"Shape(AB,BC,CA)"
] | [
"Equal(LengthOfLine(AB),x)",
"Equal(LengthOfLine(AC),x-4)",
"Equal(LengthOfLine(BC),8)",
"PerpendicularBetweenLine(BC,AC)"
] | [
"Equal(LengthOfLine(AB),x)",
"Equal(LengthOfLine(AC),x-4)",
"Equal(LengthOfLine(BC),8)",
"PerpendicularBetweenLine(BC,AC)"
] | Value(x) | 10 | [
"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)"]} | |
643 | YimingHe_2023-04-09 | Geometry3k-660 | 5 | 如图所示，∠EDF=2*x°，∠FAC=139°，∠GBD=9*x°，∠HCB=6*x°。求x的值。 | As shown in the diagram, ∠EDF=2*x°, ∠FAC=139°, ∠GBD=9*x°, ∠HCB=6*x°. Find the value of x. | 643.png | [
"Shape(FA,AC)",
"Shape(HC,CB)",
"Shape(GB,BD)",
"Shape(ED,DA)",
"Shape(AD,DB,BC,CA)",
"Collinear(FAD)",
"Collinear(ACH)",
"Collinear(EDB)",
"Collinear(GBC)"
] | [
"Equal(MeasureOfAngle(EDF),2*x)",
"Equal(MeasureOfAngle(FAC),139)",
"Equal(MeasureOfAngle(GBD),9*x)",
"Equal(MeasureOfAngle(HCB),6*x)"
] | [
"Equal(MeasureOfAngle(EDF),2*x)",
"Equal(MeasureOfAngle(FAC),139)",
"Equal(MeasureOfAngle(GBD),9*x)",
"Equal(MeasureOfAngle(HCB),6*x)"
] | Value(x) | 13 | [
"adjacent_complementary_angle(1,EDA,ADB)",
"adjacent_complementary_angle(1,FAC,CAD)",
"adjacent_complementary_angle(1,HCB,BCA)",
"adjacent_complementary_angle(1,GBD,DBC)",
"quadrilateral_property_angle_sum(1,ADBC)"
] | {"START": ["adjacent_complementary_angle(1,EDA,ADB)", "adjacent_complementary_angle(1,FAC,CAD)", "adjacent_complementary_angle(1,HCB,BCA)", "adjacent_complementary_angle(1,GBD,DBC)", "quadrilateral_property_angle_sum(1,ADBC)"]} | |
644 | YimingHe_2023-04-09 | Geometry3k-661 | 3 | 如图所示，NO=6，OP=10，PN=x，O是圆O的圆心，PN是圆O的切线。求x的值。 | As shown in the diagram, NO=6, OP=10, PN=x, the center of ⊙O is O, PN is the tangent to circle O. Find the value of x. | 644.png | [
"Shape(AO,ON,ONA)",
"Shape(NO,OA,OAN)",
"Shape(AP,PN,OAN)",
"Collinear(OAP)",
"Cocircular(O,NA)"
] | [
"Equal(LengthOfLine(NO),6)",
"Equal(LengthOfLine(OP),10)",
"Equal(LengthOfLine(PN),x)",
"IsCentreOfCircle(O,O)",
"IsTangentOfCircle(PN,O)"
] | [
"Equal(LengthOfLine(NO),6)",
"Equal(LengthOfLine(OP),10)",
"Equal(LengthOfLine(PN),x)",
"IsCentreOfCircle(O,O)"
] | Value(x) | 8 | [
"tangent_of_circle_property_perpendicular(2,PN,O,O)",
"right_triangle_judgment_angle(1,PNO)",
"right_triangle_property_pythagorean(1,PNO)"
] | {"START": ["tangent_of_circle_property_perpendicular(2,PN,O,O)"], "right_triangle_judgment_angle(1,PNO)": ["right_triangle_property_pythagorean(1,PNO)"], "tangent_of_circle_property_perpendicular(2,PN,O,O)": ["right_triangle_judgment_angle(1,PNO)"]} | |
645 | YimingHe_2023-04-09 | Geometry3k-662 | 1 | 如图所示，∠JKL=x+10°，∠KLM=x°，∠LMJ=2*x-8°，∠MJK=3*x-6°。求∠MJK的大小。 | As shown in the diagram, ∠JKL=x+10°, ∠KLM=x°, ∠LMJ=2*x-8°, ∠MJK=3*x-6°. Find the measure of ∠MJK. | 645.png | [
"Shape(JK,KL,LM,MJ)"
] | [
"Equal(MeasureOfAngle(JKL),x+10)",
"Equal(MeasureOfAngle(KLM),x)",
"Equal(MeasureOfAngle(LMJ),2*x-8)",
"Equal(MeasureOfAngle(MJK),3*x-6)"
] | [
"Equal(MeasureOfAngle(JKL),x+10)",
"Equal(MeasureOfAngle(KLM),x)",
"Equal(MeasureOfAngle(LMJ),2*x-8)",
"Equal(MeasureOfAngle(MJK),3*x-6)"
] | Value(MeasureOfAngle(MJK)) | 150 | [
"quadrilateral_property_angle_sum(1,JKLM)"
] | {"START": ["quadrilateral_property_angle_sum(1,JKLM)"]} | |
646 | YimingHe_2023-03-12 | Geometry3k-663 | 2 | 如图所示，AB=13，AC=12，BC=5，∠BAC=x°，AC⊥BC。求tan(x)。 | As shown in the diagram, AB=13, AC=12, BC=5, ∠BAC=x°, AC⊥BC. Find tan(x). | 646.png | [
"Shape(AC,CB,BA)"
] | [
"Equal(LengthOfLine(AB),13)",
"Equal(LengthOfLine(AC),12)",
"Equal(LengthOfLine(BC),5)",
"Equal(MeasureOfAngle(BAC),x)",
"PerpendicularBetweenLine(AC,BC)"
] | [
"Equal(LengthOfLine(AB),13)",
"Equal(LengthOfLine(AC),12)",
"Equal(LengthOfLine(BC),5)",
"Equal(MeasureOfAngle(BAC),x)",
"PerpendicularBetweenLine(AC,BC)"
] | Value(Tan(x)) | 5/12 | [
"sine_theorem(1,ACB)",
"sine_theorem(1,CBA)"
] | {"START": ["sine_theorem(1,ACB)", "sine_theorem(1,CBA)"]} | |
647 | YimingHe_2023-04-09 | Geometry3k-664 | 3 | 如图所示，JK=6*x-5，LK=4*x+3，MP=3*y+8，QP=5*y-7，QP=MP，MJ∥PK，PK∥QL。求x的值。 | As shown in the diagram, JK=6*x-5, LK=4*x+3, MP=3*y+8, QP=5*y-7, QP=MP, MJ is parallel to PK, PK is parallel to QL. Find the value of x. | 647.png | [
"Shape(GJ,JA)",
"Shape(AJ,JK)",
"Shape(JK,KB)",
"Shape(BK,KL)",
"Shape(KL,LC)",
"Shape(CL,LY)",
"Shape(MJ,JG)",
"Shape(HM,MJ)",
"Shape(JM,MP,PK,KJ)",
"Shape(KP,PQ,QL,LK)",
"Shape(YL,LQ)",
"Shape(LQ,QZ)",
"Shape(DM,MH)",
"Shape(PM,MD)",
"Shape(EP,PM)",
"Shape(QP,PE)",
"Shape(FQ,QP)",
... | [
"Equal(LengthOfLine(JK),6*x-5)",
"Equal(LengthOfLine(LK),4*x+3)",
"Equal(LengthOfLine(MP),3*y+8)",
"Equal(LengthOfLine(QP),5*y-7)",
"Equal(LengthOfLine(QP),LengthOfLine(MP))",
"ParallelBetweenLine(MJ,PK)",
"ParallelBetweenLine(PK,QL)"
] | [
"Equal(LengthOfLine(JK),6*x-5)",
"Equal(LengthOfLine(LK),4*x+3)",
"Equal(LengthOfLine(MP),3*y+8)",
"Equal(LengthOfLine(QP),5*y-7)",
"Equal(LengthOfLine(QP),LengthOfLine(MP))",
"ParallelBetweenLine(MJ,PK)",
"ParallelBetweenLine(PK,QL)"
] | Value(x) | 4 | [
"parallel_judgment_par_par(1,MJ,PK,QL)",
"trapezoid_judgment_parallel(1,MQLJ)",
"midsegment_of_quadrilateral_judgment_parallel(1,PK,MQLJ)"
] | {"START": ["parallel_judgment_par_par(1,MJ,PK,QL)"], "parallel_judgment_par_par(1,MJ,PK,QL)": ["trapezoid_judgment_parallel(1,MQLJ)"], "trapezoid_judgment_parallel(1,MQLJ)": ["midsegment_of_quadrilateral_judgment_parallel(1,PK,MQLJ)"]} | |
648 | YimingHe_2023-04-09 | Geometry3k-665 | 2 | 如图所示，∠ADB=11*x-1°，∠BDF=7*y-4°，∠DFH=7*x+9°，∠GAD=2*y+5°，∠HFC=z°，AG平行于DB，DB平行于FH。求y的值。 | As shown in the diagram, ∠ADB=11*x-1°, ∠BDF=7*y-4°, ∠DFH=7*x+9°, ∠GAD=2*y+5°, ∠HFC=z°, AG is parallel to DB, DB is parallel to FH. Find the value of y. | 648.png | [
"Shape(HF,FC)",
"Shape(BD,DF)",
"Shape(DF,FH)",
"Shape(AD,DB)",
"Shape(GA,AD)",
"Shape(EA,AG)",
"Shape(FD,DA)",
"Collinear(CFD)",
"Collinear(EAD)"
] | [
"Equal(MeasureOfAngle(ADB),11*x-1)",
"Equal(MeasureOfAngle(BDF),7*y-4)",
"Equal(MeasureOfAngle(DFH),7*x+9)",
"Equal(MeasureOfAngle(GAD),2*y+5)",
"Equal(MeasureOfAngle(HFC),z)",
"ParallelBetweenLine(AG,DB)",
"ParallelBetweenLine(DB,FH)"
] | [
"Equal(MeasureOfAngle(ADB),11*x-1)",
"Equal(MeasureOfAngle(BDF),7*y-4)",
"Equal(MeasureOfAngle(DFH),7*x+9)",
"Equal(MeasureOfAngle(GAD),2*y+5)",
"Equal(MeasureOfAngle(HFC),z)",
"ParallelBetweenLine(AG,DB)",
"ParallelBetweenLine(DB,FH)"
] | Value(y) | 11 | [
"parallel_property_ipsilateral_internal_angle(1,AG,DB)",
"parallel_property_ipsilateral_internal_angle(1,DB,FH)"
] | {"START": ["parallel_property_ipsilateral_internal_angle(1,AG,DB)", "parallel_property_ipsilateral_internal_angle(1,DB,FH)"]} | |
649 | YimingHe_2023-03-12 | Geometry3k-666 | 0 | 如图所示，JL=5*x-6，KJ=3*x+6，KJ=LK，KL=4*x，LK=JL。求直线KL的长度。 | As shown in the diagram, JL=5*x-6, KJ=3*x+6, KJ=LK, KL=4*x, LK=JL. Find the length of line KL. | 649.png | [
"Shape(KJ,JL,LK)"
] | [
"Equal(LengthOfLine(JL),5*x-6)",
"Equal(LengthOfLine(KJ),3*x+6)",
"Equal(LengthOfLine(KJ),LengthOfLine(LK))",
"Equal(LengthOfLine(KL),4*x)",
"Equal(LengthOfLine(LK),LengthOfLine(JL))"
] | [
"Equal(LengthOfLine(JL),5*x-6)",
"Equal(LengthOfLine(KJ),3*x+6)",
"Equal(LengthOfLine(KJ),LengthOfLine(LK))",
"Equal(LengthOfLine(KL),4*x)",
"Equal(LengthOfLine(LK),LengthOfLine(JL))"
] | Value(LengthOfLine(KL)) | 24 | [] | {"START": []} | |
650 | YimingHe_2023-04-09 | Geometry3k-667 | 1 | 如图所示，∠CDF=52°，∠DHG=38°，HG⊥DG。求∠GDH的大小。 | As shown in the diagram, ∠CDF=52°, ∠DHG=38°, HG is perpendicular to DG. Find the measure of ∠GDH. | 650.png | [
"Shape(BH,HI)",
"Shape(IH,HD)",
"Shape(HD,DC)",
"Shape(CD,DF)",
"Shape(FD,DG)",
"Shape(DG,GA)",
"Shape(AG,GE)",
"Shape(EG,GH)",
"Shape(GH,HB)",
"Shape(HG,GD,DH)",
"Collinear(IHGA)",
"Collinear(EGDC)",
"Collinear(BHDF)"
] | [
"Equal(MeasureOfAngle(CDF),52)",
"Equal(MeasureOfAngle(DHG),38)",
"PerpendicularBetweenLine(HG,DG)"
] | [
"Equal(MeasureOfAngle(CDF),52)",
"Equal(MeasureOfAngle(DHG),38)",
"PerpendicularBetweenLine(HG,DG)"
] | Value(MeasureOfAngle(GDH)) | 52 | [
"triangle_property_angle_sum(1,HGD)"
] | {"START": ["triangle_property_angle_sum(1,HGD)"]} | |
651 | YimingHe_2023-04-09 | Geometry3k-668 | 7 | 如图所示，XY=2，圆W的半径为4，⊙Z的半径为7，W是圆W的圆心，Z是圆Z的圆心，CX是圆Z的直径。求直线IC的长度。 | As shown in the diagram, XY=2, the radius of ⊙W is 4, the radius of circle Z is 7, W is the center of ⊙W, Z is the center of ⊙Z, CX is the diameter of ⊙Z. Find the length of line IC. | 651.png | [
"Shape(IW,WX,ZAX,WAI)",
"Shape(XI,WIB,ZXB)",
"Shape(WYA,ZAX,XY)",
"Shape(YX,ZXB,WBY)",
"Shape(YZ,ZC,ZCA,WYA)",
"Shape(CZ,ZY,WBY,ZBC)",
"Collinear(IWXYZC)",
"Cocircular(W,IBYA)",
"Cocircular(Z,XBCA)"
] | [
"Equal(LengthOfLine(XY),2)",
"Equal(RadiusOfCircle(W),4)",
"Equal(RadiusOfCircle(Z),7)",
"IsCentreOfCircle(W,W)",
"IsCentreOfCircle(Z,Z)",
"IsDiameterOfCircle(CX,Z)"
] | [
"Equal(LengthOfLine(XY),2)",
"Equal(RadiusOfCircle(W),4)",
"Equal(RadiusOfCircle(Z),7)",
"IsCentreOfCircle(W,W)",
"IsCentreOfCircle(Z,Z)",
"IsDiameterOfCircle(CX,Z)"
] | Value(LengthOfLine(IC)) | 20 | [
"radius_of_circle_property_length_equal(1,WI,W)",
"radius_of_circle_property_length_equal(1,WY,W)",
"diameter_of_circle_property_length_equal(1,CX,Z)",
"circle_property_length_of_radius_and_diameter(1,Z)",
"line_addition(1,WX,XY)",
"line_addition(1,IW,WX)",
"line_addition(1,IX,XC)"
] | {"START": ["radius_of_circle_property_length_equal(1,WI,W)", "radius_of_circle_property_length_equal(1,WY,W)", "diameter_of_circle_property_length_equal(1,CX,Z)", "circle_property_length_of_radius_and_diameter(1,Z)", "line_addition(1,WX,XY)", "line_addition(1,IW,WX)", "line_addition(1,IX,XC)"]} | |
652 | YimingHe_2023-04-09 | Geometry3k-669 | 2 | 如图所示，AE=3，AF=x，DE=9，AF是⊙O的切线。求x的值。 | As shown in the diagram, AE=3, AF=x, DE=9, the tangent to circle B is AF. Find the value of x. | 652.png | [
"Shape(DB,BE,BEF,BFD)",
"Shape(BEF,EA,AF)",
"Shape(EB,BD,BDE)",
"Collinear(DBEA)",
"Cocircular(B,DEF)"
] | [
"Equal(LengthOfLine(AE),3)",
"Equal(LengthOfLine(AF),x)",
"Equal(LengthOfLine(DE),9)",
"IsTangentOfCircle(AF,B)"
] | [
"Equal(LengthOfLine(AE),3)",
"Equal(LengthOfLine(AF),x)",
"Equal(LengthOfLine(DE),9)"
] | Value(x) | 6 | [
"line_addition(1,AE,ED)",
"circle_property_circular_power_tangent_and_segment_line(1,AF,AED,B)"
] | {"START": ["line_addition(1,AE,ED)", "circle_property_circular_power_tangent_and_segment_line(1,AF,AED,B)"]} | |
653 | YimingHe_2023-04-09 | Geometry3k-670 | 1 | 如图所示，RV=x，WT=15，ZY=8，TVRW的中位线为YZ。求x的值。 | As shown in the diagram, RV=x, WT=15, ZY=8, YZ is the midsegment of quadrilateral TVRW. Find the value of x. | 653.png | [
"Shape(TY,YZ,ZW,WT)",
"Shape(YV,VR,RZ,ZY)",
"Collinear(TYV)",
"Collinear(WZR)"
] | [
"Equal(LengthOfLine(RV),x)",
"Equal(LengthOfLine(WT),15)",
"Equal(LengthOfLine(ZY),8)",
"IsMidsegmentOfQuadrilateral(YZ,TVRW)"
] | [
"Equal(LengthOfLine(RV),x)",
"Equal(LengthOfLine(WT),15)",
"Equal(LengthOfLine(ZY),8)"
] | Value(x) | 1 | [
"midsegment_of_quadrilateral_property_length(1,YZ,TVRW)"
] | {"START": ["midsegment_of_quadrilateral_property_length(1,YZ,TVRW)"]} | |
654 | YimingHe_2023-03-12 | Geometry3k-671 | 7 | 如图所示，PQ=QS，QR=RS，∠SRP=72°。求∠QPS的大小。 | As shown in the diagram, PQ=QS, QR=RS, ∠SRP=72°. Find the measure of ∠QPS. | 654.png | [
"Shape(SR,RQ,QS)",
"Shape(SQ,QP,PS)",
"Collinear(RQP)"
] | [
"Equal(LengthOfLine(PQ),LengthOfLine(QS))",
"Equal(LengthOfLine(QR),LengthOfLine(RS))",
"Equal(MeasureOfAngle(SRP),72)"
] | [
"Equal(LengthOfLine(PQ),LengthOfLine(QS))",
"Equal(LengthOfLine(QR),LengthOfLine(RS))",
"Equal(MeasureOfAngle(SRP),72)"
] | Value(MeasureOfAngle(QPS)) | 27 | [
"triangle_property_angle_sum(1,SRQ)",
"triangle_property_angle_sum(1,SQP)",
"isosceles_triangle_judgment_line_equal(1,RQS)",
"isosceles_triangle_property_angle_equal(1,RQS)",
"isosceles_triangle_judgment_line_equal(1,QPS)",
"isosceles_triangle_property_angle_equal(1,QPS)",
"adjacent_complementary_angle(... | {"START": ["triangle_property_angle_sum(1,SRQ)", "triangle_property_angle_sum(1,SQP)", "isosceles_triangle_judgment_line_equal(1,RQS)", "isosceles_triangle_judgment_line_equal(1,QPS)", "adjacent_complementary_angle(1,RQS,SQP)"], "isosceles_triangle_judgment_line_equal(1,QPS)": ["isosceles_triangle_property_angle_equal(... | |
655 | YimingHe_2023-04-09 | Geometry3k-672 | 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y的值。 | As shown in the diagram, BA=5*x, BC=3*y-4, DA=29, DC=25, ∠ADF=34°, ∠DCF=54°, ∠FAD=49°, BADC is a parallelogram. Find the value of y. | 655.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(y) | 11 | [
"parallelogram_property_opposite_line_equal(1,ADCB)"
] | {"START": ["parallelogram_property_opposite_line_equal(1,ADCB)"]} | |
656 | YimingHe_2023-04-09 | Geometry3k-673 | 2 | 如图所示，CE=5，圆E的圆心为E。求圆E的直径。 | As shown in the diagram, CE=5, the center of circle E is E. Find the diameter of ⊙E. | 656.png | [
"Shape(AE,EB,BA)",
"Shape(AB,EBA)",
"Shape(DE,EA,EAD)",
"Shape(CE,ED,EDC)",
"Shape(BE,EC,ECB)",
"Collinear(AEC)",
"Collinear(DEB)",
"Cocircular(E,ADCB)"
] | [
"Equal(LengthOfLine(CE),5)",
"IsCentreOfCircle(E,E)"
] | [
"Equal(LengthOfLine(CE),5)",
"IsCentreOfCircle(E,E)"
] | Value(DiameterOfCircle(E)) | 10 | [
"radius_of_circle_property_length_equal(1,EC,E)",
"circle_property_length_of_radius_and_diameter(1,E)"
] | {"START": ["radius_of_circle_property_length_equal(1,EC,E)", "circle_property_length_of_radius_and_diameter(1,E)"]} | |
657 | YimingHe_2023-03-12 | Geometry3k-674 | 1 | 如图所示，AB=2，CB=3，∠EBA=25°，AE⊥BE。求△ACB的面积。 | As shown in the diagram, AB=2, CB=3, ∠EBA=25°, AE⊥BE. Find the area of △ACB. | 657.png | [
"Shape(AC,CE,EA)",
"Shape(AE,EB,BA)",
"Collinear(CEB)"
] | [
"Equal(LengthOfLine(AB),2)",
"Equal(LengthOfLine(CB),3)",
"Equal(MeasureOfAngle(EBA),25)",
"PerpendicularBetweenLine(AE,BE)"
] | [
"Equal(LengthOfLine(AB),2)",
"Equal(LengthOfLine(CB),3)",
"Equal(MeasureOfAngle(EBA),25)",
"PerpendicularBetweenLine(AE,BE)"
] | Value(AreaOfTriangle(ACB)) | 3*sin(5*pi/36) | [
"triangle_area_formula_sine(1,BAC)"
] | {"START": ["triangle_area_formula_sine(1,BAC)"]} | |
658 | YimingHe_2023-04-09 | Geometry3k-675 | 2 | 如图所示，∠BAE=58°，∠CBE=26°，∠EBA=47°，AB平行于EC。求∠DCE的大小。 | As shown in the diagram, ∠BAE=58°, ∠CBE=26°, ∠EBA=47°, AB is parallel to EC. Find the measure of ∠DCE. | 658.png | [
"Shape(AE,EB,BA)",
"Shape(BE,EC,CB)",
"Shape(CE,ED,DC)",
"Collinear(AED)",
"Collinear(BCD)"
] | [
"Equal(MeasureOfAngle(BAE),58)",
"Equal(MeasureOfAngle(CBE),26)",
"Equal(MeasureOfAngle(EBA),47)",
"ParallelBetweenLine(AB,EC)"
] | [
"Equal(MeasureOfAngle(BAE),58)",
"Equal(MeasureOfAngle(CBE),26)",
"Equal(MeasureOfAngle(EBA),47)",
"ParallelBetweenLine(AB,EC)"
] | Value(MeasureOfAngle(DCE)) | 73 | [
"angle_addition(1,CBE,EBA)",
"parallel_property_corresponding_angle(1,CE,BA,D)"
] | {"START": ["angle_addition(1,CBE,EBA)", "parallel_property_corresponding_angle(1,CE,BA,D)"]} | |
659 | YimingHe_2023-03-12 | Geometry3k-676 | 4 | 如图所示，AF=EA，CF=DC，FT=12，QD=EQ。求直线TQ的长度。 | As shown in the diagram, AF=EA, CF=DC, FT=12, QD=EQ. Find the length of line TQ. | 659.png | [
"Shape(FA,AT,TF)",
"Shape(AE,ET,TA)",
"Shape(TE,EQ,QT)",
"Shape(TQ,QD,DT)",
"Shape(TD,DC,CT)",
"Shape(TC,CF,FT)",
"Collinear(EAF)",
"Collinear(FTQ)",
"Collinear(ETC)",
"Collinear(FCD)",
"Collinear(EQD)",
"Collinear(ATD)"
] | [
"Equal(LengthOfLine(AF),LengthOfLine(EA))",
"Equal(LengthOfLine(CF),LengthOfLine(DC))",
"Equal(LengthOfLine(FT),12)",
"Equal(LengthOfLine(QD),LengthOfLine(EQ))"
] | [
"Equal(LengthOfLine(AF),LengthOfLine(EA))",
"Equal(LengthOfLine(CF),LengthOfLine(DC))",
"Equal(LengthOfLine(FT),12)",
"Equal(LengthOfLine(QD),LengthOfLine(EQ))"
] | Value(LengthOfLine(TQ)) | 6 | [
"median_of_triangle_judgment(1,DA,DFE)",
"median_of_triangle_judgment(1,FQ,FED)",
"centroid_of_triangle_judgment_intersection(1,T,EDF,Q,A)",
"centroid_of_triangle_property_line_ratio(1,T,FED,Q)"
] | {"START": ["median_of_triangle_judgment(1,DA,DFE)", "median_of_triangle_judgment(1,FQ,FED)"], "centroid_of_triangle_judgment_intersection(1,T,EDF,Q,A)": ["centroid_of_triangle_property_line_ratio(1,T,FED,Q)"], "median_of_triangle_judgment(1,DA,DFE)": ["centroid_of_triangle_judgment_intersection(1,T,EDF,Q,A)"], "median_... | |
660 | YimingHe_2023-04-09 | Geometry3k-677 | 2 | 如图所示，JK=2*b+3，JM=3*a，LK=21，LM=45，∠MLR=30°，∠RLK=70°，JMLK是平行四边形。求∠LKJ的大小。 | As shown in the diagram, JK=2*b+3, JM=3*a, LK=21, LM=45, ∠MLR=30°, ∠RLK=70°, JMLK is a parallelogram. Find the measure of ∠LKJ. | 660.png | [
"Shape(MR,RJ,JM)",
"Shape(RM,ML,LR)",
"Shape(RL,LK,KR)",
"Shape(RK,KJ,JR)",
"Collinear(JRL)",
"Collinear(MRK)"
] | [
"Equal(LengthOfLine(JK),2*b+3)",
"Equal(LengthOfLine(JM),3*a)",
"Equal(LengthOfLine(LK),21)",
"Equal(LengthOfLine(LM),45)",
"Equal(MeasureOfAngle(MLR),30)",
"Equal(MeasureOfAngle(RLK),70)",
"Parallelogram(JMLK)"
] | [
"Equal(LengthOfLine(JK),2*b+3)",
"Equal(LengthOfLine(JK),2*b+3)",
"Equal(LengthOfLine(JM),3*a)",
"Equal(LengthOfLine(JM),3*a)",
"Equal(LengthOfLine(LK),21)",
"Equal(LengthOfLine(LM),45)",
"Equal(MeasureOfAngle(MLR),30)",
"Equal(MeasureOfAngle(RLK),70)",
"Parallelogram(JMLK)"
] | Value(MeasureOfAngle(LKJ)) | 80 | [
"angle_addition(1,MLR,RLK)",
"parallel_property_ipsilateral_internal_angle(1,LM,KJ)"
] | {"START": ["angle_addition(1,MLR,RLK)", "parallel_property_ipsilateral_internal_angle(1,LM,KJ)"]} | |
661 | YimingHe_2023-03-12 | Geometry3k-678 | 8 | 如图所示，AD=5，BD=6，AB⊥CB，CD垂直于BD。求直线BC的长度。 | As shown in the diagram, AD=5, BD=6, AB is perpendicular to CB, CD⊥BD. Find the length of line BC. | 661.png | [
"Shape(AB,BD,DA)",
"Shape(DB,BC,CD)",
"Collinear(ADC)"
] | [
"Equal(LengthOfLine(AD),5)",
"Equal(LengthOfLine(BD),6)",
"PerpendicularBetweenLine(AB,CB)",
"PerpendicularBetweenLine(CD,BD)"
] | [
"Equal(LengthOfLine(AD),5)",
"Equal(LengthOfLine(BD),6)",
"PerpendicularBetweenLine(AB,CB)",
"PerpendicularBetweenLine(CD,BD)"
] | Value(LengthOfLine(BC)) | 6*sqrt(61)/5 | [
"adjacent_complementary_angle(1,CDB,BDA)",
"line_addition(1,AD,DC)",
"mirror_similar_triangle_judgment_aa(1,BDA,CAB)",
"right_triangle_judgment_angle(1,CDB)",
"right_triangle_property_pythagorean(1,CDB)",
"mirror_similar_triangle_property_line_ratio(1,BDA,CAB)",
"mirror_similar_triangle_property_line_ra... | {"START": ["adjacent_complementary_angle(1,CDB,BDA)", "line_addition(1,AD,DC)", "right_triangle_judgment_angle(1,CDB)"], "adjacent_complementary_angle(1,CDB,BDA)": ["mirror_similar_triangle_judgment_aa(1,BDA,CAB)"], "mirror_similar_triangle_judgment_aa(1,BDA,CAB)": ["mirror_similar_triangle_property_line_ratio(1,BDA,CA... | |
662 | YimingHe_2023-03-12 | Geometry3k-679 | 2 | 如图所示，AB=10，AC=x，BC=6，CB⊥AB。求x的值。 | As shown in the diagram, AB=10, AC=x, BC=6, CB⊥AB. Find the value of x. | 662.png | [
"Shape(AC,CB,BA)"
] | [
"Equal(LengthOfLine(AB),10)",
"Equal(LengthOfLine(AC),x)",
"Equal(LengthOfLine(BC),6)",
"PerpendicularBetweenLine(CB,AB)"
] | [
"Equal(LengthOfLine(AB),10)",
"Equal(LengthOfLine(AC),x)",
"Equal(LengthOfLine(BC),6)",
"PerpendicularBetweenLine(CB,AB)"
] | Value(x) | 2*sqrt(34) | [
"right_triangle_judgment_angle(1,CBA)",
"right_triangle_property_pythagorean(1,CBA)"
] | {"START": ["right_triangle_judgment_angle(1,CBA)"], "right_triangle_judgment_angle(1,CBA)": ["right_triangle_property_pythagorean(1,CBA)"]} | |
663 | YimingHe_2023-03-12 | Geometry3k-680 | 9 | 如图所示，AY=9，XA=5，XZ⊥YZ，ZA垂直于XA。求直线ZA的长度。 | As shown in the diagram, AY=9, XA=5, XZ is perpendicular to YZ, ZA⊥XA. Find the length of line ZA. | 663.png | [
"Shape(XZ,ZA,AX)",
"Shape(AZ,ZY,YA)",
"Collinear(XAY)"
] | [
"Equal(LengthOfLine(AY),9)",
"Equal(LengthOfLine(XA),5)",
"PerpendicularBetweenLine(XZ,YZ)",
"PerpendicularBetweenLine(ZA,XA)"
] | [
"Equal(LengthOfLine(AY),9)",
"Equal(LengthOfLine(XA),5)",
"PerpendicularBetweenLine(XZ,YZ)",
"PerpendicularBetweenLine(ZA,XA)"
] | Value(LengthOfLine(ZA)) | 3*sqrt(5) | [
"line_addition(1,XA,AY)",
"adjacent_complementary_angle(1,YAZ,ZAX)",
"mirror_similar_triangle_judgment_aa(1,ZAX,YXZ)",
"mirror_similar_triangle_judgment_aa(1,ZYA,XZY)",
"mirror_similar_triangle_property_line_ratio(1,ZAX,YXZ)",
"mirror_similar_triangle_property_line_ratio(1,AXZ,ZYX)",
"mirror_similar_tri... | {"START": ["line_addition(1,XA,AY)", "adjacent_complementary_angle(1,YAZ,ZAX)", "mirror_similar_triangle_judgment_aa(1,ZAX,YXZ)"], "adjacent_complementary_angle(1,YAZ,ZAX)": ["mirror_similar_triangle_judgment_aa(1,ZYA,XZY)"], "mirror_similar_triangle_judgment_aa(1,ZAX,YXZ)": ["mirror_similar_triangle_property_line_rati... | |
664 | JiaZou_2023-04-09 | Geometry3k-681 | 1 | 如图所示，LM=6，∠LKJ=109°，MJ和LK是▱JMLK的一组对边。求直线JK的长度。 | As shown in the diagram, LM=6, ∠LKJ=109°, MJ and LK are opposite sides of the parallelogram JMLK. Find the length of line JK. | 664.png | [
"Shape(JM,ML,LK,KJ)"
] | [
"Equal(LengthOfLine(LM),6)",
"Equal(MeasureOfAngle(LKJ),109)",
"Parallelogram(JMLK)"
] | [
"Equal(LengthOfLine(LM),6)",
"Equal(MeasureOfAngle(LKJ),109)"
] | Value(LengthOfLine(JK)) | 6 | [
"parallelogram_property_opposite_line_equal(1,MLKJ)"
] | {"START": ["parallelogram_property_opposite_line_equal(1,MLKJ)"]} | |
665 | JiaZou_2023-04-09 | Geometry3k-682 | 6 | 如图所示，∠WXV=14°，F是圆F的圆心。求弧FXV的角度。 | As shown in the diagram, ∠WXV=14°, the center of circle F is F. Find the measure of ⌒FXV. | 665.png | [
"Shape(OWX,XF,FW)",
"Shape(OXV,VX)",
"Shape(FX,XV,VF)",
"Shape(WF,FV,FVW)",
"Collinear(WFX)",
"Cocircular(F,WXV)"
] | [
"Equal(MeasureOfAngle(WXV),14)",
"IsCentreOfCircle(F,F)"
] | [
"Equal(MeasureOfAngle(WXV),14)",
"IsCentreOfCircle(F,F)"
] | Value(MeasureOfArc(FXV)) | 152 | [
"arc_property_center_angle(1,FXV,F)",
"radius_of_circle_property_length_equal(1,FV,F)",
"radius_of_circle_property_length_equal(1,FX,F)",
"isosceles_triangle_judgment_line_equal(1,FXV)",
"isosceles_triangle_property_angle_equal(1,FXV)",
"triangle_property_angle_sum(1,FXV)"
] | {"START": ["arc_property_center_angle(1,FXV,F)", "radius_of_circle_property_length_equal(1,FV,F)", "radius_of_circle_property_length_equal(1,FX,F)", "triangle_property_angle_sum(1,FXV)"], "isosceles_triangle_judgment_line_equal(1,FXV)": ["isosceles_triangle_property_angle_equal(1,FXV)"], "radius_of_circle_property_leng... | |
666 | JiaZou_2023-04-09 | Geometry3k-683 | 3 | 如图所示，BCDA的面积为100，AB=x+15，BE=x，BCDA是平行四边形，CE⊥BE。求BCDA的高。 | As shown in the diagram, the area of quadrilateral BCDA is 100, AB=x+15, BE=x, BCDA is a ▱, CE⊥BE. Find the height of BCDA. | 666.png | [
"Shape(CE,EB,BC)",
"Shape(ED,DA,AB,BE)",
"Collinear(CED)"
] | [
"Equal(AreaOfQuadrilateral(BCDA),100)",
"Equal(LengthOfLine(AB),x+15)",
"Equal(LengthOfLine(BE),x)",
"Parallelogram(BCDA)",
"PerpendicularBetweenLine(CE,BE)"
] | [
"Equal(AreaOfQuadrilateral(BCDA),100)",
"Equal(LengthOfLine(AB),x+15)",
"Equal(LengthOfLine(BE),x)",
"PerpendicularBetweenLine(CE,BE)"
] | Value(HeightOfQuadrilateral(BCDA)) | 5 | [
"altitude_of_quadrilateral_judgment_left_vertex(1,BE,BCDA)",
"parallelogram_property_opposite_line_equal(1,CDAB)",
"parallelogram_area_formula_common(1,BCDA)"
] | {"START": ["altitude_of_quadrilateral_judgment_left_vertex(1,BE,BCDA)", "parallelogram_property_opposite_line_equal(1,CDAB)", "parallelogram_area_formula_common(1,BCDA)"]} | |
667 | JiaZou_2023-04-09 | Geometry3k-684 | 5 | 如图所示，∠CGH=42°，∠DGC=3*x°，∠GCD=z°，∠GHC=y°，∠HCG=48°，GD∥HC，HG∥CD。求z的值。 | As shown in the diagram, ∠CGH=42°, ∠DGC=3*x°, ∠GCD=z°, ∠GHC=y°, ∠HCG=48°, GD is parallel to HC, HG∥CD. Find the value of z. | 667.png | [
"Shape(GH,HC,CG)",
"Shape(CD,DG,GC)"
] | [
"Equal(MeasureOfAngle(CGH),42)",
"Equal(MeasureOfAngle(DGC),3*x)",
"Equal(MeasureOfAngle(GCD),z)",
"Equal(MeasureOfAngle(GHC),y)",
"Equal(MeasureOfAngle(HCG),48)",
"ParallelBetweenLine(GD,HC)",
"ParallelBetweenLine(HG,CD)"
] | [
"Equal(MeasureOfAngle(CGH),42)",
"Equal(MeasureOfAngle(DGC),3*x)",
"Equal(MeasureOfAngle(GCD),z)",
"Equal(MeasureOfAngle(GHC),y)",
"Equal(MeasureOfAngle(HCG),48)",
"ParallelBetweenLine(GD,HC)",
"ParallelBetweenLine(HG,CD)"
] | Value(z) | 42 | [
"parallelogram_judgment_parallel_and_parallel(1,GHCD)",
"parallel_property_alternate_interior_angle(1,GD,HC)",
"angle_addition(1,DGC,CGH)",
"angle_addition(1,HCG,GCD)",
"parallelogram_property_opposite_angle_equal(1,GHCD)"
] | {"START": ["parallelogram_judgment_parallel_and_parallel(1,GHCD)", "parallel_property_alternate_interior_angle(1,GD,HC)", "angle_addition(1,DGC,CGH)", "angle_addition(1,HCG,GCD)"], "parallelogram_judgment_parallel_and_parallel(1,GHCD)": ["parallelogram_property_opposite_angle_equal(1,GHCD)"]} | |
668 | YimingHe_2023-03-12 | Geometry3k-685 | 6 | 如图所示，AC=BC，CD=AD，∠ADC=92°。求∠ACB的大小。 | As shown in the diagram, AC=BC, CD=AD, ∠ADC=92°. Find the measure of ∠ACB. | 668.png | [
"Shape(AD,DC,CA)",
"Shape(AC,CB,BA)",
"Collinear(DCB)"
] | [
"Equal(LengthOfLine(AC),LengthOfLine(BC))",
"Equal(LengthOfLine(CD),LengthOfLine(AD))",
"Equal(MeasureOfAngle(ADC),92)"
] | [
"Equal(LengthOfLine(AC),LengthOfLine(BC))",
"Equal(LengthOfLine(CD),LengthOfLine(AD))",
"Equal(MeasureOfAngle(ADC),92)"
] | Value(MeasureOfAngle(ACB)) | 136 | [
"isosceles_triangle_judgment_line_equal(1,DCA)",
"isosceles_triangle_property_angle_equal(1,DCA)",
"angle_addition(1,BAC,CAD)",
"triangle_property_angle_sum(1,ADC)",
"triangle_property_angle_sum(1,ACB)",
"triangle_property_angle_sum(1,DBA)"
] | {"START": ["isosceles_triangle_judgment_line_equal(1,DCA)", "angle_addition(1,BAC,CAD)", "triangle_property_angle_sum(1,ADC)", "triangle_property_angle_sum(1,ACB)", "triangle_property_angle_sum(1,DBA)"], "isosceles_triangle_judgment_line_equal(1,DCA)": ["isosceles_triangle_property_angle_equal(1,DCA)"]} | |
669 | JiaZou_2023-04-09 | Geometry3k-686 | 1 | 如图所示，∠ACE=109°，∠DAE=24°，∠EBD=95°，∠EDA=33°。求∠AED的大小。 | As shown in the diagram, ∠ACE=109°, ∠DAE=24°, ∠EBD=95°, ∠EDA=33°. Find the measure of ∠AED. | 669.png | [
"Shape(BD,DE,EB)",
"Shape(ED,DA,AE)",
"Shape(EA,AC,CE)",
"Collinear(BEA)",
"Collinear(DEC)"
] | [
"Equal(MeasureOfAngle(ACE),109)",
"Equal(MeasureOfAngle(DAE),24)",
"Equal(MeasureOfAngle(EBD),95)",
"Equal(MeasureOfAngle(EDA),33)"
] | [
"Equal(MeasureOfAngle(ACE),109)",
"Equal(MeasureOfAngle(DAE),24)",
"Equal(MeasureOfAngle(EBD),95)",
"Equal(MeasureOfAngle(EDA),33)"
] | Value(MeasureOfAngle(AED)) | 123 | [
"triangle_property_angle_sum(1,EDA)"
] | {"START": ["triangle_property_angle_sum(1,EDA)"]} | |
670 | JiaZou_2023-04-09 | Geometry3k-687 | 1 | 如图所示，∠EBC=3°，弧HCE的角度为5*x-6，⌒HJC的角度为4*x+8。求x的值。 | As shown in the diagram, ∠EBC=3°, the measure of ⌒HCE is 5*x-6, the measure of arc HJC is 4*x+8. Find the value of x. | 670.png | [
"Shape(BC,HJC,JB)",
"Shape(HJC,HCE,EJ)",
"Shape(JE,HEJ)",
"Collinear(EJB)",
"Cocircular(H,CEJ)"
] | [
"Equal(MeasureOfAngle(EBC),3)",
"Equal(MeasureOfArc(HCE),5*x-6)",
"Equal(MeasureOfArc(HJC),4*x+8)"
] | [
"Equal(MeasureOfAngle(EBC),3)",
"Equal(MeasureOfArc(HCE),5*x-6)",
"Equal(MeasureOfArc(HJC),4*x+8)"
] | Value(x) | 20 | [
"circle_property_circular_power_tangent_and_segment_angle(2,BC,BJE,H)"
] | {"START": ["circle_property_circular_power_tangent_and_segment_angle(2,BC,BJE,H)"]} | |
671 | YimingHe_2023-03-12 | Geometry3k-688 | 5 | 如图所示，AR=RC，AT=16，CM=7，CT=TB，RM=4，SA=SB。求直线CS的长度。 | As shown in the diagram, AR=RC, AT=16, CM=7, CT=TB, RM=4, SA=SB. Find the length of line CS. | 671.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(ASB)",
"Collinear(CMS)",
"Collinear(AMT)",
"Collinear(RMB)"
] | [
"Equal(LengthOfLine(AR),LengthOfLine(RC))",
"Equal(LengthOfLine(AT),16)",
"Equal(LengthOfLine(CM),7)",
"Equal(LengthOfLine(CT),LengthOfLine(TB))",
"Equal(LengthOfLine(RM),4)",
"Equal(LengthOfLine(SA),LengthOfLine(SB))"
] | [
"Equal(LengthOfLine(AR),LengthOfLine(RC))",
"Equal(LengthOfLine(AT),16)",
"Equal(LengthOfLine(CM),7)",
"Equal(LengthOfLine(CT),LengthOfLine(TB))",
"Equal(LengthOfLine(RM),4)",
"Equal(LengthOfLine(SA),LengthOfLine(SB))"
] | Value(LengthOfLine(CS)) | 21/2 | [
"median_of_triangle_judgment(1,BR,BAC)",
"median_of_triangle_judgment(1,AT,ACB)",
"centroid_of_triangle_judgment_intersection(1,M,CBA,T,R)",
"centroid_of_triangle_property_line_ratio(1,M,CBA,S)",
"line_addition(1,CM,MS)"
] | {"START": ["median_of_triangle_judgment(1,BR,BAC)", "median_of_triangle_judgment(1,AT,ACB)", "line_addition(1,CM,MS)"], "centroid_of_triangle_judgment_intersection(1,M,CBA,T,R)": ["centroid_of_triangle_property_line_ratio(1,M,CBA,S)"], "median_of_triangle_judgment(1,AT,ACB)": ["centroid_of_triangle_judgment_intersectio... | |
672 | JiaZou_2023-04-09 | Geometry3k-689 | 1 | 如图所示，∠WVU=34°，弧BCX的角度为128，⌒BWU的角度为x。求x的值。 | As shown in the diagram, ∠WVU=34°, the measure of arc BCX is 128, the measure of ⌒BWU is x. Find the value of x. | 672.png | [
"Shape(WV,VU,BWU)",
"Shape(WX,BXW)",
"Shape(CU,BUC)",
"Shape(BWU,UC,BCX,XW)",
"Collinear(VWX)",
"Collinear(VUC)",
"Cocircular(B,WUCX)"
] | [
"Equal(MeasureOfAngle(WVU),34)",
"Equal(MeasureOfArc(BCX),128)",
"Equal(MeasureOfArc(BWU),x)"
] | [
"Equal(MeasureOfAngle(WVU),34)",
"Equal(MeasureOfArc(BCX),128)",
"Equal(MeasureOfArc(BWU),x)"
] | Value(x) | 60 | [
"circle_property_circular_power_segment_and_segment_angle(1,VWX,VUC,B)"
] | {"START": ["circle_property_circular_power_segment_and_segment_angle(1,VWX,VUC,B)"]} | |
673 | JiaZou_2023-04-09 | Geometry3k-690 | 5 | 如图所示，NM=9，NP=10，QM=8，QP=7，WX=4，QPNM相似于WZYX。求WZYX的周长。 | As shown in the diagram, NM=9, NP=10, QM=8, QP=7, WX=4, QPNM is similar to WZYX. Find the perimeter of quadrilateral WZYX. | 673.png | [
"Shape(WZ,ZY,YX,XW)",
"Shape(NM,MQ,QP,PN)"
] | [
"Equal(LengthOfLine(NM),9)",
"Equal(LengthOfLine(NP),10)",
"Equal(LengthOfLine(QM),8)",
"Equal(LengthOfLine(QP),7)",
"Equal(LengthOfLine(WX),4)",
"SimilarBetweenQuadrilateral(QPNM,WZYX)"
] | [
"Equal(LengthOfLine(NM),9)",
"Equal(LengthOfLine(NP),10)",
"Equal(LengthOfLine(QM),8)",
"Equal(LengthOfLine(QP),7)",
"Equal(LengthOfLine(WX),4)"
] | Value(PerimeterOfQuadrilateral(WZYX)) | 17 | [
"similar_quadrilateral_property_line_ratio(1,QPNM,WZYX)",
"similar_quadrilateral_property_line_ratio(1,PNMQ,ZYXW)",
"similar_quadrilateral_property_line_ratio(1,NMQP,YXWZ)",
"similar_quadrilateral_property_line_ratio(1,MQPN,XWZY)",
"quadrilateral_perimeter_formula(1,WZYX)"
] | {"START": ["similar_quadrilateral_property_line_ratio(1,QPNM,WZYX)", "similar_quadrilateral_property_line_ratio(1,PNMQ,ZYXW)", "similar_quadrilateral_property_line_ratio(1,NMQP,YXWZ)", "similar_quadrilateral_property_line_ratio(1,MQPN,XWZY)", "quadrilateral_perimeter_formula(1,WZYX)"]} | |
674 | JiaZou_2023-04-09 | Geometry3k-691 | 1 | 如图所示，QR=20，TS=12，∠QRS=45°，∠STQ=120°，AB是四边形TQRS的中位线，四边形QRST是梯形。求直线AB的长度。 | As shown in the diagram, QR=20, TS=12, ∠QRS=45°, ∠STQ=120°, the midsegment of TQRS is AB, QT and RS are the parallel sides of trapezoid QRST. Find the length of line AB. | 674.png | [
"Shape(TA,AB,BS,ST)",
"Shape(AQ,QR,RB,BA)",
"Collinear(TAQ)",
"Collinear(SBR)"
] | [
"Equal(LengthOfLine(QR),20)",
"Equal(LengthOfLine(TS),12)",
"Equal(MeasureOfAngle(QRS),45)",
"Equal(MeasureOfAngle(STQ),120)",
"IsMidsegmentOfQuadrilateral(AB,TQRS)",
"Trapezoid(QRST)"
] | [
"Equal(LengthOfLine(QR),20)",
"Equal(LengthOfLine(TS),12)",
"Equal(MeasureOfAngle(QRS),45)",
"Equal(MeasureOfAngle(STQ),120)"
] | Value(LengthOfLine(AB)) | 16 | [
"midsegment_of_quadrilateral_property_length(1,AB,TQRS)"
] | {"START": ["midsegment_of_quadrilateral_property_length(1,AB,TQRS)"]} | |
675 | JiaZou_2023-04-09 | Geometry3k-692 | 6 | 如图所示，BC=33，DE=10，∠CDE=45°，四边形CDAB是▱，CE⊥AE。求四边形CDAB的面积。 | As shown in the diagram, BC=33, DE=10, ∠CDE=45°, quadrilateral CDAB is a parallelogram, CE is perpendicular to AE. Find the area of quadrilateral CDAB. | 675.png | [
"Shape(CD,DE,EC)",
"Shape(CE,EA,AB,BC)",
"Collinear(DEA)"
] | [
"Equal(LengthOfLine(BC),33)",
"Equal(LengthOfLine(DE),10)",
"Equal(MeasureOfAngle(CDE),45)",
"Parallelogram(CDAB)",
"PerpendicularBetweenLine(CE,AE)"
] | [
"Equal(LengthOfLine(BC),33)",
"Equal(LengthOfLine(DE),10)",
"Equal(MeasureOfAngle(CDE),45)",
"PerpendicularBetweenLine(CE,AE)"
] | Value(AreaOfQuadrilateral(CDAB)) | 330 | [
"adjacent_complementary_angle(1,DEC,CEA)",
"triangle_property_angle_sum(1,DEC)",
"isosceles_triangle_judgment_angle_equal(1,ECD)",
"altitude_of_quadrilateral_judgment_left_vertex(1,CE,CDAB)",
"parallelogram_property_opposite_line_equal(1,BCDA)",
"parallelogram_area_formula_common(1,CDAB)"
] | {"START": ["adjacent_complementary_angle(1,DEC,CEA)", "triangle_property_angle_sum(1,DEC)", "parallelogram_property_opposite_line_equal(1,BCDA)", "parallelogram_area_formula_common(1,CDAB)"], "adjacent_complementary_angle(1,DEC,CEA)": ["altitude_of_quadrilateral_judgment_left_vertex(1,CE,CDAB)", "isosceles_triangle_jud... | |
676 | JiaZou_2023-04-09 | Geometry3k-693 | 1 | 如图所示，∠CGH=42°，∠DGC=3*x°，∠GCD=z°，∠GHC=y°，∠HCG=48°，GD平行于HC，HG∥CD。求y的值。 | As shown in the diagram, ∠CGH=42°, ∠DGC=3*x°, ∠GCD=z°, ∠GHC=y°, ∠HCG=48°, GD is parallel to HC, HG∥CD. Find the value of y. | 676.png | [
"Shape(GH,HC,CG)",
"Shape(CD,DG,GC)"
] | [
"Equal(MeasureOfAngle(CGH),42)",
"Equal(MeasureOfAngle(DGC),3*x)",
"Equal(MeasureOfAngle(GCD),z)",
"Equal(MeasureOfAngle(GHC),y)",
"Equal(MeasureOfAngle(HCG),48)",
"ParallelBetweenLine(GD,HC)",
"ParallelBetweenLine(HG,CD)"
] | [
"Equal(MeasureOfAngle(CGH),42)",
"Equal(MeasureOfAngle(DGC),3*x)",
"Equal(MeasureOfAngle(GCD),z)",
"Equal(MeasureOfAngle(GHC),y)",
"Equal(MeasureOfAngle(HCG),48)",
"ParallelBetweenLine(GD,HC)",
"ParallelBetweenLine(HG,CD)"
] | Value(y) | 90 | [
"triangle_property_angle_sum(1,GHC)"
] | {"START": ["triangle_property_angle_sum(1,GHC)"]} | |
677 | YimingHe_2023-03-12 | Geometry3k-694 | 3 | 如图所示，AB=4*y-2，AB=AC，AC=2*y+2，∠BCA=6*x+8°，∠CAB=80°。求x的值。 | As shown in the diagram, AB=4*y-2, AB=AC, AC=2*y+2, ∠BCA=6*x+8°, ∠CAB=80°. Find the value of x. | 677.png | [
"Shape(AB,BC,CA)"
] | [
"Equal(LengthOfLine(AB),4*y-2)",
"Equal(LengthOfLine(AB),LengthOfLine(AC))",
"Equal(LengthOfLine(AC),2*y+2)",
"Equal(MeasureOfAngle(BCA),6*x+8)",
"Equal(MeasureOfAngle(CAB),80)"
] | [
"Equal(LengthOfLine(AB),4*y-2)",
"Equal(LengthOfLine(AB),LengthOfLine(AC))",
"Equal(LengthOfLine(AC),2*y+2)",
"Equal(MeasureOfAngle(BCA),6*x+8)",
"Equal(MeasureOfAngle(CAB),80)"
] | Value(x) | 7 | [
"isosceles_triangle_judgment_line_equal(1,ABC)",
"isosceles_triangle_property_angle_equal(1,ABC)",
"triangle_property_angle_sum(1,ABC)"
] | {"START": ["isosceles_triangle_judgment_line_equal(1,ABC)", "triangle_property_angle_sum(1,ABC)"], "isosceles_triangle_judgment_line_equal(1,ABC)": ["isosceles_triangle_property_angle_equal(1,ABC)"]} | |
678 | YimingHe_2023-03-12 | Geometry3k-695 | 3 | 如图所示，∠ABE=57°，∠BCE=42°，∠EAB=28°，∠ECD=36°。求∠CEB的大小。 | As shown in the diagram, ∠ABE=57°, ∠BCE=42°, ∠EAB=28°, ∠ECD=36°. Find the measure of ∠CEB. | 678.png | [
"Shape(DE,EC,CD)",
"Shape(EA,AB,BE)",
"Shape(EB,BC,CE)",
"Collinear(AEC)",
"Collinear(DEB)"
] | [
"Equal(MeasureOfAngle(ABE),57)",
"Equal(MeasureOfAngle(BCE),42)",
"Equal(MeasureOfAngle(EAB),28)",
"Equal(MeasureOfAngle(ECD),36)"
] | [
"Equal(MeasureOfAngle(ABE),57)",
"Equal(MeasureOfAngle(BCE),42)",
"Equal(MeasureOfAngle(EAB),28)",
"Equal(MeasureOfAngle(ECD),36)"
] | Value(MeasureOfAngle(CEB)) | 85 | [
"triangle_property_angle_sum(1,EBC)",
"triangle_property_angle_sum(1,ABC)",
"angle_addition(1,ABE,EBC)"
] | {"START": ["triangle_property_angle_sum(1,EBC)", "triangle_property_angle_sum(1,ABC)", "angle_addition(1,ABE,EBC)"]} | |
679 | YimingHe_2023-03-12 | Geometry3k-696 | 1 | 如图所示，AB=y，AC=x，BC=20，∠ACB=60°，BA⊥CA。求y的值。 | As shown in the diagram, AB=y, AC=x, BC=20, ∠ACB=60°, BA⊥CA. Find the value of y. | 679.png | [
"Shape(BA,AC,CB)"
] | [
"Equal(LengthOfLine(AB),y)",
"Equal(LengthOfLine(AC),x)",
"Equal(LengthOfLine(BC),20)",
"Equal(MeasureOfAngle(ACB),60)",
"PerpendicularBetweenLine(BA,CA)"
] | [
"Equal(LengthOfLine(AB),y)",
"Equal(LengthOfLine(AC),x)",
"Equal(LengthOfLine(BC),20)",
"Equal(MeasureOfAngle(ACB),60)",
"PerpendicularBetweenLine(BA,CA)"
] | Value(y) | 10*sqrt(3) | [
"sine_theorem(1,BAC)"
] | {"START": ["sine_theorem(1,BAC)"]} | |
680 | JiaZou_2023-04-09 | Geometry3k-697 | 1 | 如图所示，KL=3*y，KN=36，LJ=7，LM=9*x，NJ=y+15，KNML是▱。求y的值。 | As shown in the diagram, KL=3*y, KN=36, LJ=7, LM=9*x, NJ=y+15, KL and NM are opposite sides of the parallelogram KNML. Find the value of y. | 680.png | [
"Shape(KN,NJ,JK)",
"Shape(JN,NM,MJ)",
"Shape(JL,LK,KJ)",
"Shape(JM,ML,LJ)",
"Collinear(KJM)",
"Collinear(NJL)"
] | [
"Equal(LengthOfLine(KL),3*y)",
"Equal(LengthOfLine(KN),36)",
"Equal(LengthOfLine(LJ),7)",
"Equal(LengthOfLine(LM),9*x)",
"Equal(LengthOfLine(NJ),y+15)",
"Parallelogram(KNML)"
] | [
"Equal(LengthOfLine(KL),3*y)",
"Equal(LengthOfLine(KN),36)",
"Equal(LengthOfLine(LJ),7)",
"Equal(LengthOfLine(LM),9*x)",
"Equal(LengthOfLine(NJ),y+15)"
] | Value(y) | -8 | [
"parallelogram_property_diagonal_bisection(1,NMLK,J)"
] | {"START": ["parallelogram_property_diagonal_bisection(1,NMLK,J)"]} | |
681 | JiaZou_2023-04-09 | Geometry3k-698 | 3 | 如图所示，∠SVT=75°，∠TVP=72°，圆V的圆心为V，RV⊥SV。求⌒VTQ的角度。 | As shown in the diagram, ∠SVT=75°, ∠TVP=72°, V is the center of circle V, RV⊥SV. Find the measure of ⌒VTQ. | 681.png | [
"Shape(VR,VRQ,QV)",
"Shape(VS,VSR,RV)",
"Shape(VT,VTS,SV)",
"Shape(VP,VPT,TV)",
"Shape(VQ,VQP,PV)",
"Collinear(QVS)",
"Cocircular(V,SRQPT)"
] | [
"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(VTQ)) | 255 | [
"flat_angle(1,QVS)",
"angle_addition(1,QVS,SVT)",
"arc_property_center_angle(1,VTQ,V)"
] | {"START": ["flat_angle(1,QVS)", "angle_addition(1,QVS,SVT)", "arc_property_center_angle(1,VTQ,V)"]} | |
682 | JiaZou_2023-04-09 | Geometry3k-699 | 1 | 如图所示，OW=x-9，OY=x，XO=x+4，ZO=x-12。求x的值。 | As shown in the diagram, OW=x-9, OY=x, XO=x+4, ZO=x-12. Find the value of x. | 682.png | [
"Shape(OZ,AZW,WO)",
"Shape(OW,AWX,XA,AO)",
"Shape(OA,AX,AXY,YO)",
"Shape(OY,OYZ,ZO)",
"Collinear(XAOZ)",
"Collinear(YOW)",
"Cocircular(A,WXYZ)"
] | [
"Equal(LengthOfLine(OW),x-9)",
"Equal(LengthOfLine(OY),x)",
"Equal(LengthOfLine(XO),x+4)",
"Equal(LengthOfLine(ZO),x-12)"
] | [
"Equal(LengthOfLine(OW),x-9)",
"Equal(LengthOfLine(OY),x)",
"Equal(LengthOfLine(XO),x+4)",
"Equal(LengthOfLine(ZO),x-12)"
] | Value(x) | 48 | [
"circle_property_circular_power_chord_and_chord(1,XOZ,YOW,A)"
] | {"START": ["circle_property_circular_power_chord_and_chord(1,XOZ,YOW,A)"]} | |
683 | JiaZou_2023-04-09 | Geometry3k-700 | 7 | 如图所示，AB=6，AE=9，BC=4，EB∥DC。求直线ED的长度。 | As shown in the diagram, AB=6, AE=9, BC=4, EB is parallel to DC. Find the length of line ED. | 683.png | [
"Shape(BA,AE,EB)",
"Shape(BE,ED,DC,CB)",
"Collinear(ABC)",
"Collinear(AED)"
] | [
"Equal(LengthOfLine(AB),6)",
"Equal(LengthOfLine(AE),9)",
"Equal(LengthOfLine(BC),4)",
"ParallelBetweenLine(EB,DC)"
] | [
"Equal(LengthOfLine(AB),6)",
"Equal(LengthOfLine(AE),9)",
"Equal(LengthOfLine(BC),4)",
"ParallelBetweenLine(EB,DC)"
] | Value(LengthOfLine(ED)) | 6 | [
"parallel_property_corresponding_angle(1,EB,DC,A)",
"parallel_property_corresponding_angle(2,CD,BE,A)",
"similar_triangle_judgment_aa(1,ADC,AEB)",
"line_addition(1,AB,BC)",
"line_addition(1,AE,ED)",
"similar_triangle_property_line_ratio(1,DCA,EBA)",
"similar_triangle_property_line_ratio(1,CAD,BAE)"
] | {"START": ["parallel_property_corresponding_angle(1,EB,DC,A)", "parallel_property_corresponding_angle(2,CD,BE,A)", "line_addition(1,AB,BC)", "line_addition(1,AE,ED)"], "parallel_property_corresponding_angle(1,EB,DC,A)": ["similar_triangle_judgment_aa(1,ADC,AEB)"], "parallel_property_corresponding_angle(2,CD,BE,A)": ["s... | |
684 | JiaZou_2023-04-09 | Geometry3k-701 | 1 | 如图所示，MN=3*x-4，NQ=15.4，PN=2*y+5，PQ=11.1，RM=17.9，RP=20，RQ=3*z-3，∠MRQ=38°，∠NQP=83°，∠QNM=33°，MRPN是平行四边形。求∠NRP的大小。 | As shown in the diagram, MN=3*x-4, NQ=15.4, PN=2*y+5, PQ=11.1, RM=17.9, RP=20, RQ=3*z-3, ∠MRQ=38°, ∠NQP=83°, ∠QNM=33°, MRPN is a ▱. Find the measure of ∠NRP. | 684.png | [
"Shape(QN,NM,MQ)",
"Shape(QM,MR,RQ)",
"Shape(QR,RP,PQ)",
"Shape(QP,PN,NQ)",
"Collinear(MQP)",
"Collinear(RQN)"
] | [
"Equal(LengthOfLine(MN),3*x-4)",
"Equal(LengthOfLine(NQ),15.4)",
"Equal(LengthOfLine(PN),2*y+5)",
"Equal(LengthOfLine(PQ),11.1)",
"Equal(LengthOfLine(RM),17.9)",
"Equal(LengthOfLine(RP),20)",
"Equal(LengthOfLine(RQ),3*z-3)",
"Equal(MeasureOfAngle(MRQ),38)",
"Equal(MeasureOfAngle(NQP),83)",
"Equal(... | [
"Equal(LengthOfLine(MN),3*x-4)",
"Equal(LengthOfLine(MN),3*x-4)",
"Equal(LengthOfLine(NQ),15.4)",
"Equal(LengthOfLine(PN),2*y+5)",
"Equal(LengthOfLine(PQ),11.1)",
"Equal(LengthOfLine(RM),17.9)",
"Equal(LengthOfLine(RP),20)",
"Equal(LengthOfLine(RQ),3*z-3)",
"Equal(MeasureOfAngle(MRQ),38)",
"Equal(... | Value(MeasureOfAngle(NRP)) | 33 | [
"parallel_property_alternate_interior_angle(2,MN,RP)"
] | {"START": ["parallel_property_alternate_interior_angle(2,MN,RP)"]} | |
685 | YimingHe_2023-03-12 | Geometry3k-702 | 0 | 如图所示，WZ=25，XY=YZ，YZ=22，WY垂直于XY。求直线XY的长度。 | As shown in the diagram, WZ=25, XY=YZ, YZ=22, WY⊥XY. Find the length of line XY. | 685.png | [
"Shape(XW,WY,YX)",
"Shape(WZ,ZY,YW)",
"Collinear(DWY)",
"Collinear(XYZ)",
"Collinear(WYT)"
] | [
"Equal(LengthOfLine(WZ),25)",
"Equal(LengthOfLine(XY),LengthOfLine(YZ))",
"Equal(LengthOfLine(YZ),22)",
"PerpendicularBetweenLine(WY,XY)"
] | [
"Equal(LengthOfLine(WZ),25)",
"Equal(LengthOfLine(XY),LengthOfLine(YZ))",
"Equal(LengthOfLine(YZ),22)",
"PerpendicularBetweenLine(WY,XY)"
] | Value(LengthOfLine(XY)) | 22 | [] | {"START": []} | |
686 | JiaZou_2023-04-09 | Geometry3k-703 | 8 | 如图所示，AB=DC，AC=188，AD=BC，BD=214，∠BPC=70°，P是线段AC的中点。求ADCB的周长。 | As shown in the diagram, AB=DC, AC=188, AD=BC, BD=214, ∠BPC=70°, P bisects segment AC. Find the perimeter of ADCB. | 686.png | [
"Shape(AD,DP,PA)",
"Shape(PD,DC,CP)",
"Shape(PC,CB,BP)",
"Shape(PB,BA,AP)",
"Collinear(APC)",
"Collinear(DPB)"
] | [
"Equal(LengthOfLine(AB),LengthOfLine(DC))",
"Equal(LengthOfLine(AC),188)",
"Equal(LengthOfLine(AD),LengthOfLine(BC))",
"Equal(LengthOfLine(BD),214)",
"Equal(MeasureOfAngle(BPC),70)",
"IsMidpointOfLine(P,AC)"
] | [
"Equal(LengthOfLine(AB),LengthOfLine(DC))",
"Equal(LengthOfLine(AD),LengthOfLine(BC))"
] | Value(PerimeterOfQuadrilateral(ADCB)) | 2*sqrt(20285-20116*sin(pi/9))+2*sqrt(20116*sin(pi/9)+20285) | [
"parallelogram_judgment_equal_and_equal(1,ADCB)",
"parallelogram_property_diagonal_bisection(1,DCBA,P)",
"adjacent_complementary_angle(1,APB,BPC)",
"line_addition(1,AP,PC)",
"line_addition(1,DP,PB)",
"cosine_theorem(1,PCB)",
"cosine_theorem(1,PBA)",
"quadrilateral_perimeter_formula(1,ADCB)"
] | {"START": ["parallelogram_judgment_equal_and_equal(1,ADCB)", "adjacent_complementary_angle(1,APB,BPC)", "line_addition(1,AP,PC)", "line_addition(1,DP,PB)", "cosine_theorem(1,PCB)", "cosine_theorem(1,PBA)", "quadrilateral_perimeter_formula(1,ADCB)"], "parallelogram_judgment_equal_and_equal(1,ADCB)": ["parallelogram_prop... | |
687 | JiaZou_2023-04-09 | Geometry3k-704 | 1 | 如图所示，KJ=3*f-6，LM=2*f+8，∠JML=3*d-2°，∠KJM=56°，JMLK是平行四边形。求f的值。 | As shown in the diagram, KJ=3*f-6, LM=2*f+8, ∠JML=3*d-2°, ∠KJM=56°, JMLK is a ▱. Find the value of f. | 687.png | [
"Shape(JM,ML,LK,KJ)"
] | [
"Equal(LengthOfLine(KJ),3*f-6)",
"Equal(LengthOfLine(LM),2*f+8)",
"Equal(MeasureOfAngle(JML),3*d-2)",
"Equal(MeasureOfAngle(KJM),56)",
"Parallelogram(JMLK)"
] | [
"Equal(LengthOfLine(KJ),3*f-6)",
"Equal(LengthOfLine(LM),2*f+8)",
"Equal(MeasureOfAngle(JML),3*d-2)",
"Equal(MeasureOfAngle(KJM),56)"
] | Value(f) | 14 | [
"parallelogram_property_opposite_line_equal(1,KJML)"
] | {"START": ["parallelogram_property_opposite_line_equal(1,KJML)"]} | |
688 | YimingHe_2023-03-12 | Geometry3k-705 | 1 | 如图所示，AB=12，AC=h，∠ABC=30°，BC垂直于AC。求h的值。 | As shown in the diagram, AB=12, AC=h, ∠ABC=30°, BC⊥AC. Find the value of h. | 688.png | [
"Shape(AB,BC,CA)"
] | [
"Equal(LengthOfLine(AB),12)",
"Equal(LengthOfLine(AC),h)",
"Equal(MeasureOfAngle(ABC),30)",
"PerpendicularBetweenLine(BC,AC)"
] | [
"Equal(LengthOfLine(AB),12)",
"Equal(LengthOfLine(AC),h)",
"Equal(MeasureOfAngle(ABC),30)",
"PerpendicularBetweenLine(BC,AC)"
] | Value(h) | 6 | [
"sine_theorem(1,ABC)"
] | {"START": ["sine_theorem(1,ABC)"]} | |
689 | JiaZou_2023-04-09 | Geometry3k-706 | 2 | 如图所示，∠ACD=50°，∠BFE=56°，∠CDE=78°，∠FGA=120°。求∠EAG的大小。 | As shown in the diagram, ∠ACD=50°, ∠BFE=56°, ∠CDE=78°, ∠FGA=120°. Find the measure of ∠EAG. | 689.png | [
"Shape(CD,DA,AC)",
"Shape(EA,AG,GA)",
"Shape(GF,FB,BG)",
"Collinear(CAGBH)",
"Collinear(DAE)",
"Collinear(EGF)"
] | [
"Equal(MeasureOfAngle(ACD),50)",
"Equal(MeasureOfAngle(BFE),56)",
"Equal(MeasureOfAngle(CDE),78)",
"Equal(MeasureOfAngle(FGA),120)"
] | [
"Equal(MeasureOfAngle(ACD),50)",
"Equal(MeasureOfAngle(BFE),56)",
"Equal(MeasureOfAngle(CDE),78)",
"Equal(MeasureOfAngle(FGA),120)"
] | Value(MeasureOfAngle(EAG)) | 52 | [
"triangle_property_angle_sum(1,CDA)",
"vertical_angle(1,DAC,EAG)"
] | {"START": ["triangle_property_angle_sum(1,CDA)", "vertical_angle(1,DAC,EAG)"]} | |
690 | YimingHe_2023-03-12 | Geometry3k-707 | 3 | 如图所示，∠EBK=120°，∠HKB=54°，∠JKH=36°，BK平行于HJ。求∠BHK的大小。 | As shown in the diagram, ∠EBK=120°, ∠HKB=54°, ∠JKH=36°, BK is parallel to HJ. Find the measure of ∠BHK. | 690.png | [
"Shape(KB,BH,HK)",
"Shape(KH,HJ,JK)",
"Shape(EB,BK)",
"Collinear(EBH)",
"Collinear(BHD)"
] | [
"Equal(MeasureOfAngle(EBK),120)",
"Equal(MeasureOfAngle(HKB),54)",
"Equal(MeasureOfAngle(JKH),36)",
"ParallelBetweenLine(BK,HJ)"
] | [
"Equal(MeasureOfAngle(EBK),120)",
"Equal(MeasureOfAngle(HKB),54)",
"Equal(MeasureOfAngle(JKH),36)",
"ParallelBetweenLine(BK,HJ)"
] | Value(MeasureOfAngle(BHK)) | 66 | [
"flat_angle(1,EBH)",
"angle_addition(1,EBK,KBH)",
"triangle_property_angle_sum(1,KBH)"
] | {"START": ["flat_angle(1,EBH)", "angle_addition(1,EBK,KBH)", "triangle_property_angle_sum(1,KBH)"]} | |
691 | YimingHe_2023-03-12 | Geometry3k-709 | 1 | 如图所示，AB=17，BC=8，CA=15，BC⊥AC。求tan(CA)的值。 | As shown in the diagram, AB=17, BC=8, CA=15, BC⊥AC. Find the value of tan(CA). | 691.png | [
"Shape(BC,CA,AB)"
] | [
"Equal(LengthOfLine(AB),17)",
"Equal(LengthOfLine(BC),8)",
"Equal(LengthOfLine(CA),15)",
"PerpendicularBetweenLine(BC,AC)"
] | [
"Equal(LengthOfLine(AB),17)",
"Equal(LengthOfLine(BC),8)",
"Equal(LengthOfLine(CA),15)",
"PerpendicularBetweenLine(BC,AC)"
] | Value(Tan(MeasureOfAngle(CAB))) | 8/15 | [
"cosine_theorem(1,ABC)"
] | {"START": ["cosine_theorem(1,ABC)"]} | |
692 | YimingHe_2023-03-12 | Geometry3k-711 | 6 | 如图所示，AD=BD，AF=CF，CA=15，CE=EB，EF=9，∠BDE=82°。求直线DB的长度。 | As shown in the diagram, AD=BD, AF=CF, CA=15, CE=EB, EF=9, ∠BDE=82°. Find the length of line DB. | 692.png | [
"Shape(FC,CE,EF)",
"Shape(AF,FE,ED,DA)",
"Shape(DE,EB,BD)",
"Collinear(AFC)",
"Collinear(CEB)",
"Collinear(ADB)"
] | [
"Equal(LengthOfLine(AD),LengthOfLine(BD))",
"Equal(LengthOfLine(AF),LengthOfLine(CF))",
"Equal(LengthOfLine(CA),15)",
"Equal(LengthOfLine(CE),LengthOfLine(EB))",
"Equal(LengthOfLine(EF),9)",
"Equal(MeasureOfAngle(BDE),82)"
] | [
"Equal(LengthOfLine(AD),LengthOfLine(BD))",
"Equal(LengthOfLine(AF),LengthOfLine(CF))",
"Equal(LengthOfLine(CA),15)",
"Equal(LengthOfLine(CE),LengthOfLine(EB))",
"Equal(LengthOfLine(EF),9)",
"Equal(MeasureOfAngle(BDE),82)"
] | Value(LengthOfLine(DB)) | 9 | [
"line_addition(1,AF,FC)",
"line_addition(1,CE,EB)",
"line_addition(1,AD,DB)",
"similar_triangle_judgment_sas(1,CEF,CBA)",
"similar_triangle_property_line_ratio(1,EFC,BAC)",
"similar_triangle_property_line_ratio(1,CEF,CBA)"
] | {"START": ["line_addition(1,AF,FC)", "line_addition(1,CE,EB)", "line_addition(1,AD,DB)"], "line_addition(1,AF,FC)": ["similar_triangle_judgment_sas(1,CEF,CBA)"], "line_addition(1,CE,EB)": ["similar_triangle_judgment_sas(1,CEF,CBA)"], "similar_triangle_judgment_sas(1,CEF,CBA)": ["similar_triangle_property_line_ratio(1,C... | |
693 | YimingHe_2023-03-12 | Geometry3k-712 | 2 | 如图所示，AC=6，∠CAB=45°，BC垂直于AC。求直线AB的长度。 | As shown in the diagram, AC=6, ∠CAB=45°, BC⊥AC. Find the length of line AB. | 693.png | [
"Shape(CA,AB,BC)"
] | [
"Equal(LengthOfLine(AC),6)",
"Equal(MeasureOfAngle(CAB),45)",
"PerpendicularBetweenLine(BC,AC)"
] | [
"Equal(LengthOfLine(AC),6)",
"Equal(MeasureOfAngle(CAB),45)",
"PerpendicularBetweenLine(BC,AC)"
] | Value(LengthOfLine(AB)) | 6*sqrt(2) | [
"triangle_property_angle_sum(1,BCA)",
"sine_theorem(1,ABC)"
] | {"START": ["triangle_property_angle_sum(1,BCA)", "sine_theorem(1,ABC)"]} | |
694 | YimingHe_2023-03-12 | Geometry3k-713 | 3 | 如图所示，MQ=18，QP=18，∠PNQ=4*x-8°，∠QNM=3*x+5°，NM⊥QM，QP⊥NP。求∠PNM的大小。 | As shown in the diagram, MQ=18, QP=18, ∠PNQ=4*x-8°, ∠QNM=3*x+5°, NM⊥QM, QP⊥NP. Find the measure of ∠PNM. | 694.png | [
"Shape(NM,MQ,QN)",
"Shape(NQ,QP,PN)",
"Collinear(BMN)",
"Collinear(CPN)"
] | [
"Equal(LengthOfLine(MQ),18)",
"Equal(LengthOfLine(QP),18)",
"Equal(MeasureOfAngle(PNQ),4*x-8)",
"Equal(MeasureOfAngle(QNM),3*x+5)",
"PerpendicularBetweenLine(NM,QM)",
"PerpendicularBetweenLine(QP,NP)"
] | [
"Equal(LengthOfLine(MQ),18)",
"Equal(LengthOfLine(QP),18)",
"Equal(MeasureOfAngle(PNQ),4*x-8)",
"Equal(MeasureOfAngle(QNM),3*x+5)",
"PerpendicularBetweenLine(NM,QM)",
"PerpendicularBetweenLine(QP,NP)"
] | Value(MeasureOfAngle(PNM)) | 88 | [
"mirror_congruent_triangle_judgment_hl(1,NMQ,NQP)",
"mirror_congruent_triangle_property_angle_equal(1,NMQ,NQP)",
"angle_addition(1,PNQ,QNM)"
] | {"START": ["mirror_congruent_triangle_judgment_hl(1,NMQ,NQP)", "angle_addition(1,PNQ,QNM)"], "mirror_congruent_triangle_judgment_hl(1,NMQ,NQP)": ["mirror_congruent_triangle_property_angle_equal(1,NMQ,NQP)"]} | |
695 | JiaZou_2023-04-09 | Geometry3k-714 | 3 | 如图所示，∠JQR=131°，QR∥TS，TQ平行于SR。求∠TSR的大小。 | As shown in the diagram, ∠JQR=131°, QR is parallel to TS, TQ is parallel to SR. Find the measure of ∠TSR. | 695.png | [
"Shape(JQ,QR)",
"Shape(QR,RH)",
"Shape(QT,TS,SR,RQ)",
"Shape(ST,TC)",
"Shape(BS,ST)",
"Collinear(JQTC)",
"Collinear(HRSB)"
] | [
"Equal(MeasureOfAngle(JQR),131)",
"ParallelBetweenLine(QR,TS)",
"ParallelBetweenLine(TQ,SR)"
] | [
"Equal(MeasureOfAngle(JQR),131)",
"ParallelBetweenLine(QR,TS)",
"ParallelBetweenLine(TQ,SR)"
] | Value(MeasureOfAngle(TSR)) | 49 | [
"parallelogram_judgment_parallel_and_parallel(1,QTSR)",
"adjacent_complementary_angle(1,JQR,RQT)",
"parallelogram_property_opposite_angle_equal(1,QTSR)"
] | {"START": ["parallelogram_judgment_parallel_and_parallel(1,QTSR)", "adjacent_complementary_angle(1,JQR,RQT)"], "parallelogram_judgment_parallel_and_parallel(1,QTSR)": ["parallelogram_property_opposite_angle_equal(1,QTSR)"]} | |
696 | JiaZou_2023-04-09 | Geometry3k-715 | 5 | 如图所示，AF=2*x，AG=y，BD=x，BF=24，CG=12，DC=9，E是⊙E的圆心，⊙O的切线为DC。求y的值。 | As shown in the diagram, AF=2*x, AG=y, BD=x, BF=24, CG=12, DC=9, the center of circle E is E, the tangent to ⊙E is DC. Find the value of y. | 696.png | [
"Shape(EFB,BF)",
"Shape(BD,DC,EBC)",
"Shape(GA,AF,EGF)",
"Shape(EBC,CG,EGF,FB)",
"Shape(ECG,GC)",
"Collinear(DBFA)",
"Collinear(AGC)",
"Cocircular(E,BCGF)"
] | [
"Equal(LengthOfLine(AF),2*x)",
"Equal(LengthOfLine(AG),y)",
"Equal(LengthOfLine(BD),x)",
"Equal(LengthOfLine(BF),24)",
"Equal(LengthOfLine(CG),12)",
"Equal(LengthOfLine(DC),9)",
"IsCentreOfCircle(E,E)",
"IsTangentOfCircle(DC,E)"
] | [
"Equal(LengthOfLine(AF),2*x)",
"Equal(LengthOfLine(AG),y)",
"Equal(LengthOfLine(BD),x)",
"Equal(LengthOfLine(BF),24)",
"Equal(LengthOfLine(CG),12)",
"Equal(LengthOfLine(DC),9)",
"IsCentreOfCircle(E,E)"
] | Value(y) | -6+6*sqrt(6) | [
"line_addition(1,DB,BF)",
"circle_property_circular_power_tangent_and_segment_line(1,DC,DBF,E)",
"line_addition(1,AF,FB)",
"line_addition(1,AG,GC)",
"circle_property_circular_power_segment_and_segment_line(1,AFB,AGC,E)"
] | {"START": ["line_addition(1,DB,BF)", "circle_property_circular_power_tangent_and_segment_line(1,DC,DBF,E)", "line_addition(1,AF,FB)", "line_addition(1,AG,GC)", "circle_property_circular_power_segment_and_segment_line(1,AFB,AGC,E)"]} | |
697 | YimingHe_2023-03-12 | Geometry3k-716 | 4 | 如图所示，BE=7*sqrt(3)，∠ABC=60°，∠CAB=30°，AE⊥CE，BC垂直于AC。求直线CE的长度。 | As shown in the diagram, BE=7*sqrt(3), ∠ABC=60°, ∠CAB=30°, AE⊥CE, BC⊥AC. Find the length of line CE. | 697.png | [
"Shape(BC,CE,EB)",
"Shape(EC,CA,AE)",
"Collinear(BEA)"
] | [
"Equal(LengthOfLine(BE),7*sqrt(3))",
"Equal(MeasureOfAngle(ABC),60)",
"Equal(MeasureOfAngle(CAB),30)",
"PerpendicularBetweenLine(AE,CE)",
"PerpendicularBetweenLine(BC,AC)"
] | [
"Equal(LengthOfLine(BE),7*sqrt(3))",
"Equal(MeasureOfAngle(ABC),60)",
"Equal(MeasureOfAngle(CAB),30)",
"PerpendicularBetweenLine(AE,CE)",
"PerpendicularBetweenLine(BC,AC)"
] | Value(LengthOfLine(CE)) | 21 | [
"adjacent_complementary_angle(1,AEC,CEB)",
"triangle_property_angle_sum(1,CEB)",
"sine_theorem(1,CEB)",
"sine_theorem(1,BCE)"
] | {"START": ["adjacent_complementary_angle(1,AEC,CEB)", "triangle_property_angle_sum(1,CEB)", "sine_theorem(1,CEB)", "sine_theorem(1,BCE)"]} | |
698 | YimingHe_2023-03-12 | Geometry3k-717 | 5 | 如图所示，KN=9，LN=16，PM=Mul(LengthOfLine(KP),2)，PR平行于KL，KN垂直于MN，LM垂直于KM。求直线KP的长度。 | As shown in the diagram, KN=9, LN=16, PM=Mul(LengthOfLine(KP),2), PR∥KL, KN is perpendicular to MN, LM⊥KM. Find the length of line KP. | 698.png | [
"Shape(LR,RQ,QN,NL)",
"Shape(RM,MQ,QR)",
"Shape(QM,MP,PQ)",
"Shape(NQ,QP,PK,KN)",
"Collinear(LNK)",
"Collinear(RQP)",
"Collinear(LRM)",
"Collinear(MPK)",
"Collinear(NQM)"
] | [
"Equal(LengthOfLine(KN),9)",
"Equal(LengthOfLine(LN),16)",
"Equal(LengthOfLine(PM),Mul(LengthOfLine(KP),2))",
"ParallelBetweenLine(PR,KL)",
"PerpendicularBetweenLine(KN,MN)",
"PerpendicularBetweenLine(LM,KM)"
] | [
"Equal(LengthOfLine(KN),9)",
"Equal(LengthOfLine(LN),16)",
"Equal(LengthOfLine(PM),Mul(LengthOfLine(KP),2))",
"ParallelBetweenLine(PR,KL)",
"PerpendicularBetweenLine(KN,MN)",
"PerpendicularBetweenLine(LM,KM)"
] | Value(LengthOfLine(KP)) | 5 | [
"mirror_similar_triangle_judgment_aa(1,MKN,LMK)",
"line_addition(1,LN,NK)",
"line_addition(1,MP,PK)",
"mirror_similar_triangle_property_line_ratio(1,MKN,LMK)",
"mirror_similar_triangle_property_line_ratio(1,NMK,MKL)"
] | {"START": ["mirror_similar_triangle_judgment_aa(1,MKN,LMK)", "line_addition(1,LN,NK)", "line_addition(1,MP,PK)"], "mirror_similar_triangle_judgment_aa(1,MKN,LMK)": ["mirror_similar_triangle_property_line_ratio(1,MKN,LMK)", "mirror_similar_triangle_property_line_ratio(1,NMK,MKL)"]} | |
699 | YimingHe_2023-03-12 | Geometry3k-718 | 6 | 如图所示，AB=20，AC=x，AD=10，BC=z，BD=y，CA垂直于BA，DB垂直于CB。求直线CB的长度。 | As shown in the diagram, AB=20, AC=x, AD=10, BC=z, BD=y, CA is perpendicular to BA, DB is perpendicular to CB. Find the length of line CB. | 699.png | [
"Shape(CA,AB,BC)",
"Shape(AD,DB,BA)",
"Collinear(CAD)"
] | [
"Equal(LengthOfLine(AB),20)",
"Equal(LengthOfLine(AC),x)",
"Equal(LengthOfLine(AD),10)",
"Equal(LengthOfLine(BC),z)",
"Equal(LengthOfLine(BD),y)",
"PerpendicularBetweenLine(CA,BA)",
"PerpendicularBetweenLine(DB,CB)"
] | [
"Equal(LengthOfLine(AB),20)",
"Equal(LengthOfLine(AC),x)",
"Equal(LengthOfLine(AD),10)",
"Equal(LengthOfLine(BC),z)",
"Equal(LengthOfLine(BD),y)",
"PerpendicularBetweenLine(CA,BA)",
"PerpendicularBetweenLine(DB,CB)"
] | Value(LengthOfLine(CB)) | 20*sqrt(5) | [
"adjacent_complementary_angle(1,CAB,BAD)",
"right_triangle_judgment_angle(1,BAD)",
"right_triangle_property_pythagorean(1,BAD)",
"mirror_similar_triangle_judgment_aa(1,BAD,CDB)",
"mirror_similar_triangle_property_line_ratio(1,BAD,CDB)",
"mirror_similar_triangle_property_line_ratio(1,DBA,DBC)"
] | {"START": ["adjacent_complementary_angle(1,CAB,BAD)"], "adjacent_complementary_angle(1,CAB,BAD)": ["right_triangle_judgment_angle(1,BAD)", "mirror_similar_triangle_judgment_aa(1,BAD,CDB)"], "mirror_similar_triangle_judgment_aa(1,BAD,CDB)": ["mirror_similar_triangle_property_line_ratio(1,BAD,CDB)", "mirror_similar_trian... | |
700 | JiaZou_2023-04-09 | Geometry3k-719 | 2 | 如图所示，∠WZY=4*x°，∠XWZ=10*x°，∠YXW=120°，XWZY是风筝形。求∠ZYX的大小。 | As shown in the diagram, ∠WZY=4*x°, ∠XWZ=10*x°, ∠YXW=120°, ZW and ZY are one pair of adjacent sides of the kite XWZY. Find the measure of ∠ZYX. | 700.png | [
"Shape(WZ,ZU,UW)",
"Shape(ZY,YU,UZ)",
"Shape(UY,YX,XU)",
"Shape(WU,UX,XW)",
"Collinear(ZUX)",
"Collinear(WUY)"
] | [
"Equal(MeasureOfAngle(WZY),4*x)",
"Equal(MeasureOfAngle(XWZ),10*x)",
"Equal(MeasureOfAngle(YXW),120)",
"Kite(XWZY)"
] | [
"Equal(MeasureOfAngle(WZY),4*x)",
"Equal(MeasureOfAngle(XWZ),10*x)",
"Equal(MeasureOfAngle(YXW),120)",
"Kite(XWZY)"
] | Value(MeasureOfAngle(ZYX)) | 100 | [
"kite_property_opposite_angle_equal(1,XWZY)",
"quadrilateral_property_angle_sum(1,WZYX)"
] | {"START": ["kite_property_opposite_angle_equal(1,XWZY)", "quadrilateral_property_angle_sum(1,WZYX)"]} |
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