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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
701 | JiaZou_2023-04-09 | Geometry3k-720 | 4 | 如图所示，∠GKM=62°，∠HBF=38°，NO平行于MH。求∠JCI的大小。 | As shown in the diagram, ∠GKM=62°, ∠HBF=38°, NO∥MH. Find the measure of ∠JCI. | 701.png | [
"Shape(NC,CJ)",
"Shape(JC,CI)",
"Shape(IC,CO)",
"Shape(KC,CN)",
"Shape(OC,CB)",
"Shape(MK,KC)",
"Shape(CB,BH)",
"Shape(GK,KM)",
"Shape(BK,KG)",
"Shape(FB,BK)",
"Shape(HB,BF)",
"Shape(CK,KB,BC)",
"Collinear(JCBF)",
"Collinear(ICKG)",
"Collinear(NCO)",
"Collinear(MKBH)"
] | [
"Equal(MeasureOfAngle(GKM),62)",
"Equal(MeasureOfAngle(HBF),38)",
"ParallelBetweenLine(NO,MH)"
] | [
"Equal(MeasureOfAngle(GKM),62)",
"Equal(MeasureOfAngle(HBF),38)",
"ParallelBetweenLine(NO,MH)"
] | Value(MeasureOfAngle(JCI)) | 80 | [
"vertical_angle(1,GKM,CKB)",
"vertical_angle(1,KBC,HBF)",
"triangle_property_angle_sum(1,CKB)",
"vertical_angle(1,BCK,JCI)"
] | {"START": ["vertical_angle(1,GKM,CKB)", "vertical_angle(1,KBC,HBF)", "triangle_property_angle_sum(1,CKB)", "vertical_angle(1,BCK,JCI)"]} | |
702 | JiaZou_2023-04-09 | Geometry3k-721 | 5 | 如图所示，KJ=2，LK=4，LP=2，MP=3，PQ=6，RS=6，QK平行于PL，RJ平行于QK，SH平行于RJ。求直线QK的长度。 | As shown in the diagram, KJ=2, LK=4, LP=2, MP=3, PQ=6, RS=6, QK is parallel to PL, RJ∥QK, SH is parallel to RJ. Find the length of line QK. | 702.png | [
"Shape(HS,SR,RJ,JH)",
"Shape(JR,RQ,QK,KJ)",
"Shape(KQ,QP,PL,LK)",
"Shape(LP,PM,ML)",
"Collinear(HJKLM)",
"Collinear(SRQPM)"
] | [
"Equal(LengthOfLine(KJ),2)",
"Equal(LengthOfLine(LK),4)",
"Equal(LengthOfLine(LP),2)",
"Equal(LengthOfLine(MP),3)",
"Equal(LengthOfLine(PQ),6)",
"Equal(LengthOfLine(RS),6)",
"ParallelBetweenLine(QK,PL)",
"ParallelBetweenLine(RJ,QK)",
"ParallelBetweenLine(SH,RJ)"
] | [
"ParallelBetweenLine(QK,PL)",
"ParallelBetweenLine(RJ,QK)",
"ParallelBetweenLine(SH,RJ)"
] | Value(LengthOfLine(QK)) | 6 | [
"parallel_property_corresponding_angle(1,LP,KQ,M)",
"similar_triangle_judgment_aa(1,QMK,PML)",
"line_addition(1,QP,PM)",
"similar_triangle_property_line_ratio(1,KQM,LPM)",
"similar_triangle_property_line_ratio(1,MKQ,MLP)"
] | {"START": ["parallel_property_corresponding_angle(1,LP,KQ,M)", "line_addition(1,QP,PM)"], "parallel_property_corresponding_angle(1,LP,KQ,M)": ["similar_triangle_judgment_aa(1,QMK,PML)"], "similar_triangle_judgment_aa(1,QMK,PML)": ["similar_triangle_property_line_ratio(1,MKQ,MLP)", "similar_triangle_property_line_ratio(... | |
703 | JiaZou_2023-04-09 | Geometry3k-722 | 2 | 如图所示，∠EDF=39°，∠FBA=48°，FC平行于ED，AF⊥BF，DC垂直于FC，FE垂直于DE。求∠FDC的大小。 | As shown in the diagram, ∠EDF=39°, ∠FBA=48°, FC∥ED, AF is perpendicular to BF, DC is perpendicular to FC, FE⊥DE. Find the measure of ∠FDC. | 703.png | [
"Shape(AF,FB,BA)",
"Shape(FE,ED,DF)",
"Shape(FD,DC,CB,BF)",
"Collinear(FBC)"
] | [
"Equal(MeasureOfAngle(EDF),39)",
"Equal(MeasureOfAngle(FBA),48)",
"ParallelBetweenLine(FC,ED)",
"PerpendicularBetweenLine(AF,BF)",
"PerpendicularBetweenLine(DC,FC)",
"PerpendicularBetweenLine(FE,DE)"
] | [
"Equal(MeasureOfAngle(EDF),39)",
"Equal(MeasureOfAngle(FBA),48)",
"ParallelBetweenLine(FC,ED)",
"PerpendicularBetweenLine(AF,BF)",
"PerpendicularBetweenLine(DC,FC)",
"PerpendicularBetweenLine(FE,DE)"
] | Value(MeasureOfAngle(FDC)) | 51 | [
"parallel_property_alternate_interior_angle(1,FC,ED)",
"triangle_property_angle_sum(1,FDC)"
] | {"START": ["parallel_property_alternate_interior_angle(1,FC,ED)", "triangle_property_angle_sum(1,FDC)"]} | |
704 | JiaZou_2023-04-09 | Geometry3k-723 | 3 | 如图所示，NM=9，NP=10，QM=8，QP=7，WX=4，XWZY与MQPN相似。求四边形XWZY的周长。 | As shown in the diagram, NM=9, NP=10, QM=8, QP=7, WX=4, quadrilateral XWZY is similar to quadrilateral MQPN. Find the perimeter of XWZY. | 704.png | [
"Shape(XW,WZ,ZY,YX)",
"Shape(MQ,QP,PN,NM)"
] | [
"Equal(LengthOfLine(NM),9)",
"Equal(LengthOfLine(NP),10)",
"Equal(LengthOfLine(QM),8)",
"Equal(LengthOfLine(QP),7)",
"Equal(LengthOfLine(WX),4)",
"SimilarBetweenQuadrilateral(XWZY,MQPN)"
] | [
"Equal(LengthOfLine(NM),9)",
"Equal(LengthOfLine(NP),10)",
"Equal(LengthOfLine(QM),8)",
"Equal(LengthOfLine(QP),7)",
"Equal(LengthOfLine(WX),4)",
"SimilarBetweenQuadrilateral(XWZY,MQPN)"
] | Value(PerimeterOfQuadrilateral(XWZY)) | 17 | [
"similar_quadrilateral_property_line_ratio(1,XWZY,MQPN)",
"quadrilateral_perimeter_formula(1,MQPN)",
"similar_quadrilateral_property_perimeter_ratio(1,XWZY,MQPN)"
] | {"START": ["similar_quadrilateral_property_line_ratio(1,XWZY,MQPN)", "quadrilateral_perimeter_formula(1,MQPN)", "similar_quadrilateral_property_perimeter_ratio(1,XWZY,MQPN)"]} | |
705 | JiaZou_2023-04-09 | Geometry3k-724 | 4 | 如图所示，∠ACH=x-10°，∠GMO=104°，JO平行于HD。求x的值。 | As shown in the diagram, ∠ACH=x-10°, ∠GMO=104°, JO is parallel to HD. Find the value of x. | 705.png | [
"Shape(GM,MO)",
"Shape(OM,MC)",
"Shape(MC,CD)",
"Shape(DC,CA)",
"Shape(JM,MG)",
"Shape(CM,MJ)",
"Shape(HC,CM)",
"Shape(AC,CH)",
"Collinear(GMCA)",
"Collinear(OMJ)",
"Collinear(DCH)"
] | [
"Equal(MeasureOfAngle(ACH),x-10)",
"Equal(MeasureOfAngle(GMO),104)",
"ParallelBetweenLine(JO,HD)"
] | [
"Equal(MeasureOfAngle(ACH),x-10)",
"Equal(MeasureOfAngle(GMO),104)",
"ParallelBetweenLine(JO,HD)"
] | Value(x) | 114 | [
"parallel_property_collinear_extend(3,JO,HD,M)",
"parallel_property_collinear_extend(3,DH,OM,C)",
"parallel_property_corresponding_angle(1,MO,CD,G)",
"vertical_angle(1,MCD,ACH)"
] | {"START": ["parallel_property_collinear_extend(3,JO,HD,M)", "vertical_angle(1,MCD,ACH)"], "parallel_property_collinear_extend(3,DH,OM,C)": ["parallel_property_corresponding_angle(1,MO,CD,G)"], "parallel_property_collinear_extend(3,JO,HD,M)": ["parallel_property_collinear_extend(3,DH,OM,C)"]} | |
706 | YimingHe_2023-03-12 | Geometry3k-725 | 2 | 如图所示，PA=8，∠PBA=∠CBP，BA⊥PA，PC垂直于BC。求直线CP的长度。 | As shown in the diagram, PA=8, ∠PBA=∠CBP, BA is perpendicular to PA, PC is perpendicular to BC. Find the length of line CP. | 706.png | [
"Shape(BA,AP,PB)",
"Shape(BP,PC,CB)"
] | [
"Equal(LengthOfLine(PA),8)",
"Equal(MeasureOfAngle(PBA),MeasureOfAngle(CBP))",
"PerpendicularBetweenLine(BA,PA)",
"PerpendicularBetweenLine(PC,BC)"
] | [
"Equal(LengthOfLine(PA),8)",
"Equal(MeasureOfAngle(PBA),MeasureOfAngle(CBP))",
"PerpendicularBetweenLine(BA,PA)",
"PerpendicularBetweenLine(PC,BC)"
] | Value(LengthOfLine(CP)) | 8 | [
"mirror_congruent_triangle_judgment_aas(3,PCB,PBA)",
"mirror_congruent_triangle_property_line_equal(1,BPC,BAP)"
] | {"START": ["mirror_congruent_triangle_judgment_aas(3,PCB,PBA)"], "mirror_congruent_triangle_judgment_aas(3,PCB,PBA)": ["mirror_congruent_triangle_property_line_equal(1,BPC,BAP)"]} | |
707 | JiaZou_2023-04-09 | Geometry3k-727 | 4 | 如图所示，∠FJE=75°，GD平行于IM，IM平行于CE。求∠IFB的大小。 | As shown in the diagram, ∠FJE=75°, GD is parallel to IM, IM is parallel to CE. Find the measure of ∠IFB. | 707.png | [
"Shape(LB,BD)",
"Shape(GB,BL)",
"Shape(DB,BF)",
"Shape(FB,BG)",
"Shape(BF,FM)",
"Shape(IF,FB)",
"Shape(MF,FJ)",
"Shape(JF,FI)",
"Shape(FJ,JE)",
"Shape(CJ,JF)",
"Shape(EJ,JT)",
"Shape(TJ,JC)",
"Collinear(LBFJT)",
"Collinear(DBG)",
"Collinear(MFI)",
"Collinear(EJC)"
] | [
"Equal(MeasureOfAngle(FJE),75)",
"ParallelBetweenLine(GD,IM)",
"ParallelBetweenLine(IM,CE)"
] | [
"Equal(MeasureOfAngle(FJE),75)",
"ParallelBetweenLine(GD,IM)",
"ParallelBetweenLine(IM,CE)"
] | Value(MeasureOfAngle(IFB)) | 105 | [
"parallel_property_collinear_extend(3,IM,CE,F)",
"parallel_property_collinear_extend(3,EC,MF,J)",
"parallel_property_corresponding_angle(1,FM,JE,B)",
"adjacent_complementary_angle(1,IFB,BFM)"
] | {"START": ["parallel_property_collinear_extend(3,IM,CE,F)", "adjacent_complementary_angle(1,IFB,BFM)"], "parallel_property_collinear_extend(3,EC,MF,J)": ["parallel_property_corresponding_angle(1,FM,JE,B)"], "parallel_property_collinear_extend(3,IM,CE,F)": ["parallel_property_collinear_extend(3,EC,MF,J)"]} | |
708 | JiaZou_2023-04-09 | Geometry3k-728 | 2 | 如图所示，∠WXY=4*x+15°，∠ZXV=2*x+65°。求∠YXZ的大小。 | As shown in the diagram, ∠WXY=4*x+15°, ∠ZXV=2*x+65°. Find the measure of ∠YXZ. | 708.png | [
"Shape(XZ,XZY,YX)",
"Shape(XY,XYW,WX)",
"Shape(XW,XWV,VX)",
"Shape(XV,XVZ,ZX)",
"Collinear(ZXW)",
"Collinear(YXV)"
] | [
"Equal(MeasureOfAngle(WXY),4*x+15)",
"Equal(MeasureOfAngle(ZXV),2*x+65)"
] | [
"Equal(MeasureOfAngle(WXY),4*x+15)",
"Equal(MeasureOfAngle(ZXV),2*x+65)"
] | Value(MeasureOfAngle(YXZ)) | 65 | [
"vertical_angle(1,ZXV,WXY)",
"adjacent_complementary_angle(1,YXZ,ZXV)"
] | {"START": ["vertical_angle(1,ZXV,WXY)", "adjacent_complementary_angle(1,YXZ,ZXV)"]} | |
709 | JiaZou_2023-04-09 | Geometry3k-729 | 8 | 如图所示，DE=60，FC=16，C是⊙C的圆心，AB是⊙C的直径，CF垂直于EF。求直线AB的长度。 | As shown in the diagram, DE=60, FC=16, the center of circle C is C, the diameter of ⊙C is AB, CF is perpendicular to EF. Find the length of line AB. | 709.png | [
"Shape(FC,CD,DF)",
"Shape(FD,CDA,AF)",
"Shape(FA,CAE,EF)",
"Shape(CF,FE,CEB,BC)",
"Shape(CB,CBD,DC)",
"Collinear(AFCB)",
"Collinear(EFD)",
"Cocircular(C,AEBD)"
] | [
"Equal(LengthOfLine(DE),60)",
"Equal(LengthOfLine(FC),16)",
"IsCentreOfCircle(C,C)",
"IsDiameterOfCircle(AB,C)",
"PerpendicularBetweenLine(CF,EF)"
] | [
"Equal(LengthOfLine(DE),60)",
"Equal(LengthOfLine(FC),16)",
"IsCentreOfCircle(C,C)",
"IsDiameterOfCircle(AB,C)",
"PerpendicularBetweenLine(CF,EF)"
] | Value(LengthOfLine(AB)) | 68 | [
"adjacent_complementary_angle(1,DFC,CFE)",
"right_triangle_judgment_angle(1,DFC)",
"circle_property_chord_perpendicular_bisect_chord(1,C,CF,DE)",
"line_addition(1,EF,FD)",
"right_triangle_property_pythagorean(1,DFC)",
"radius_of_circle_property_length_equal(1,CD,C)",
"circle_property_length_of_radius_an... | {"START": ["adjacent_complementary_angle(1,DFC,CFE)", "line_addition(1,EF,FD)", "radius_of_circle_property_length_equal(1,CD,C)", "circle_property_length_of_radius_and_diameter(1,C)", "diameter_of_circle_property_length_equal(1,AB,C)"], "adjacent_complementary_angle(1,DFC,CFE)": ["right_triangle_judgment_angle(1,DFC)",... | |
710 | YimingHe_2023-03-12 | Geometry3k-730 | 6 | 如图所示，EH=9，FL=6，HG=21，EF∥HL。求直线LG的长度。 | As shown in the diagram, EH=9, FL=6, HG=21, EF is parallel to HL. Find the length of line LG. | 710.png | [
"Shape(EH,HL,LF,FE)",
"Shape(HG,GL,LH)",
"Collinear(EHG)",
"Collinear(FLG)"
] | [
"Equal(LengthOfLine(EH),9)",
"Equal(LengthOfLine(FL),6)",
"Equal(LengthOfLine(HG),21)",
"ParallelBetweenLine(EF,HL)"
] | [
"Equal(LengthOfLine(EH),9)",
"Equal(LengthOfLine(FL),6)",
"Equal(LengthOfLine(HG),21)",
"ParallelBetweenLine(EF,HL)",
"ParallelBetweenLine(EF,HL)"
] | Value(LengthOfLine(LG)) | 14 | [
"parallel_property_corresponding_angle(1,LH,FE,G)",
"similar_triangle_judgment_aa(1,HGL,EGF)",
"line_addition(1,GL,LF)",
"line_addition(1,GH,HE)",
"similar_triangle_property_line_ratio(1,HGL,EGF)",
"similar_triangle_property_line_ratio(1,LHG,FEG)"
] | {"START": ["parallel_property_corresponding_angle(1,LH,FE,G)", "line_addition(1,GL,LF)", "line_addition(1,GH,HE)"], "parallel_property_corresponding_angle(1,LH,FE,G)": ["similar_triangle_judgment_aa(1,HGL,EGF)"], "similar_triangle_judgment_aa(1,HGL,EGF)": ["similar_triangle_property_line_ratio(1,HGL,EGF)", "similar_tri... | |
711 | JiaZou_2023-04-09 | Geometry3k-731 | 1 | 如图所示，∠DCF=53°。求∠ECB的大小。 | As shown in the diagram, ∠DCF=53°. Find the measure of ∠ECB. | 711.png | [
"Shape(FC,CE)",
"Shape(DC,CF)",
"Shape(EC,CB)",
"Shape(BC,CD)",
"Collinear(FCB)",
"Collinear(DCE)"
] | [
"Equal(MeasureOfAngle(DCF),53)"
] | [
"Equal(MeasureOfAngle(DCF),53)"
] | Value(MeasureOfAngle(ECB)) | 53 | [
"vertical_angle(1,DCF,ECB)"
] | {"START": ["vertical_angle(1,DCF,ECB)"]} | |
712 | YimingHe_2023-03-12 | Geometry3k-732 | 1 | 如图所示，AC=12，∠BCA=60°，AB垂直于CB。求直线AB的长度。 | As shown in the diagram, AC=12, ∠BCA=60°, AB⊥CB. Find the length of line AB. | 712.png | [
"Shape(BC,CA,AB)"
] | [
"Equal(LengthOfLine(AC),12)",
"Equal(MeasureOfAngle(BCA),60)",
"PerpendicularBetweenLine(AB,CB)"
] | [
"Equal(LengthOfLine(AC),12)",
"Equal(MeasureOfAngle(BCA),60)",
"PerpendicularBetweenLine(AB,CB)"
] | Value(LengthOfLine(AB)) | 6*sqrt(3) | [
"sine_theorem(1,ABC)"
] | {"START": ["sine_theorem(1,ABC)"]} | |
713 | JiaZou_2023-04-09 | Geometry3k-733 | 2 | 如图所示，DB=4，DE=5，FH=3，∠GDF=32°，AD垂直于HD。求∠EDG的大小。 | As shown in the diagram, DB=4, DE=5, FH=3, ∠GDF=32°, AD⊥HD. Find the measure of ∠EDG. | 713.png | [
"Shape(GD,DF)",
"Shape(FD,DA)",
"Shape(AD,DH)",
"Shape(ED,DG)",
"Shape(HD,DE)",
"Collinear(FDH)",
"Collinear(ADE)"
] | [
"Equal(LengthOfLine(DB),4)",
"Equal(LengthOfLine(DE),5)",
"Equal(LengthOfLine(FH),3)",
"Equal(MeasureOfAngle(GDF),32)",
"PerpendicularBetweenLine(AD,HD)"
] | [
"Equal(LengthOfLine(DB),4)",
"Equal(LengthOfLine(DE),5)",
"Equal(LengthOfLine(FH),3)",
"Equal(MeasureOfAngle(GDF),32)",
"PerpendicularBetweenLine(AD,HD)"
] | Value(MeasureOfAngle(EDG)) | 58 | [
"vertical_angle(1,EDF,ADH)",
"angle_addition(1,EDG,GDF)"
] | {"START": ["vertical_angle(1,EDF,ADH)", "angle_addition(1,EDG,GDF)"]} | |
714 | JiaZou_2023-04-09 | Geometry3k-735 | 2 | 如图所示，PS=4*x+8，QP=3*x+11，四边形QTSR是矩形。求直线QS的长度。 | As shown in the diagram, PS=4*x+8, QP=3*x+11, quadrilateral QTSR is a rectangle. Find the length of line QS. | 714.png | [
"Shape(QP,PR,RQ)",
"Shape(TP,PQ,QT)",
"Shape(PT,TS,SP)",
"Shape(PS,SR,RP)",
"Collinear(QPS)",
"Collinear(TPR)"
] | [
"Equal(LengthOfLine(PS),4*x+8)",
"Equal(LengthOfLine(QP),3*x+11)",
"Rectangle(QTSR)"
] | [
"Equal(LengthOfLine(PS),4*x+8)",
"Equal(LengthOfLine(QP),3*x+11)",
"Rectangle(QTSR)"
] | Value(LengthOfLine(QS)) | 40 | [
"parallelogram_property_diagonal_bisection(1,QTSR,P)",
"line_addition(1,QP,PS)"
] | {"START": ["parallelogram_property_diagonal_bisection(1,QTSR,P)", "line_addition(1,QP,PS)"]} | |
715 | YimingHe_2023-03-12 | Geometry3k-737 | 3 | 如图所示，∠BDF=78°，∠EGF=120°，∠FBD=50°，∠GEC=56°，∠GFD=x°。求x的值。 | As shown in the diagram, ∠BDF=78°, ∠EGF=120°, ∠FBD=50°, ∠GEC=56°, ∠GFD=x°. Find the value of x. | 715.png | [
"Shape(BD,DF,FB)",
"Shape(FG,GA,AF)",
"Shape(GE,EC,CG)",
"Shape(GF,FD)",
"Shape(EG,GF)",
"Collinear(BFGC)",
"Collinear(DFA)",
"Collinear(AGE)"
] | [
"Equal(MeasureOfAngle(BDF),78)",
"Equal(MeasureOfAngle(EGF),120)",
"Equal(MeasureOfAngle(FBD),50)",
"Equal(MeasureOfAngle(GEC),56)",
"Equal(MeasureOfAngle(GFD),x)"
] | [
"Equal(MeasureOfAngle(BDF),78)",
"Equal(MeasureOfAngle(EGF),120)",
"Equal(MeasureOfAngle(FBD),50)",
"Equal(MeasureOfAngle(GEC),56)",
"Equal(MeasureOfAngle(GFD),x)"
] | Value(x) | 128 | [
"triangle_property_angle_sum(1,BDF)",
"flat_angle(1,GFB)",
"angle_addition(1,GFD,DFB)"
] | {"START": ["triangle_property_angle_sum(1,BDF)", "flat_angle(1,GFB)", "angle_addition(1,GFD,DFB)"]} | |
716 | JiaZou_2023-04-09 | Geometry3k-738 | 9 | 如图所示，∠MJN=35°，KLJM是平行四边形，PNML是矩形。求∠MPN的大小。 | As shown in the diagram, ∠MJN=35°, KLJM is a parallelogram, PNML is a rectangle. Find the measure of ∠MPN. | 716.png | [
"Shape(JP,PN,NJ)",
"Shape(PJ,JL,LP)",
"Shape(LJ,JM,ML)",
"Shape(JN,NM,MJ)",
"Shape(LM,MK,KL)",
"Collinear(PJM)",
"Collinear(NJL)"
] | [
"Equal(MeasureOfAngle(MJN),35)",
"Parallelogram(KLJM)",
"Rectangle(PNML)"
] | [
"Equal(MeasureOfAngle(MJN),35)"
] | Value(MeasureOfAngle(MPN)) | 35/2 | [
"rectangle_property_diagonal_equal(1,PNML)",
"parallelogram_property_diagonal_bisection(1,PNML,J)",
"parallelogram_property_diagonal_bisection(1,NMLP,J)",
"line_addition(1,PJ,JM)",
"line_addition(1,NJ,JL)",
"adjacent_complementary_angle(1,MJN,NJP)",
"isosceles_triangle_judgment_line_equal(1,JPN)",
"is... | {"START": ["rectangle_property_diagonal_equal(1,PNML)", "parallelogram_property_diagonal_bisection(1,PNML,J)", "parallelogram_property_diagonal_bisection(1,NMLP,J)", "line_addition(1,PJ,JM)", "line_addition(1,NJ,JL)", "adjacent_complementary_angle(1,MJN,NJP)", "triangle_property_angle_sum(1,JPN)"], "isosceles_triangle_... | |
717 | YimingHe_2023-03-12 | Geometry3k-739 | 3 | 如图所示，CD=22，∠DCX=18°，∠XDC=105°。求直线XD的长度。 | As shown in the diagram, CD=22, ∠DCX=18°, ∠XDC=105°. Find the length of line XD. | 717.png | [
"Shape(CX,XD,DC)"
] | [
"Equal(LengthOfLine(CD),22)",
"Equal(MeasureOfAngle(DCX),18)",
"Equal(MeasureOfAngle(XDC),105)"
] | [
"Equal(LengthOfLine(CD),22)",
"Equal(MeasureOfAngle(DCX),18)",
"Equal(MeasureOfAngle(XDC),105)"
] | Value(LengthOfLine(XD)) | 88*(-1+sqrt(5))/(-sqrt(30)-sqrt(2)+sqrt(5-sqrt(5))+sqrt(6)+sqrt(3)*sqrt(5-sqrt(5))+sqrt(10)+sqrt(5)*sqrt(5-sqrt(5))+sqrt(15)*sqrt(5-sqrt(5))) | [
"triangle_property_angle_sum(1,CXD)",
"sine_theorem(1,CXD)",
"sine_theorem(1,XDC)"
] | {"START": ["triangle_property_angle_sum(1,CXD)", "sine_theorem(1,CXD)", "sine_theorem(1,XDC)"]} | |
718 | JiaZou_2023-04-09 | Geometry3k-740 | 2 | 如图所示，ADBC的面积为400，EFGH的面积为64，CB=40，GH=x，ADBC相似于EFGH。求x的值。 | As shown in the diagram, the area of ADBC is 400, the area of quadrilateral EFGH is 64, CB=40, GH=x, ADBC is similar to EFGH. Find the value of x. | 718.png | [
"Shape(AD,DB,BC,CA)",
"Shape(EF,FG,GH,HE)"
] | [
"Equal(AreaOfQuadrilateral(ADBC),400)",
"Equal(AreaOfQuadrilateral(EFGH),64)",
"Equal(LengthOfLine(CB),40)",
"Equal(LengthOfLine(GH),x)",
"SimilarBetweenQuadrilateral(ADBC,EFGH)"
] | [
"Equal(AreaOfQuadrilateral(ADBC),400)",
"Equal(AreaOfQuadrilateral(EFGH),64)",
"Equal(LengthOfLine(CB),40)",
"Equal(LengthOfLine(GH),x)"
] | Value(x) | 16 | [
"similar_quadrilateral_property_area_square_ratio(1,ADBC,EFGH)",
"similar_quadrilateral_property_line_ratio(1,BCAD,GHEF)"
] | {"START": ["similar_quadrilateral_property_area_square_ratio(1,ADBC,EFGH)", "similar_quadrilateral_property_line_ratio(1,BCAD,GHEF)"]} | |
719 | JiaZou_2023-04-09 | Geometry3k-741 | 2 | 如图所示，四边形ADCB的面积为150，四边形FJHG的面积为54，CD=10，JH=x，AB和DC是▱ADCB的一组对边，JF和HG是▱FJHG的一组对边，四边形FJHG与四边形ADCB相似。求x的值。 | As shown in the diagram, the area of ADCB is 150, the area of quadrilateral FJHG is 54, CD=10, JH=x, AB and DC are opposite sides of the parallelogram ADCB, JF and HG are opposite sides of the parallelogram FJHG, quadrilateral FJHG is similar to quadrilateral ADCB. Find the value of x. | 719.png | [
"Shape(FJ,JH,HG,GF)",
"Shape(AD,DC,CB,BA)"
] | [
"Equal(AreaOfQuadrilateral(ADCB),150)",
"Equal(AreaOfQuadrilateral(FJHG),54)",
"Equal(LengthOfLine(CD),10)",
"Equal(LengthOfLine(JH),x)",
"Parallelogram(ADCB)",
"Parallelogram(FJHG)",
"SimilarBetweenQuadrilateral(FJHG,ADCB)"
] | [
"Equal(LengthOfLine(CD),10)",
"Equal(LengthOfLine(JH),x)"
] | Value(x) | 6 | [
"similar_quadrilateral_property_area_square_ratio(1,FJHG,ADCB)",
"similar_quadrilateral_property_line_ratio(1,JHGF,DCBA)"
] | {"START": ["similar_quadrilateral_property_area_square_ratio(1,FJHG,ADCB)", "similar_quadrilateral_property_line_ratio(1,JHGF,DCBA)"]} | |
720 | YimingHe_2023-03-12 | Geometry3k-743 | 6 | 如图所示，AB=16，AC=x-3，BE=20，CD=x+5，BC∥ED。求直线AC的长度。 | As shown in the diagram, AB=16, AC=x-3, BE=20, CD=x+5, BC is parallel to ED. Find the length of line AC. | 720.png | [
"Shape(AB,BC,CA)",
"Shape(CB,BE,ED,DC)",
"Collinear(ABE)",
"Collinear(ACD)"
] | [
"Equal(LengthOfLine(AB),16)",
"Equal(LengthOfLine(AC),x-3)",
"Equal(LengthOfLine(BE),20)",
"Equal(LengthOfLine(CD),x+5)",
"ParallelBetweenLine(BC,ED)"
] | [
"Equal(LengthOfLine(AB),16)",
"Equal(LengthOfLine(AC),x-3)",
"Equal(LengthOfLine(BE),20)",
"Equal(LengthOfLine(CD),x+5)",
"ParallelBetweenLine(BC,ED)"
] | Value(LengthOfLine(AC)) | 32 | [
"parallel_property_corresponding_angle(1,BC,ED,A)",
"similar_triangle_judgment_aa(1,CAB,DAE)",
"line_addition(1,AB,BE)",
"line_addition(1,AC,CD)",
"similar_triangle_property_line_ratio(1,CAB,DAE)",
"similar_triangle_property_line_ratio(1,BCA,EDA)"
] | {"START": ["parallel_property_corresponding_angle(1,BC,ED,A)", "line_addition(1,AB,BE)", "line_addition(1,AC,CD)"], "parallel_property_corresponding_angle(1,BC,ED,A)": ["similar_triangle_judgment_aa(1,CAB,DAE)"], "similar_triangle_judgment_aa(1,CAB,DAE)": ["similar_triangle_property_line_ratio(1,CAB,DAE)", "similar_tri... | |
721 | JiaZou_2023-04-09 | Geometry3k-745 | 1 | 如图所示，AB=15，RC=26，AB是RVTC的中位线，RV和TC是梯形RVTC的腰。求直线VT的长度。 | As shown in the diagram, AB=15, RC=26, the midsegment of RVTC is AB, RVTC is a trapezoid. Find the length of line VT. | 721.png | [
"Shape(RA,AB,BC,CR)",
"Shape(AV,VT,TB,BA)",
"Collinear(RAV)",
"Collinear(TBC)"
] | [
"Equal(LengthOfLine(AB),15)",
"Equal(LengthOfLine(RC),26)",
"IsMidsegmentOfQuadrilateral(AB,RVTC)",
"Trapezoid(RVTC)"
] | [
"Equal(LengthOfLine(AB),15)",
"Equal(LengthOfLine(RC),26)",
"IsMidsegmentOfQuadrilateral(AB,RVTC)",
"Trapezoid(RVTC)"
] | Value(LengthOfLine(VT)) | 4 | [
"midsegment_of_quadrilateral_property_length(1,AB,RVTC)"
] | {"START": ["midsegment_of_quadrilateral_property_length(1,AB,RVTC)"]} | |
722 | YimingHe_2023-03-12 | Geometry3k-746 | 1 | 如图所示，AB=y，AR=3*x+6，RB=5*x-14，CP是三角形CAB的高，CQ平分∠CCB，R是线段AB的中点。求y的值。 | As shown in the diagram, AB=y, AR=3*x+6, RB=5*x-14, CP is the altitude of triangle CAB, CQ bisects ∠CCB, R is the midpoint of segment AB. Find the value of y. | 722.png | [
"Shape(CA,AP,PC)",
"Shape(CP,PQ,QC)",
"Shape(CQ,QR,RC)",
"Shape(CR,RB,BC)",
"Collinear(APQRB)"
] | [
"Equal(LengthOfLine(AB),y)",
"Equal(LengthOfLine(AR),3*x+6)",
"Equal(LengthOfLine(RB),5*x-14)",
"IsAltitudeOfTriangle(CP,CAB)",
"IsBisectorOfAngle(CQ,CAB)",
"IsMidpointOfLine(R,AB)"
] | [
"Equal(LengthOfLine(AB),y)",
"Equal(LengthOfLine(AR),3*x+6)",
"Equal(LengthOfLine(RB),5*x-14)",
"IsAltitudeOfTriangle(CP,CAB)",
"IsBisectorOfAngle(CQ,CAB)",
"IsMidpointOfLine(R,AB)"
] | Value(y) | 72 | [
"line_addition(1,AR,RB)"
] | {"START": ["line_addition(1,AR,RB)"]} | |
723 | YimingHe_2023-03-12 | Geometry3k-747 | 6 | 如图所示，QZ=12，XQ=15，YR=20，XY平行于QR。求直线RZ的长度。 | As shown in the diagram, QZ=12, XQ=15, YR=20, XY∥QR. Find the length of line RZ. | 723.png | [
"Shape(QZ,ZR,RQ)",
"Shape(XQ,QR,RY,YX)",
"Collinear(XQZ)",
"Collinear(ZRY)"
] | [
"Equal(LengthOfLine(QZ),12)",
"Equal(LengthOfLine(XQ),15)",
"Equal(LengthOfLine(YR),20)",
"ParallelBetweenLine(XY,QR)"
] | [
"Equal(LengthOfLine(QZ),12)",
"Equal(LengthOfLine(XQ),15)",
"Equal(LengthOfLine(YR),20)",
"ParallelBetweenLine(XY,QR)"
] | Value(LengthOfLine(RZ)) | 16 | [
"parallel_property_corresponding_angle(1,RQ,YX,Z)",
"similar_triangle_judgment_aa(1,QZR,XZY)",
"line_addition(1,ZR,RY)",
"line_addition(1,ZQ,QX)",
"similar_triangle_property_line_ratio(1,QZR,XZY)",
"similar_triangle_property_line_ratio(1,RQZ,YXZ)"
] | {"START": ["parallel_property_corresponding_angle(1,RQ,YX,Z)", "line_addition(1,ZR,RY)", "line_addition(1,ZQ,QX)"], "parallel_property_corresponding_angle(1,RQ,YX,Z)": ["similar_triangle_judgment_aa(1,QZR,XZY)"], "similar_triangle_judgment_aa(1,QZR,XZY)": ["similar_triangle_property_line_ratio(1,QZR,XZY)", "similar_tri... | |
724 | JiaZou_2023-04-09 | Geometry3k-748 | 4 | 如图所示，∠AGB=30°，⊙G的圆心为G，CG垂直于DG。求弧GFC的角度。 | As shown in the diagram, ∠AGB=30°, the center of circle G is G, CG is perpendicular to DG. Find the measure of ⌒GFC. | 724.png | [
"Shape(AG,GB,GBA)",
"Shape(BG,GC,GCB)",
"Shape(CG,GD,GDC)",
"Shape(DG,GF,GFD)",
"Shape(FG,GA,GAF)",
"Collinear(AGD)",
"Collinear(BGF)",
"Cocircular(G,AFDCB)"
] | [
"Equal(MeasureOfAngle(AGB),30)",
"IsCentreOfCircle(G,G)",
"PerpendicularBetweenLine(CG,DG)"
] | [
"IsCentreOfCircle(G,G)"
] | Value(MeasureOfArc(GFC)) | 120 | [
"vertical_angle(1,AGB,DGF)",
"arc_property_center_angle(1,GFD,G)",
"arc_property_center_angle(1,GDC,G)",
"arc_addition_measure(1,GFD,GDC)"
] | {"START": ["vertical_angle(1,AGB,DGF)", "arc_property_center_angle(1,GFD,G)", "arc_property_center_angle(1,GDC,G)", "arc_addition_measure(1,GFD,GDC)"]} | |
725 | YimingHe_2023-03-12 | Geometry3k-750 | 1 | 如图所示，∠AEC=74°，∠EAB=15°，BC垂直于AC。求∠CAE的大小。 | As shown in the diagram, ∠AEC=74°, ∠EAB=15°, BC⊥AC. Find the measure of ∠CAE. | 725.png | [
"Shape(BE,EA,AB)",
"Shape(EC,CA,AE)",
"Collinear(BEC)"
] | [
"Equal(MeasureOfAngle(AEC),74)",
"Equal(MeasureOfAngle(EAB),15)",
"PerpendicularBetweenLine(BC,AC)"
] | [
"Equal(MeasureOfAngle(AEC),74)",
"Equal(MeasureOfAngle(EAB),15)",
"PerpendicularBetweenLine(BC,AC)"
] | Value(MeasureOfAngle(CAE)) | 16 | [
"triangle_property_angle_sum(1,ECA)"
] | {"START": ["triangle_property_angle_sum(1,ECA)"]} | |
726 | YimingHe_2023-03-12 | Geometry3k-751 | 7 | 如图所示，GH=HK，HJ=JK，∠GJK=100°。求∠KGJ的大小。 | As shown in the diagram, GH=HK, HJ=JK, ∠GJK=100°. Find the measure of ∠KGJ. | 726.png | [
"Shape(KG,GH,HK)",
"Shape(KH,HJ,JK)",
"Collinear(GHJ)"
] | [
"Equal(LengthOfLine(GH),LengthOfLine(HK))",
"Equal(LengthOfLine(HJ),LengthOfLine(JK))",
"Equal(MeasureOfAngle(GJK),100)"
] | [
"Equal(LengthOfLine(GH),LengthOfLine(HK))",
"Equal(LengthOfLine(HJ),LengthOfLine(JK))",
"Equal(MeasureOfAngle(GJK),100)"
] | Value(MeasureOfAngle(KGJ)) | 20 | [
"isosceles_triangle_judgment_line_equal(1,HKG)",
"isosceles_triangle_property_angle_equal(1,HKG)",
"isosceles_triangle_judgment_line_equal(1,JKH)",
"isosceles_triangle_property_angle_equal(1,JKH)",
"triangle_property_angle_sum(1,KGH)",
"triangle_property_angle_sum(1,KHJ)",
"adjacent_complementary_angle(... | {"START": ["isosceles_triangle_judgment_line_equal(1,HKG)", "isosceles_triangle_judgment_line_equal(1,JKH)", "triangle_property_angle_sum(1,KGH)", "triangle_property_angle_sum(1,KHJ)", "adjacent_complementary_angle(1,GHK,KHJ)"], "isosceles_triangle_judgment_line_equal(1,HKG)": ["isosceles_triangle_property_angle_equal(... | |
727 | YimingHe_2023-03-12 | Geometry3k-752 | 0 | 如图所示，ML=17，MN=2*x+7，NL=3*x-4，NL=MN。求直线MN的长度。 | As shown in the diagram, ML=17, MN=2*x+7, NL=3*x-4, NL=MN. Find the length of line MN. | 727.png | [
"Shape(ML,LN,NM)"
] | [
"Equal(LengthOfLine(ML),17)",
"Equal(LengthOfLine(MN),2*x+7)",
"Equal(LengthOfLine(NL),3*x-4)",
"Equal(LengthOfLine(NL),LengthOfLine(MN))"
] | [
"Equal(LengthOfLine(ML),17)",
"Equal(LengthOfLine(MN),2*x+7)",
"Equal(LengthOfLine(NL),3*x-4)",
"Equal(LengthOfLine(NL),LengthOfLine(MN))"
] | Value(LengthOfLine(MN)) | 29 | [] | {"START": []} | |
728 | JiaZou_2023-04-09 | Geometry3k-753 | 4 | 如图所示，∠WCY=128°，⌒AXZ的角度为x，⌒AYW的角度为154。求x的值。 | As shown in the diagram, ∠WCY=128°, the measure of arc AXZ is x, the measure of arc AYW is 154. Find the value of x. | 728.png | [
"Shape(CY,YW,WC)",
"Shape(CW,WX,XC)",
"Shape(CX,XZ,ZC)",
"Shape(WY,AYW)",
"Shape(XW,AWX)",
"Shape(ZX,AXZ)",
"Shape(YC,CZ,AZY)",
"Collinear(WCZ)",
"Collinear(YCX)",
"Cocircular(A,WXZY)"
] | [
"Equal(MeasureOfAngle(WCY),128)",
"Equal(MeasureOfArc(AXZ),x)",
"Equal(MeasureOfArc(AYW),154)"
] | [
"Equal(MeasureOfAngle(WCY),128)",
"Equal(MeasureOfArc(AXZ),x)",
"Equal(MeasureOfArc(AYW),154)"
] | Value(x) | 102 | [
"arc_property_circumference_angle_external(1,AYW,X)",
"arc_property_circumference_angle_external(1,AXZ,W)",
"adjacent_complementary_angle(1,XCW,WCY)",
"triangle_property_angle_sum(1,XCW)"
] | {"START": ["arc_property_circumference_angle_external(1,AYW,X)", "arc_property_circumference_angle_external(1,AXZ,W)", "adjacent_complementary_angle(1,XCW,WCY)", "triangle_property_angle_sum(1,XCW)"]} | |
729 | YimingHe_2023-03-12 | Geometry3k-754 | 6 | 如图所示，FH=12，GH=12，FE垂直于GE，GH垂直于EH。求直线EH的长度。 | As shown in the diagram, FH=12, GH=12, FE is perpendicular to GE, GH⊥EH. Find the length of line EH. | 729.png | [
"Shape(FE,EH,HF)",
"Shape(HE,EG,GH)",
"Collinear(FHG)"
] | [
"Equal(LengthOfLine(FH),12)",
"Equal(LengthOfLine(GH),12)",
"PerpendicularBetweenLine(FE,GE)",
"PerpendicularBetweenLine(GH,EH)"
] | [
"Equal(LengthOfLine(FH),12)",
"Equal(LengthOfLine(GH),12)",
"PerpendicularBetweenLine(FE,GE)",
"PerpendicularBetweenLine(GH,EH)"
] | Value(LengthOfLine(EH)) | 12 | [
"mirror_similar_triangle_judgment_aa(1,EGH,FEG)",
"line_addition(1,FH,HG)",
"right_triangle_judgment_angle(1,GHE)",
"right_triangle_property_pythagorean(1,GHE)",
"mirror_similar_triangle_property_line_ratio(1,EGH,FEG)",
"mirror_similar_triangle_property_line_ratio(1,HEG,EGF)"
] | {"START": ["mirror_similar_triangle_judgment_aa(1,EGH,FEG)", "line_addition(1,FH,HG)", "right_triangle_judgment_angle(1,GHE)"], "mirror_similar_triangle_judgment_aa(1,EGH,FEG)": ["mirror_similar_triangle_property_line_ratio(1,EGH,FEG)", "mirror_similar_triangle_property_line_ratio(1,HEG,EGF)"], "right_triangle_judgment... | |
730 | JiaZou_2023-04-09 | Geometry3k-755 | 1 | 如图所示，∠TZY=30*x°，∠TZY=∠ZYW，∠WTZ=20*x°，∠WTZ=∠YWT，TW和ZY是等腰梯形TZYW的平行边。求∠YWT的大小。 | As shown in the diagram, ∠TZY=30*x°, ∠TZY=∠ZYW, ∠WTZ=20*x°, ∠WTZ=∠YWT, quadrilateral TZYW is a isosceles trapezoid. Find the measure of ∠YWT. | 730.png | [
"Shape(TZ,ZY,YW,WT)"
] | [
"Equal(MeasureOfAngle(TZY),30*x)",
"Equal(MeasureOfAngle(TZY),MeasureOfAngle(ZYW))",
"Equal(MeasureOfAngle(WTZ),20*x)",
"Equal(MeasureOfAngle(WTZ),MeasureOfAngle(YWT))",
"IsoscelesTrapezoid(TZYW)"
] | [
"Equal(MeasureOfAngle(TZY),30*x)",
"Equal(MeasureOfAngle(TZY),MeasureOfAngle(ZYW))",
"Equal(MeasureOfAngle(WTZ),20*x)",
"Equal(MeasureOfAngle(WTZ),MeasureOfAngle(YWT))"
] | Value(MeasureOfAngle(YWT)) | 72 | [
"quadrilateral_property_angle_sum(1,TZYW)"
] | {"START": ["quadrilateral_property_angle_sum(1,TZYW)"]} | |
731 | JiaZou_2023-04-09 | Geometry3k-756 | 1 | 如图所示，∠QRS=x°，∠RST=2*x+7°，∠STQ=x°，∠TQR=2*x+5°。求∠TQR的大小。 | As shown in the diagram, ∠QRS=x°, ∠RST=2*x+7°, ∠STQ=x°, ∠TQR=2*x+5°. Find the measure of ∠TQR. | 731.png | [
"Shape(QR,RS,ST,TQ)"
] | [
"Equal(MeasureOfAngle(QRS),x)",
"Equal(MeasureOfAngle(RST),2*x+7)",
"Equal(MeasureOfAngle(STQ),x)",
"Equal(MeasureOfAngle(TQR),2*x+5)"
] | [
"Equal(MeasureOfAngle(QRS),x)",
"Equal(MeasureOfAngle(RST),2*x+7)",
"Equal(MeasureOfAngle(STQ),x)",
"Equal(MeasureOfAngle(TQR),2*x+5)"
] | Value(MeasureOfAngle(TQR)) | 121 | [
"quadrilateral_property_angle_sum(1,QRST)"
] | {"START": ["quadrilateral_property_angle_sum(1,QRST)"]} | |
732 | JiaZou_2023-04-09 | Geometry3k-757 | 7 | 如图所示，GK=14，MF=8，弧FKG的角度为122，圆F的圆心为F，HJ⊥KJ。求弧FHG的角度。 | As shown in the diagram, GK=14, MF=8, the measure of ⌒FKG is 122, F is the center of circle F, HJ is perpendicular to KJ. Find the measure of ⌒FHG. | 732.png | [
"Shape(GF,FJ,JG)",
"Shape(JH,FHG,GJ)",
"Shape(FG,FGM,MF)",
"Shape(JF,FM,FMK,KJ)",
"Shape(HJ,JK,FKH)",
"Collinear(GJK)",
"Collinear(MFJH)",
"Cocircular(F,GMKH)"
] | [
"Equal(LengthOfLine(GK),14)",
"Equal(LengthOfLine(MF),8)",
"Equal(MeasureOfArc(FKG),122)",
"IsCentreOfCircle(F,F)",
"PerpendicularBetweenLine(HJ,KJ)"
] | [
"Equal(LengthOfLine(GK),14)",
"Equal(LengthOfLine(MF),8)",
"Equal(MeasureOfArc(FKG),122)",
"IsCentreOfCircle(F,F)",
"PerpendicularBetweenLine(HJ,KJ)"
] | Value(MeasureOfArc(FHG)) | 180*asin(7/8)/pi | [
"adjacent_complementary_angle(1,HJK,KJM)",
"circle_property_chord_perpendicular_bisect_chord(1,F,FJ,KG)",
"line_addition(1,GJ,JK)",
"radius_of_circle_property_length_equal(1,FM,F)",
"radius_of_circle_property_length_equal(1,FG,F)",
"sine_theorem(1,GFJ)",
"arc_property_center_angle(1,FHG,F)"
] | {"START": ["adjacent_complementary_angle(1,HJK,KJM)", "line_addition(1,GJ,JK)", "radius_of_circle_property_length_equal(1,FM,F)", "radius_of_circle_property_length_equal(1,FG,F)", "sine_theorem(1,GFJ)", "arc_property_center_angle(1,FHG,F)"], "adjacent_complementary_angle(1,HJK,KJM)": ["circle_property_chord_perpendicul... | |
733 | JiaZou_2023-04-09 | Geometry3k-758 | 5 | 如图所示，DE=7，EX=24，圆D的圆心为D，DA⊥XA，XE垂直于DE。求直线QX的长度。 | As shown in the diagram, DE=7, EX=24, the center of circle D is D, DA⊥XA, XE is perpendicular to DE. Find the length of line QX. | 733.png | [
"Shape(DA,DAQ,QD)",
"Shape(DQ,DQE,ED)",
"Shape(DE,DET,TD)",
"Shape(DT,DTA,AD)",
"Shape(AX,XQ,DAQ)",
"Shape(QX,XE,DQE)",
"Collinear(XQDT)",
"Cocircular(D,AQET)"
] | [
"Equal(LengthOfLine(DE),7)",
"Equal(LengthOfLine(EX),24)",
"IsCentreOfCircle(D,D)",
"PerpendicularBetweenLine(DA,XA)",
"PerpendicularBetweenLine(XE,DE)"
] | [
"Equal(LengthOfLine(DE),7)",
"Equal(LengthOfLine(EX),24)",
"IsCentreOfCircle(D,D)",
"PerpendicularBetweenLine(DA,XA)",
"PerpendicularBetweenLine(XE,DE)"
] | Value(LengthOfLine(QX)) | 18 | [
"radius_of_circle_property_length_equal(1,DE,D)",
"radius_of_circle_property_length_equal(1,DQ,D)",
"right_triangle_judgment_angle(1,XED)",
"right_triangle_property_pythagorean(1,XED)",
"line_addition(1,XQ,QD)"
] | {"START": ["radius_of_circle_property_length_equal(1,DE,D)", "radius_of_circle_property_length_equal(1,DQ,D)", "right_triangle_judgment_angle(1,XED)", "line_addition(1,XQ,QD)"], "right_triangle_judgment_angle(1,XED)": ["right_triangle_property_pythagorean(1,XED)"]} | |
734 | YimingHe_2023-03-12 | Geometry3k-759 | 3 | 如图所示，AB=41，AC=30，NB=19，NC=27，AC垂直于BC。求△BAN的周长。 | As shown in the diagram, AB=41, AC=30, NB=19, NC=27, AC⊥BC. Find the perimeter of △BAN. | 734.png | [
"Shape(BA,AN,NB)",
"Shape(NA,AC,CN)",
"Collinear(BNC)"
] | [
"Equal(LengthOfLine(AB),41)",
"Equal(LengthOfLine(AC),30)",
"Equal(LengthOfLine(NB),19)",
"Equal(LengthOfLine(NC),27)",
"PerpendicularBetweenLine(AC,BC)"
] | [
"Equal(LengthOfLine(AB),41)",
"Equal(LengthOfLine(AC),30)",
"Equal(LengthOfLine(NB),19)",
"Equal(LengthOfLine(NC),27)",
"PerpendicularBetweenLine(AC,BC)"
] | Value(PerimeterOfTriangle(BAN)) | 3*sqrt(181)+60 | [
"right_triangle_judgment_angle(1,ACN)",
"right_triangle_property_pythagorean(1,ACN)",
"triangle_perimeter_formula(1,BAN)"
] | {"START": ["right_triangle_judgment_angle(1,ACN)", "triangle_perimeter_formula(1,BAN)"], "right_triangle_judgment_angle(1,ACN)": ["right_triangle_property_pythagorean(1,ACN)"]} | |
735 | JiaZou_2023-04-09 | Geometry3k-760 | 5 | 如图所示，AD=12，DC=10，∠DCB=60°，DCBA是▱，AE垂直于BE。求DCBA的面积。 | As shown in the diagram, AD=12, DC=10, ∠DCB=60°, CD and BA are opposite sides of the ▱ DCBA, AE is perpendicular to BE. Find the area of quadrilateral DCBA. | 735.png | [
"Shape(DC,CB,BE,ED)",
"Shape(EB,BA,AE)",
"Collinear(DEA)"
] | [
"Equal(LengthOfLine(AD),12)",
"Equal(LengthOfLine(DC),10)",
"Equal(MeasureOfAngle(DCB),60)",
"Parallelogram(DCBA)",
"PerpendicularBetweenLine(AE,BE)"
] | [
"Equal(LengthOfLine(AD),12)",
"Equal(LengthOfLine(DC),10)",
"Equal(MeasureOfAngle(DCB),60)",
"PerpendicularBetweenLine(AE,BE)"
] | Value(AreaOfQuadrilateral(DCBA)) | 60*sqrt(3) | [
"altitude_of_quadrilateral_judgment_left_vertex(1,BE,BADC)",
"parallelogram_property_opposite_angle_equal(1,CBAD)",
"parallelogram_property_opposite_line_equal(1,DCBA)",
"sine_theorem(1,BAE)",
"parallelogram_area_formula_common(1,BADC)"
] | {"START": ["altitude_of_quadrilateral_judgment_left_vertex(1,BE,BADC)", "parallelogram_property_opposite_angle_equal(1,CBAD)", "parallelogram_property_opposite_line_equal(1,DCBA)", "sine_theorem(1,BAE)", "parallelogram_area_formula_common(1,BADC)"]} | |
736 | YimingHe_2023-03-12 | Geometry3k-761 | 2 | 如图所示，AB=5，BC=5，CB⊥AB。求直线CA的长度。 | As shown in the diagram, AB=5, BC=5, CB⊥AB. Find the length of line CA. | 736.png | [
"Shape(CB,BA,AC)"
] | [
"Equal(LengthOfLine(AB),5)",
"Equal(LengthOfLine(BC),5)",
"PerpendicularBetweenLine(CB,AB)"
] | [
"Equal(LengthOfLine(AB),5)",
"Equal(LengthOfLine(BC),5)",
"PerpendicularBetweenLine(CB,AB)"
] | Value(LengthOfLine(CA)) | 5*sqrt(2) | [
"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)"]} | |
737 | YimingHe_2023-03-12 | Geometry3k-762 | 5 | 如图所示，QR=10，QX=QZ，ZQ=8，XY∥QR。求直线XY的长度。 | As shown in the diagram, QR=10, QX=QZ, ZQ=8, XY∥QR. Find the length of line XY. | 737.png | [
"Shape(XQ,QR,RY,YX)",
"Shape(QZ,ZR,RQ)",
"Collinear(ZQX)",
"Collinear(ZRY)"
] | [
"Equal(LengthOfLine(QR),10)",
"Equal(LengthOfLine(QX),LengthOfLine(QZ))",
"Equal(LengthOfLine(ZQ),8)",
"ParallelBetweenLine(XY,QR)"
] | [
"Equal(LengthOfLine(QR),10)",
"Equal(LengthOfLine(QX),LengthOfLine(QZ))",
"Equal(LengthOfLine(ZQ),8)",
"ParallelBetweenLine(XY,QR)"
] | Value(LengthOfLine(XY)) | 20 | [
"line_addition(1,ZQ,QX)",
"parallel_property_corresponding_angle(1,RQ,YX,Z)",
"similar_triangle_judgment_aa(1,QZR,XZY)",
"similar_triangle_property_line_ratio(1,ZRQ,ZYX)",
"similar_triangle_property_line_ratio(1,RQZ,YXZ)"
] | {"START": ["line_addition(1,ZQ,QX)", "parallel_property_corresponding_angle(1,RQ,YX,Z)"], "parallel_property_corresponding_angle(1,RQ,YX,Z)": ["similar_triangle_judgment_aa(1,QZR,XZY)"], "similar_triangle_judgment_aa(1,QZR,XZY)": ["similar_triangle_property_line_ratio(1,ZRQ,ZYX)", "similar_triangle_property_line_ratio(... | |
738 | YimingHe_2023-03-12 | Geometry3k-763 | 2 | 如图所示，三角形JKL的面积为30，JK=12，PQ=15，三角形JKL与三角形PQR是相似三角形。求△PQR的面积。 | As shown in the diagram, the area of △JKL is 30, JK=12, PQ=15, △JKL is similar to △PQR.. Find the area of triangle PQR. | 738.png | [
"Shape(JK,KL,LJ)",
"Shape(PQ,QR,RP)"
] | [
"Equal(AreaOfTriangle(JKL),30)",
"Equal(LengthOfLine(JK),12)",
"Equal(LengthOfLine(PQ),15)",
"SimilarBetweenTriangle(JKL,PQR)"
] | [
"Equal(AreaOfTriangle(JKL),30)",
"Equal(LengthOfLine(JK),12)",
"Equal(LengthOfLine(PQ),15)",
"SimilarBetweenTriangle(JKL,PQR)"
] | Value(AreaOfTriangle(PQR)) | 375/8 | [
"similar_triangle_property_line_ratio(1,LJK,RPQ)",
"similar_triangle_property_area_square_ratio(1,LJK,RPQ)"
] | {"START": ["similar_triangle_property_line_ratio(1,LJK,RPQ)", "similar_triangle_property_area_square_ratio(1,LJK,RPQ)"]} | |
739 | JiaZou_2023-04-09 | Geometry3k-764 | 1 | 如图所示，∠DFH=81°。求⌒AHD的角度。 | As shown in the diagram, ∠DFH=81°. Find the measure of arc AHD. | 739.png | [
"Shape(DF,FH,HD)",
"Shape(FD,ADF)",
"Shape(HF,AFH)",
"Shape(DH,AHD)",
"Cocircular(A,DFH)"
] | [
"Equal(MeasureOfAngle(DFH),81)"
] | [
"Equal(MeasureOfAngle(DFH),81)"
] | Value(MeasureOfArc(AHD)) | 162 | [
"arc_property_circumference_angle_external(1,AHD,F)"
] | {"START": ["arc_property_circumference_angle_external(1,AHD,F)"]} | |
740 | JiaZou_2023-04-09 | Geometry3k-765 | 11 | 如图所示，BC=4，BO=OT，CO=OA，∠ABO=58°，CO⊥BO。求BCTA的周长。 | As shown in the diagram, BC=4, BO=OT, CO=OA, ∠ABO=58°, CO⊥BO. Find the perimeter of BCTA. | 740.png | [
"Shape(BC,CO,OB)",
"Shape(OC,CT,TO)",
"Shape(OT,TA,AO)",
"Shape(BO,OA,AB)",
"Collinear(COA)",
"Collinear(BOT)"
] | [
"Equal(LengthOfLine(BC),4)",
"Equal(LengthOfLine(BO),LengthOfLine(OT))",
"Equal(LengthOfLine(CO),LengthOfLine(OA))",
"Equal(MeasureOfAngle(ABO),58)",
"PerpendicularBetweenLine(CO,BO)"
] | [
"Equal(LengthOfLine(BC),4)",
"Equal(LengthOfLine(BO),LengthOfLine(OT))",
"Equal(LengthOfLine(CO),LengthOfLine(OA))",
"Equal(MeasureOfAngle(ABO),58)",
"PerpendicularBetweenLine(CO,BO)"
] | Value(PerimeterOfQuadrilateral(BCTA)) | 16 | [
"midpoint_of_line_judgment(1,O,CA)",
"midpoint_of_line_judgment(1,O,BT)",
"parallelogram_judgment_diagonal_bisection(1,BCTA,O)",
"vertical_angle(1,COB,AOT)",
"perpendicular_bisector_judgment_per_and_mid(1,BO,CA)",
"perpendicular_bisector_judgment_per_and_mid(1,TO,AC)",
"perpendicular_bisector_property_d... | {"START": ["midpoint_of_line_judgment(1,O,CA)", "midpoint_of_line_judgment(1,O,BT)", "vertical_angle(1,COB,AOT)", "perpendicular_bisector_judgment_per_and_mid(1,BO,CA)", "quadrilateral_perimeter_formula(1,BCTA)"], "kite_judgment_equal_and_equal(1,BCTA)": ["rhombus_judgment_parallelogram_and_kite(1,BCTA)"], "midpoint_of... | |
741 | JiaZou_2023-04-09 | Geometry3k-766 | 1 | 如图所示，MN=60，RV=6*x+11，ST=4*x-1，MN是RSTV的中位线。求x的值。 | As shown in the diagram, MN=60, RV=6*x+11, ST=4*x-1, the midsegment of quadrilateral RSTV is MN. Find the value of x. | 741.png | [
"Shape(RM,MN,NV,VR)",
"Shape(MS,ST,TN,NM)",
"Collinear(RMS)",
"Collinear(VNT)"
] | [
"Equal(LengthOfLine(MN),60)",
"Equal(LengthOfLine(RV),6*x+11)",
"Equal(LengthOfLine(ST),4*x-1)",
"IsMidsegmentOfQuadrilateral(MN,RSTV)"
] | [
"Equal(LengthOfLine(MN),60)",
"Equal(LengthOfLine(RV),6*x+11)",
"Equal(LengthOfLine(ST),4*x-1)",
"IsMidsegmentOfQuadrilateral(MN,RSTV)"
] | Value(x) | 11 | [
"midsegment_of_quadrilateral_property_length(1,MN,RSTV)"
] | {"START": ["midsegment_of_quadrilateral_property_length(1,MN,RSTV)"]} | |
742 | YimingHe_2023-03-12 | Geometry3k-767 | 9 | 如图所示，AD=8，BD=12，BC⊥AC，CD⊥BD。求直线CD的长度。 | As shown in the diagram, AD=8, BD=12, BC is perpendicular to AC, CD is perpendicular to BD. Find the length of line CD. | 742.png | [
"Shape(CA,AD,DC)",
"Shape(CD,DB,BC)",
"Collinear(ADB)"
] | [
"Equal(LengthOfLine(AD),8)",
"Equal(LengthOfLine(BD),12)",
"PerpendicularBetweenLine(BC,AC)",
"PerpendicularBetweenLine(CD,BD)"
] | [
"Equal(LengthOfLine(AD),8)",
"Equal(LengthOfLine(BD),12)",
"PerpendicularBetweenLine(BC,AC)",
"PerpendicularBetweenLine(CD,BD)"
] | Value(LengthOfLine(CD)) | 4*sqrt(6) | [
"adjacent_complementary_angle(1,ADC,CDB)",
"mirror_similar_triangle_judgment_aa(1,CAD,BCA)",
"mirror_similar_triangle_judgment_aa(1,CDB,ABC)",
"mirror_similar_triangle_property_line_ratio(1,CAD,BCA)",
"mirror_similar_triangle_property_line_ratio(1,ADC,ABC)",
"mirror_similar_triangle_property_line_ratio(1,... | {"START": ["adjacent_complementary_angle(1,ADC,CDB)", "mirror_similar_triangle_judgment_aa(1,CDB,ABC)"], "adjacent_complementary_angle(1,ADC,CDB)": ["mirror_similar_triangle_judgment_aa(1,CAD,BCA)"], "mirror_similar_triangle_judgment_aa(1,CAD,BCA)": ["mirror_similar_triangle_property_line_ratio(1,CAD,BCA)", "mirror_sim... | |
743 | YimingHe_2023-03-12 | Geometry3k-768 | 2 | 如图所示，AC=7*x-4，AD=6*x+1，∠ABC=30°，∠ADB=90°，∠BCA=90°，∠DBA=30°。求x的值。 | As shown in the diagram, AC=7*x-4, AD=6*x+1, ∠ABC=30°, ∠ADB=90°, ∠BCA=90°, ∠DBA=30°. Find the value of x. | 743.png | [
"Shape(BC,CA,AB)",
"Shape(BA,AD,DB)"
] | [
"Equal(LengthOfLine(AC),7*x-4)",
"Equal(LengthOfLine(AD),6*x+1)",
"Equal(MeasureOfAngle(ABC),30)",
"Equal(MeasureOfAngle(ADB),90)",
"Equal(MeasureOfAngle(BCA),90)",
"Equal(MeasureOfAngle(DBA),30)"
] | [
"Equal(LengthOfLine(AC),7*x-4)",
"Equal(LengthOfLine(AD),6*x+1)",
"Equal(MeasureOfAngle(ABC),30)",
"Equal(MeasureOfAngle(ADB),90)",
"Equal(MeasureOfAngle(BCA),90)",
"Equal(MeasureOfAngle(DBA),30)"
] | Value(x) | 5 | [
"mirror_congruent_triangle_judgment_aas(3,ADB,ABC)",
"mirror_congruent_triangle_property_line_equal(1,BAD,BCA)"
] | {"START": ["mirror_congruent_triangle_judgment_aas(3,ADB,ABC)"], "mirror_congruent_triangle_judgment_aas(3,ADB,ABC)": ["mirror_congruent_triangle_property_line_equal(1,BAD,BCA)"]} | |
744 | JiaZou_2023-04-09 | Geometry3k-769 | 5 | 如图所示，圆O的直径与直线QS的长度相等，∠SVT=75°，∠TVP=72°，圆V的圆心为V，RV垂直于SV。求弧VRP的角度。 | As shown in the diagram, the diameter of circle O is equal to the length of line QS, ∠SVT=75°, ∠TVP=72°, the center of ⊙V is V, RV is perpendicular to SV. Find the measure of ⌒VRP. | 744.png | [
"Shape(VQ,VQP,PV)",
"Shape(VP,VPT,TV)",
"Shape(VT,VTS,SV)",
"Shape(VS,VSR,RV)",
"Shape(VR,VRQ,QV)",
"Collinear(QVS)",
"Cocircular(V,RQPTS)"
] | [
"Equal(DiameterOfCircle(O),LengthOfLine(QS))",
"Equal(MeasureOfAngle(SVT),75)",
"Equal(MeasureOfAngle(TVP),72)",
"IsCentreOfCircle(V,V)",
"PerpendicularBetweenLine(RV,SV)"
] | [
"Equal(DiameterOfCircle(O),LengthOfLine(QS))",
"Equal(MeasureOfAngle(SVT),75)",
"Equal(MeasureOfAngle(TVP),72)",
"IsCentreOfCircle(V,V)",
"PerpendicularBetweenLine(RV,SV)"
] | Value(MeasureOfArc(VRP)) | 123 | [
"adjacent_complementary_angle(1,QVR,RVS)",
"adjacent_complementary_angle(1,SVP,PVQ)",
"angle_addition(1,SVT,TVP)",
"angle_addition(1,PVQ,QVR)",
"arc_property_center_angle(1,VRP,V)"
] | {"START": ["adjacent_complementary_angle(1,QVR,RVS)", "adjacent_complementary_angle(1,SVP,PVQ)", "angle_addition(1,SVT,TVP)", "angle_addition(1,PVQ,QVR)", "arc_property_center_angle(1,VRP,V)"]} | |
745 | YimingHe_2023-03-12 | Geometry3k-770 | 9 | 如图所示，AD=3，CD=x，DB=12，AC垂直于BC，CD⊥AD。求x的值。 | As shown in the diagram, AD=3, CD=x, DB=12, AC is perpendicular to BC, CD is perpendicular to AD. Find the value of x. | 745.png | [
"Shape(AC,CD,DA)",
"Shape(DC,CB,BD)",
"Collinear(ADB)"
] | [
"Equal(LengthOfLine(AD),3)",
"Equal(LengthOfLine(CD),x)",
"Equal(LengthOfLine(DB),12)",
"PerpendicularBetweenLine(AC,BC)",
"PerpendicularBetweenLine(CD,AD)"
] | [
"Equal(LengthOfLine(AD),3)",
"Equal(LengthOfLine(CD),x)",
"Equal(LengthOfLine(DB),12)",
"PerpendicularBetweenLine(AC,BC)",
"PerpendicularBetweenLine(CD,AD)"
] | Value(x) | 6 | [
"adjacent_complementary_angle(1,BDC,CDA)",
"mirror_similar_triangle_judgment_aa(1,CDA,BAC)",
"mirror_similar_triangle_judgment_aa(1,CBD,ACB)",
"mirror_similar_triangle_property_line_ratio(1,CDA,BAC)",
"mirror_similar_triangle_property_line_ratio(1,DAC,CBA)",
"mirror_similar_triangle_property_line_ratio(1,... | {"START": ["adjacent_complementary_angle(1,BDC,CDA)", "mirror_similar_triangle_judgment_aa(1,CDA,BAC)"], "adjacent_complementary_angle(1,BDC,CDA)": ["mirror_similar_triangle_judgment_aa(1,CBD,ACB)"], "mirror_similar_triangle_judgment_aa(1,CBD,ACB)": ["mirror_similar_triangle_property_line_ratio(1,CBD,ACB)", "mirror_sim... | |
746 | JiaZou_2023-04-09 | Geometry3k-771 | 3 | 如图所示，AB=20，AD=18，CE=16，BC和AD是▱BADC的一组对边，CE垂直于DE。求四边形BADC的面积。 | As shown in the diagram, AB=20, AD=18, CE=16, BADC is a parallelogram, CE is perpendicular to DE. Find the area of BADC. | 746.png | [
"Shape(BA,AE,EC,CB)",
"Shape(CE,ED,DC)",
"Collinear(AED)"
] | [
"Equal(LengthOfLine(AB),20)",
"Equal(LengthOfLine(AD),18)",
"Equal(LengthOfLine(CE),16)",
"Parallelogram(BADC)",
"PerpendicularBetweenLine(CE,DE)"
] | [
"Equal(LengthOfLine(AB),20)",
"Equal(LengthOfLine(AD),18)",
"Equal(LengthOfLine(CE),16)",
"PerpendicularBetweenLine(CE,DE)"
] | Value(AreaOfQuadrilateral(BADC)) | 288 | [
"adjacent_complementary_angle(1,AEC,CED)",
"altitude_of_quadrilateral_judgment_right_vertex(1,CE,BADC)",
"parallelogram_area_formula_common(1,BADC)"
] | {"START": ["adjacent_complementary_angle(1,AEC,CED)", "parallelogram_area_formula_common(1,BADC)"], "adjacent_complementary_angle(1,AEC,CED)": ["altitude_of_quadrilateral_judgment_right_vertex(1,CE,BADC)"]} | |
747 | YimingHe_2023-03-12 | Geometry3k-772 | 1 | 如图所示，BC=17*sqrt(2)，∠BAC=45°，∠CBA=45°，AC垂直于BC。求直线AB的长度。 | As shown in the diagram, BC=17*sqrt(2), ∠BAC=45°, ∠CBA=45°, AC⊥BC. Find the length of line AB. | 747.png | [
"Shape(BA,AC,CB)"
] | [
"Equal(LengthOfLine(BC),17*sqrt(2))",
"Equal(MeasureOfAngle(BAC),45)",
"Equal(MeasureOfAngle(CBA),45)",
"PerpendicularBetweenLine(AC,BC)"
] | [
"Equal(LengthOfLine(BC),17*sqrt(2))",
"Equal(MeasureOfAngle(BAC),45)",
"Equal(MeasureOfAngle(CBA),45)",
"PerpendicularBetweenLine(AC,BC)"
] | Value(LengthOfLine(AB)) | 34 | [
"sine_theorem(1,BAC)"
] | {"START": ["sine_theorem(1,BAC)"]} | |
748 | YimingHe_2023-03-12 | Geometry3k-773 | 3 | 如图所示，BC=11，CA=23，OA=25，OB=35，OA垂直于CA。求△OCB的周长。 | As shown in the diagram, BC=11, CA=23, OA=25, OB=35, OA⊥CA. Find the perimeter of △OCB. | 748.png | [
"Shape(OA,AC,CO)",
"Shape(OC,CB,BO)",
"Collinear(ACB)"
] | [
"Equal(LengthOfLine(BC),11)",
"Equal(LengthOfLine(CA),23)",
"Equal(LengthOfLine(OA),25)",
"Equal(LengthOfLine(OB),35)",
"PerpendicularBetweenLine(OA,CA)"
] | [
"Equal(LengthOfLine(BC),11)",
"Equal(LengthOfLine(CA),23)",
"Equal(LengthOfLine(OA),25)",
"Equal(LengthOfLine(OB),35)",
"PerpendicularBetweenLine(OA,CA)"
] | Value(PerimeterOfTriangle(OCB)) | sqrt(1154)+46 | [
"right_triangle_judgment_angle(1,OAC)",
"right_triangle_property_pythagorean(1,OAC)",
"triangle_perimeter_formula(1,OCB)"
] | {"START": ["right_triangle_judgment_angle(1,OAC)", "triangle_perimeter_formula(1,OCB)"], "right_triangle_judgment_angle(1,OAC)": ["right_triangle_property_pythagorean(1,OAC)"]} | |
749 | YimingHe_2023-03-12 | Geometry3k-774 | 1 | 如图所示，∠UTS=47°，RU垂直于SU，TS垂直于RS，TV⊥UV。求∠SRU的大小。 | As shown in the diagram, ∠UTS=47°, RU is perpendicular to SU, TS is perpendicular to RS, TV is perpendicular to UV. Find the measure of ∠SRU. | 749.png | [
"Shape(SR,RU,US)",
"Shape(SU,UV,VS)",
"Shape(VU,UT,TV)",
"Collinear(RUT)",
"Collinear(SVT)"
] | [
"Equal(MeasureOfAngle(UTS),47)",
"PerpendicularBetweenLine(RU,SU)",
"PerpendicularBetweenLine(TS,RS)",
"PerpendicularBetweenLine(TV,UV)"
] | [
"Equal(MeasureOfAngle(UTS),47)",
"PerpendicularBetweenLine(RU,SU)",
"PerpendicularBetweenLine(TS,RS)",
"PerpendicularBetweenLine(TV,UV)"
] | Value(MeasureOfAngle(SRU)) | 43 | [
"triangle_property_angle_sum(1,TSR)"
] | {"START": ["triangle_property_angle_sum(1,TSR)"]} | |
750 | JiaZou_2023-04-09 | Geometry3k-775 | 3 | 如图所示，∠ACB=5*x+21°，∠CDG=12*x+6°，PA∥EG。求x的值。 | As shown in the diagram, ∠ACB=5*x+21°, ∠CDG=12*x+6°, PA∥EG. Find the value of x. | 750.png | [
"Shape(FC,CA)",
"Shape(PC,CF)",
"Shape(AC,CD)",
"Shape(DC,CP)",
"Shape(CD,DG)",
"Shape(ED,DC)",
"Shape(GD,DB)",
"Shape(BD,DE)",
"Collinear(ECDB)",
"Collinear(ACP)",
"Collinear(GDE)"
] | [
"Equal(MeasureOfAngle(ACB),5*x+21)",
"Equal(MeasureOfAngle(CDG),12*x+6)",
"ParallelBetweenLine(PA,EG)"
] | [
"Equal(MeasureOfAngle(ACB),5*x+21)",
"Equal(MeasureOfAngle(CDG),12*x+6)",
"ParallelBetweenLine(PA,EG)"
] | Value(x) | 9 | [
"parallel_property_collinear_extend(3,PA,EG,C)",
"parallel_property_collinear_extend(3,GE,AC,D)",
"parallel_property_ipsilateral_internal_angle(1,CA,DG)"
] | {"START": ["parallel_property_collinear_extend(3,PA,EG,C)"], "parallel_property_collinear_extend(3,GE,AC,D)": ["parallel_property_ipsilateral_internal_angle(1,CA,DG)"], "parallel_property_collinear_extend(3,PA,EG,C)": ["parallel_property_collinear_extend(3,GE,AC,D)"]} | |
751 | YimingHe_2023-03-12 | Geometry3k-776 | 6 | 如图所示，AB=16，AC=x-3，BE=20，CD=x+5，DE∥CB。求x的值。 | As shown in the diagram, AB=16, AC=x-3, BE=20, CD=x+5, DE is parallel to CB. Find the value of x. | 751.png | [
"Shape(AB,BC,CA)",
"Shape(CB,BE,ED,DC)",
"Collinear(ABE)",
"Collinear(ACD)"
] | [
"Equal(LengthOfLine(AB),16)",
"Equal(LengthOfLine(AC),x-3)",
"Equal(LengthOfLine(BE),20)",
"Equal(LengthOfLine(CD),x+5)",
"ParallelBetweenLine(DE,CB)"
] | [
"Equal(LengthOfLine(AB),16)",
"Equal(LengthOfLine(AC),x-3)",
"Equal(LengthOfLine(BE),20)",
"Equal(LengthOfLine(CD),x+5)",
"ParallelBetweenLine(DE,CB)"
] | Value(x) | 35 | [
"parallel_property_corresponding_angle(1,BC,ED,A)",
"similar_triangle_judgment_aa(1,CAB,DAE)",
"line_addition(1,AB,BE)",
"line_addition(1,AC,CD)",
"similar_triangle_property_line_ratio(1,CAB,DAE)",
"similar_triangle_property_line_ratio(1,BCA,EDA)"
] | {"START": ["parallel_property_corresponding_angle(1,BC,ED,A)", "line_addition(1,AB,BE)", "line_addition(1,AC,CD)"], "parallel_property_corresponding_angle(1,BC,ED,A)": ["similar_triangle_judgment_aa(1,CAB,DAE)"], "similar_triangle_judgment_aa(1,CAB,DAE)": ["similar_triangle_property_line_ratio(1,CAB,DAE)", "similar_tri... | |
752 | YimingHe_2023-03-12 | Geometry3k-777 | 2 | 如图所示，DA=39，DC=39，∠CBD=17°，BA⊥DA，DC垂直于BC。求∠DBA的大小。 | As shown in the diagram, DA=39, DC=39, ∠CBD=17°, BA⊥DA, DC⊥BC. Find the measure of ∠DBA. | 752.png | [
"Shape(AD,DB,BA)",
"Shape(DC,CB,BD)"
] | [
"Equal(LengthOfLine(DA),39)",
"Equal(LengthOfLine(DC),39)",
"Equal(MeasureOfAngle(CBD),17)",
"PerpendicularBetweenLine(BA,DA)",
"PerpendicularBetweenLine(DC,BC)"
] | [
"Equal(LengthOfLine(DA),39)",
"Equal(LengthOfLine(DC),39)",
"Equal(MeasureOfAngle(CBD),17)",
"PerpendicularBetweenLine(BA,DA)",
"PerpendicularBetweenLine(DC,BC)"
] | Value(MeasureOfAngle(DBA)) | 17 | [
"mirror_similar_triangle_judgment_hl(2,BAD,BDC)",
"mirror_similar_triangle_property_angle_equal(1,BAD,BDC)"
] | {"START": ["mirror_similar_triangle_judgment_hl(2,BAD,BDC)"], "mirror_similar_triangle_judgment_hl(2,BAD,BDC)": ["mirror_similar_triangle_property_angle_equal(1,BAD,BDC)"]} | |
753 | YimingHe_2023-03-12 | Geometry3k-778 | 1 | 如图所示，AC=x，BC=6*sqrt(2)，∠CAB=45°，AB垂直于CB。求x的值。 | As shown in the diagram, AC=x, BC=6*sqrt(2), ∠CAB=45°, AB⊥CB. Find the value of x. | 753.png | [
"Shape(AB,BC,CA)"
] | [
"Equal(LengthOfLine(AC),x)",
"Equal(LengthOfLine(BC),6*sqrt(2))",
"Equal(MeasureOfAngle(CAB),45)",
"PerpendicularBetweenLine(AB,CB)"
] | [
"Equal(LengthOfLine(AC),x)",
"Equal(LengthOfLine(BC),6*sqrt(2))",
"Equal(MeasureOfAngle(CAB),45)",
"PerpendicularBetweenLine(AB,CB)"
] | Value(x) | 12 | [
"sine_theorem(1,CAB)"
] | {"START": ["sine_theorem(1,CAB)"]} | |
754 | YimingHe_2023-03-12 | Geometry3k-779 | 3 | 如图所示，AB=12，AC=x，BC=y，∠BCA=60°，CA垂直于BA。求x的值。 | As shown in the diagram, AB=12, AC=x, BC=y, ∠BCA=60°, CA⊥BA. Find the value of x. | 754.png | [
"Shape(CA,AB,BC)"
] | [
"Equal(LengthOfLine(AB),12)",
"Equal(LengthOfLine(AC),x)",
"Equal(LengthOfLine(BC),y)",
"Equal(MeasureOfAngle(BCA),60)",
"PerpendicularBetweenLine(CA,BA)"
] | [
"Equal(LengthOfLine(AB),12)",
"Equal(LengthOfLine(AC),x)",
"Equal(LengthOfLine(BC),y)",
"Equal(MeasureOfAngle(BCA),60)",
"PerpendicularBetweenLine(CA,BA)"
] | Value(x) | 4*sqrt(3) | [
"triangle_property_angle_sum(1,CAB)",
"sine_theorem(1,CAB)",
"sine_theorem(1,BCA)"
] | {"START": ["triangle_property_angle_sum(1,CAB)", "sine_theorem(1,CAB)", "sine_theorem(1,BCA)"]} | |
755 | YimingHe_2023-03-12 | Geometry3k-780 | 3 | 如图所示，AB=14，AC=20，AD=x，BC=11，∠DBC=∠ABD。求x的值。 | As shown in the diagram, AB=14, AC=20, AD=x, BC=11, ∠DBC=∠ABD. Find the value of x. | 755.png | [
"Shape(BC,CD,DB)",
"Shape(BD,DA,AB)",
"Collinear(CDA)"
] | [
"Equal(LengthOfLine(AB),14)",
"Equal(LengthOfLine(AC),20)",
"Equal(LengthOfLine(AD),x)",
"Equal(LengthOfLine(BC),11)",
"Equal(MeasureOfAngle(DBC),MeasureOfAngle(ABD))"
] | [
"Equal(LengthOfLine(AB),14)",
"Equal(LengthOfLine(AC),20)",
"Equal(LengthOfLine(AD),x)",
"Equal(LengthOfLine(BC),11)",
"Equal(MeasureOfAngle(DBC),MeasureOfAngle(ABD))"
] | Value(x) | 56/5 | [
"bisector_of_angle_judgment_angle_equal(1,BD,ABC)",
"bisector_of_angle_property_line_ratio(1,BD,ABC)",
"line_addition(1,CD,DA)"
] | {"START": ["bisector_of_angle_judgment_angle_equal(1,BD,ABC)", "line_addition(1,CD,DA)"], "bisector_of_angle_judgment_angle_equal(1,BD,ABC)": ["bisector_of_angle_property_line_ratio(1,BD,ABC)"]} | |
756 | YimingHe_2023-03-12 | Geometry3k-781 | 3 | 如图所示，∠VWX=67°，∠XWZ=∠WZX，∠XZY=65°，∠ZYX=58°。求∠WXV的大小。 | As shown in the diagram, ∠VWX=67°, ∠XWZ=∠WZX, ∠XZY=65°, ∠ZYX=58°. Find the measure of ∠WXV. | 756.png | [
"Shape(VW,WX,XV)",
"Shape(XW,WZ,ZX)",
"Shape(XZ,ZY,YX)",
"Collinear(VXZ)",
"Collinear(WXY)"
] | [
"Equal(MeasureOfAngle(VWX),67)",
"Equal(MeasureOfAngle(XWZ),MeasureOfAngle(WZX))",
"Equal(MeasureOfAngle(XZY),65)",
"Equal(MeasureOfAngle(ZYX),58)"
] | [
"Equal(MeasureOfAngle(VWX),67)",
"Equal(MeasureOfAngle(XWZ),MeasureOfAngle(WZX))",
"Equal(MeasureOfAngle(XZY),65)",
"Equal(MeasureOfAngle(ZYX),58)"
] | Value(MeasureOfAngle(WXV)) | 57 | [
"adjacent_complementary_angle(1,ZXW,WXV)",
"adjacent_complementary_angle(1,YXZ,ZXW)",
"triangle_property_angle_sum(1,XZY)"
] | {"START": ["adjacent_complementary_angle(1,ZXW,WXV)", "adjacent_complementary_angle(1,YXZ,ZXW)", "triangle_property_angle_sum(1,XZY)"]} | |
757 | YimingHe_2023-03-12 | Geometry3k-782 | 7 | 如图所示，JM=PM，ML=PL，∠JLP=34°。求∠MPJ的大小。 | As shown in the diagram, JM=PM, ML=PL, ∠JLP=34°. Find the measure of ∠MPJ. | 757.png | [
"Shape(PJ,JM,MP)",
"Shape(PM,ML,LP)",
"Collinear(JML)"
] | [
"Equal(LengthOfLine(JM),LengthOfLine(PM))",
"Equal(LengthOfLine(ML),LengthOfLine(PL))",
"Equal(MeasureOfAngle(JLP),34)"
] | [
"Equal(LengthOfLine(JM),LengthOfLine(PM))",
"Equal(LengthOfLine(ML),LengthOfLine(PL))",
"Equal(MeasureOfAngle(JLP),34)"
] | Value(MeasureOfAngle(MPJ)) | 73/2 | [
"isosceles_triangle_judgment_line_equal(1,MPJ)",
"isosceles_triangle_property_angle_equal(1,MPJ)",
"isosceles_triangle_judgment_line_equal(1,LPM)",
"isosceles_triangle_property_angle_equal(1,LPM)",
"triangle_property_angle_sum(1,PJM)",
"triangle_property_angle_sum(1,PML)",
"adjacent_complementary_angle(... | {"START": ["isosceles_triangle_judgment_line_equal(1,MPJ)", "isosceles_triangle_judgment_line_equal(1,LPM)", "triangle_property_angle_sum(1,PJM)", "triangle_property_angle_sum(1,PML)", "adjacent_complementary_angle(1,JMP,PML)"], "isosceles_triangle_judgment_line_equal(1,LPM)": ["isosceles_triangle_property_angle_equal(... | |
758 | JiaZou_2023-04-09 | Geometry3k-783 | 2 | 如图所示，∠AGB=30°，⊙G的圆心为G，CG垂直于DG。求⌒GDB的角度。 | As shown in the diagram, ∠AGB=30°, G is the center of circle G, CG is perpendicular to DG. Find the measure of arc GDB. | 758.png | [
"Shape(BG,GC,GCB)",
"Shape(AG,GB,GBA)",
"Shape(FG,GA,GAF)",
"Shape(DG,GF,GFD)",
"Shape(CG,GD,GDC)",
"Collinear(AGD)",
"Cocircular(G,AFDCB)"
] | [
"Equal(MeasureOfAngle(AGB),30)",
"IsCentreOfCircle(G,G)",
"PerpendicularBetweenLine(CG,DG)"
] | [
"IsCentreOfCircle(G,G)",
"PerpendicularBetweenLine(CG,DG)"
] | Value(MeasureOfArc(GDB)) | 150 | [
"adjacent_complementary_angle(1,AGB,BGD)",
"arc_property_center_angle(1,GDB,G)"
] | {"START": ["adjacent_complementary_angle(1,AGB,BGD)", "arc_property_center_angle(1,GDB,G)"]} | |
759 | JiaZou_2023-04-09 | Geometry3k-784 | 6 | 如图所示，AB=17，CE=9，∠ACD=45°，CA和DB是▱ACDB的一组对边，AE⊥DE。求ACDB的面积。 | As shown in the diagram, AB=17, CE=9, ∠ACD=45°, AB and CD are opposite sides of the ▱ ACDB, AE⊥DE. Find the area of quadrilateral ACDB. | 759.png | [
"Shape(AC,CE,EA)",
"Shape(AE,ED,DB,BA)",
"Collinear(CED)"
] | [
"Equal(LengthOfLine(AB),17)",
"Equal(LengthOfLine(CE),9)",
"Equal(MeasureOfAngle(ACD),45)",
"Parallelogram(ACDB)",
"PerpendicularBetweenLine(AE,DE)"
] | [
"Equal(LengthOfLine(AB),17)",
"Equal(LengthOfLine(CE),9)",
"Equal(MeasureOfAngle(ACD),45)",
"PerpendicularBetweenLine(AE,DE)"
] | Value(AreaOfQuadrilateral(ACDB)) | 153 | [
"triangle_property_angle_sum(1,ACE)",
"sine_theorem(1,EAC)",
"adjacent_complementary_angle(1,CEA,AED)",
"altitude_of_quadrilateral_judgment_left_vertex(1,AE,ACDB)",
"parallelogram_property_opposite_line_equal(1,CDBA)",
"parallelogram_area_formula_common(1,ACDB)"
] | {"START": ["triangle_property_angle_sum(1,ACE)", "sine_theorem(1,EAC)", "adjacent_complementary_angle(1,CEA,AED)", "parallelogram_property_opposite_line_equal(1,CDBA)", "parallelogram_area_formula_common(1,ACDB)"], "adjacent_complementary_angle(1,CEA,AED)": ["altitude_of_quadrilateral_judgment_left_vertex(1,AE,ACDB)"]} | |
760 | JiaZou_2023-04-09 | Geometry3k-785 | 2 | 如图所示，⊙P的直径与直线CB的长度相等，CB=9，AD⊥BD，BC垂直于AC，CA⊥DA，DB⊥CB。求圆P的周长。 | As shown in the diagram, the diameter of circle P is equal to the length of line CB, CB=9, AD⊥BD, BC is perpendicular to AC, CA is perpendicular to DA, DB⊥CB. Find the circumference of the ⊙P. | 760.png | [
"Shape(FC,CH,PFH)",
"Shape(HA,AG,PHG)",
"Shape(GD,DE,PGE)",
"Shape(EB,BF,PEF)",
"Collinear(CFB)",
"Collinear(CHA)",
"Collinear(AGD)",
"Collinear(DEB)",
"Cocircular(P,FHGE)"
] | [
"Equal(DiameterOfCircle(P),LengthOfLine(CB))",
"Equal(LengthOfLine(CB),9)",
"PerpendicularBetweenLine(AD,BD)",
"PerpendicularBetweenLine(BC,AC)",
"PerpendicularBetweenLine(CA,DA)",
"PerpendicularBetweenLine(DB,CB)"
] | [
"Equal(DiameterOfCircle(P),LengthOfLine(CB))",
"Equal(LengthOfLine(CB),9)",
"PerpendicularBetweenLine(AD,BD)",
"PerpendicularBetweenLine(BC,AC)",
"PerpendicularBetweenLine(CA,DA)",
"PerpendicularBetweenLine(DB,CB)"
] | Value(PerimeterOfCircle(P)) | 9*pi | [
"circle_property_length_of_radius_and_diameter(1,P)",
"circle_perimeter_formula(1,P)"
] | {"START": ["circle_property_length_of_radius_and_diameter(1,P)", "circle_perimeter_formula(1,P)"]} | |
761 | JiaZou_2023-04-09 | Geometry3k-786 | 10 | 如图所示，AB=10，弧OBA的角度为60，⊙O的半径为10，O是圆O的圆心，BX垂直于OX。求直线OX的长度。 | As shown in the diagram, AB=10, the measure of arc OBA is 60, the radius of ⊙O is 10, the center of ⊙O is O, BX is perpendicular to OX. Find the length of line OX. | 761.png | [
"Shape(AX,XY,OYA)",
"Shape(YX,XB,OBY)",
"Shape(OA,OAB,BO)",
"Shape(OX,XA,AO)",
"Shape(XO,OB,BX)",
"Collinear(YXO)",
"Collinear(AXB)",
"Cocircular(O,BYA)"
] | [
"Equal(LengthOfLine(AB),10)",
"Equal(MeasureOfArc(OBA),60)",
"Equal(RadiusOfCircle(O),10)",
"IsCentreOfCircle(O,O)",
"PerpendicularBetweenLine(BX,OX)"
] | [
"IsCentreOfCircle(O,O)",
"PerpendicularBetweenLine(BX,OX)"
] | Value(LengthOfLine(OX)) | 5*sqrt(3) | [
"radius_of_circle_property_length_equal(1,OA,O)",
"radius_of_circle_property_length_equal(1,OB,O)",
"isosceles_triangle_judgment_line_equal(1,OBA)",
"isosceles_triangle_property_angle_equal(1,OBA)",
"arc_property_center_angle(1,OBA,O)",
"triangle_property_angle_sum(1,OBA)",
"circle_property_chord_perpen... | {"START": ["radius_of_circle_property_length_equal(1,OA,O)", "radius_of_circle_property_length_equal(1,OB,O)", "arc_property_center_angle(1,OBA,O)", "triangle_property_angle_sum(1,OBA)", "circle_property_chord_perpendicular_bisect_chord(1,O,OX,BA)", "line_addition(1,AX,XB)", "triangle_property_angle_sum(1,BXO)", "sine_... | |
762 | JiaZou_2023-04-09 | Geometry3k-787 | 3 | 如图所示，∠ADB=11*x-1°，∠BDF=7*y-4°，∠DFH=7*x+9°，∠GAD=2*y+5°，∠HFC=z°，BD∥GA，HF平行于BD。求z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°, BD is parallel to GA, HF is parallel to BD. Find the value of z. | 762.png | [
"Shape(HF,FC)",
"Shape(DF,FH)",
"Shape(BD,DF)",
"Shape(AD,DB)",
"Shape(GA,AD)",
"Shape(EA,AG)",
"Shape(FD,DA)",
"Collinear(DFC)",
"Collinear(DAE)"
] | [
"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(BD,GA)",
"ParallelBetweenLine(HF,BD)"
] | [
"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(BD,GA)",
"ParallelBetweenLine(HF,BD)"
] | Value(z) | 73 | [
"parallel_property_ipsilateral_internal_angle(1,DB,FH)",
"parallel_property_ipsilateral_internal_angle(1,AG,DB)",
"parallel_property_corresponding_angle(2,DB,FH,C)"
] | {"START": ["parallel_property_ipsilateral_internal_angle(1,DB,FH)", "parallel_property_ipsilateral_internal_angle(1,AG,DB)", "parallel_property_corresponding_angle(2,DB,FH,C)"]} | |
763 | JiaZou_2023-04-09 | Geometry3k-788 | 3 | 如图所示，GK=14，MF=8，弧FKG的角度为142，圆F的圆心为F，HJ⊥KJ。求直线JK的长度。 | As shown in the diagram, GK=14, MF=8, the measure of ⌒FKG is 142, F is the center of circle F, HJ is perpendicular to KJ. Find the length of line JK. | 763.png | [
"Shape(GJ,JH,FHG)",
"Shape(HJ,JK,FKH)",
"Shape(MF,FJ,JG,FGM)",
"Shape(KJ,JF,FM,FMK)",
"Collinear(GJK)",
"Collinear(HJFM)",
"Cocircular(F,GMKH)"
] | [
"Equal(LengthOfLine(GK),14)",
"Equal(LengthOfLine(MF),8)",
"Equal(MeasureOfArc(FKG),142)",
"IsCentreOfCircle(F,F)",
"PerpendicularBetweenLine(HJ,KJ)"
] | [
"Equal(LengthOfLine(GK),14)",
"Equal(LengthOfLine(MF),8)",
"Equal(MeasureOfArc(FKG),142)",
"IsCentreOfCircle(F,F)",
"PerpendicularBetweenLine(HJ,KJ)"
] | Value(LengthOfLine(JK)) | 7 | [
"adjacent_complementary_angle(1,HJK,KJF)",
"circle_property_chord_perpendicular_bisect_chord(1,F,FJ,KG)",
"line_addition(1,GJ,JK)"
] | {"START": ["adjacent_complementary_angle(1,HJK,KJF)", "line_addition(1,GJ,JK)"], "adjacent_complementary_angle(1,HJK,KJF)": ["circle_property_chord_perpendicular_bisect_chord(1,F,FJ,KG)"]} | |
764 | YimingHe_2023-03-12 | Geometry3k-789 | 5 | 如图所示，AD=7*y，CA=5*y+16，CE=8*x-18，CE=BE，EB=12-2*x，∠BDA=∠EAC。求y的值。 | As shown in the diagram, AD=7*y, CA=5*y+16, CE=8*x-18, CE=BE, EB=12-2*x, ∠BDA=∠EAC. Find the value of y. | 764.png | [
"Shape(DA,AE,EB,BD)",
"Shape(AC,CE,EA)",
"Collinear(BEC)",
"Collinear(DAC)"
] | [
"Equal(LengthOfLine(AD),7*y)",
"Equal(LengthOfLine(CA),5*y+16)",
"Equal(LengthOfLine(CE),8*x-18)",
"Equal(LengthOfLine(CE),LengthOfLine(BE))",
"Equal(LengthOfLine(EB),12-2*x)",
"Equal(MeasureOfAngle(BDA),MeasureOfAngle(EAC))"
] | [
"Equal(LengthOfLine(AD),7*y)",
"Equal(LengthOfLine(CA),5*y+16)",
"Equal(LengthOfLine(CE),8*x-18)",
"Equal(LengthOfLine(CE),LengthOfLine(BE))",
"Equal(LengthOfLine(EB),12-2*x)",
"Equal(MeasureOfAngle(BDA),MeasureOfAngle(EAC))"
] | Value(y) | 8 | [
"similar_triangle_judgment_aa(1,EAC,BDC)",
"line_addition(1,BE,EC)",
"line_addition(1,DA,AC)",
"similar_triangle_property_line_ratio(1,ACE,DCB)",
"similar_triangle_property_line_ratio(1,EAC,BDC)"
] | {"START": ["similar_triangle_judgment_aa(1,EAC,BDC)", "line_addition(1,BE,EC)", "line_addition(1,DA,AC)"], "similar_triangle_judgment_aa(1,EAC,BDC)": ["similar_triangle_property_line_ratio(1,EAC,BDC)", "similar_triangle_property_line_ratio(1,ACE,DCB)"]} | |
765 | JiaZou_2023-04-09 | Geometry3k-790 | 3 | 如图所示，∠JQR=131°，QR平行于TG，TQ平行于GR。求∠QRH的大小。 | As shown in the diagram, ∠JQR=131°, QR is parallel to TG, TQ is parallel to GR. Find the measure of ∠QRH. | 765.png | [
"Shape(JQ,QR)",
"Shape(QR,RH)",
"Shape(GT,TC)",
"Shape(BG,GT)",
"Shape(QT,TG,GR,RQ)",
"Collinear(JQTC)",
"Collinear(HRGB)"
] | [
"Equal(MeasureOfAngle(JQR),131)",
"ParallelBetweenLine(QR,TG)",
"ParallelBetweenLine(TQ,GR)"
] | [
"Equal(MeasureOfAngle(JQR),131)",
"ParallelBetweenLine(QR,TG)",
"ParallelBetweenLine(TQ,GR)"
] | Value(MeasureOfAngle(QRH)) | 49 | [
"parallel_property_collinear_extend(2,TQ,GR,J)",
"parallel_property_collinear_extend(1,RG,JQ,H)",
"parallel_property_ipsilateral_internal_angle(1,QJ,RH)"
] | {"START": ["parallel_property_collinear_extend(2,TQ,GR,J)"], "parallel_property_collinear_extend(1,RG,JQ,H)": ["parallel_property_ipsilateral_internal_angle(1,QJ,RH)"], "parallel_property_collinear_extend(2,TQ,GR,J)": ["parallel_property_collinear_extend(1,RG,JQ,H)"]} | |
766 | JiaZou_2023-04-09 | Geometry3k-791 | 1 | 如图所示，∠BDA=32°，∠CAS=125°，∠CBA=62°。求∠BAC的大小。 | As shown in the diagram, ∠BDA=32°, ∠CAS=125°, ∠CBA=62°. Find the measure of ∠BAC. | 766.png | [
"Shape(CB,BA,AC)",
"Shape(AB,BD,DA)",
"Shape(CA,AS)",
"Shape(SA,AD)",
"Collinear(BAS)",
"Collinear(CAD)"
] | [
"Equal(MeasureOfAngle(BDA),32)",
"Equal(MeasureOfAngle(CAS),125)",
"Equal(MeasureOfAngle(CBA),62)"
] | [
"Equal(MeasureOfAngle(BDA),32)",
"Equal(MeasureOfAngle(CAS),125)",
"Equal(MeasureOfAngle(CBA),62)"
] | Value(MeasureOfAngle(BAC)) | 55 | [
"adjacent_complementary_angle(1,BAC,CAS)"
] | {"START": ["adjacent_complementary_angle(1,BAC,CAS)"]} | |
767 | JiaZou_2023-04-09 | Geometry3k-792 | 3 | 如图所示，QR=6，RT=x，UT=4，VW=8，WP=3，RQ是圆O的切线，RS是圆O的切线，TS是圆O的切线，TU是圆O的切线。求x的值。 | As shown in the diagram, QR=6, RT=x, UT=4, VW=8, WP=3, the tangent to circle Z is RQ, RS is the tangent to ⊙Z, the tangent to circle Z is TS, TU is the tangent to ⊙Z. Find the value of x. | 767.png | [
"Shape(QP,PW,ZQW)",
"Shape(WV,VU,ZWU)",
"Shape(UT,TS,ZUS)",
"Shape(SR,RQ,ZSQ)",
"Collinear(PQR)",
"Collinear(PWV)",
"Collinear(VUT)",
"Collinear(RST)",
"Cocircular(Z,QWUS)"
] | [
"Equal(LengthOfLine(QR),6)",
"Equal(LengthOfLine(RT),x)",
"Equal(LengthOfLine(UT),4)",
"Equal(LengthOfLine(VW),8)",
"Equal(LengthOfLine(WP),3)",
"IsTangentOfCircle(RQ,Z)",
"IsTangentOfCircle(RS,Z)",
"IsTangentOfCircle(TS,Z)",
"IsTangentOfCircle(TU,Z)"
] | [
"Equal(LengthOfLine(QR),6)",
"Equal(LengthOfLine(RT),x)",
"Equal(LengthOfLine(UT),4)",
"Equal(LengthOfLine(VW),8)",
"Equal(LengthOfLine(WP),3)",
"IsTangentOfCircle(RQ,Z)",
"IsTangentOfCircle(RS,Z)",
"IsTangentOfCircle(TS,Z)",
"IsTangentOfCircle(TU,Z)"
] | Value(x) | 10 | [
"tangent_of_circle_property_length_equal(1,RS,RQ,Z)",
"tangent_of_circle_property_length_equal(1,TU,TS,Z)",
"line_addition(1,RS,ST)"
] | {"START": ["tangent_of_circle_property_length_equal(1,RS,RQ,Z)", "tangent_of_circle_property_length_equal(1,TU,TS,Z)", "line_addition(1,RS,ST)"]} | |
768 | JiaZou_2023-04-09 | Geometry3k-793 | 5 | 如图所示，PM=LM，⌒OMP的角度为x，⌒OPL的角度为106。求x的值。 | As shown in the diagram, PM=LM, the measure of arc OMP is x, the measure of ⌒OPL is 106. Find the value of x. | 768.png | [
"Shape(LM,MP,PL)",
"Shape(ML,OLM)",
"Shape(PM,OMP)",
"Shape(LP,OOL)",
"Cocircular(O,LMP)"
] | [
"Equal(LengthOfLine(PM),LengthOfLine(LM))",
"Equal(MeasureOfArc(OMP),x)",
"Equal(MeasureOfArc(OPL),106)"
] | [
"Equal(LengthOfLine(PM),LengthOfLine(LM))",
"Equal(MeasureOfArc(OMP),x)",
"Equal(MeasureOfArc(OPL),106)"
] | Value(x) | 127 | [
"arc_property_circumference_angle_external(1,OPL,M)",
"arc_property_circumference_angle_external(1,OMP,L)",
"isosceles_triangle_judgment_line_equal(1,MPL)",
"isosceles_triangle_property_angle_equal(1,MPL)",
"triangle_property_angle_sum(1,MPL)"
] | {"START": ["arc_property_circumference_angle_external(1,OPL,M)", "arc_property_circumference_angle_external(1,OMP,L)", "isosceles_triangle_judgment_line_equal(1,MPL)", "triangle_property_angle_sum(1,MPL)"], "isosceles_triangle_judgment_line_equal(1,MPL)": ["isosceles_triangle_property_angle_equal(1,MPL)"]} | |
769 | JiaZou_2023-04-09 | Geometry3k-794 | 1 | 如图所示，∠AEJ=3*y+44°，∠CAE=94°，∠EJC=2*x°，∠JCA=96°，AC平行于EJ。求x的值。 | As shown in the diagram, ∠AEJ=3*y+44°, ∠CAE=94°, ∠EJC=2*x°, ∠JCA=96°, AC is parallel to EJ. Find the value of x. | 769.png | [
"Shape(CA,AE,EJ,JC)"
] | [
"Equal(MeasureOfAngle(AEJ),3*y+44)",
"Equal(MeasureOfAngle(CAE),94)",
"Equal(MeasureOfAngle(EJC),2*x)",
"Equal(MeasureOfAngle(JCA),96)",
"ParallelBetweenLine(AC,EJ)"
] | [
"Equal(MeasureOfAngle(AEJ),3*y+44)",
"Equal(MeasureOfAngle(CAE),94)",
"Equal(MeasureOfAngle(EJC),2*x)",
"Equal(MeasureOfAngle(JCA),96)",
"ParallelBetweenLine(AC,EJ)"
] | Value(x) | 42 | [
"parallel_property_ipsilateral_internal_angle(1,JE,CA)"
] | {"START": ["parallel_property_ipsilateral_internal_angle(1,JE,CA)"]} | |
770 | JiaZou_2023-04-09 | Geometry3k-795 | 3 | 如图所示，DA=7，F是圆F的圆心，DA是圆F的直径。求直线EF的长度。 | As shown in the diagram, DA=7, the center of circle F is F, DA is the diameter of ⊙F. Find the length of line EF. | 770.png | [
"Shape(CF,FD,FDC)",
"Shape(BF,FC,FCB)",
"Shape(AF,FB,FBA)",
"Shape(FA,AE,EF)",
"Shape(DF,FE,ED)",
"Shape(EA,FAE)",
"Shape(DE,FED)",
"Collinear(BFE)",
"Collinear(AFD)",
"Cocircular(F,AEDCB)"
] | [
"Equal(LengthOfLine(DA),7)",
"IsCentreOfCircle(F,F)",
"IsDiameterOfCircle(DA,F)"
] | [
"Equal(LengthOfLine(DA),7)",
"IsCentreOfCircle(F,F)",
"IsDiameterOfCircle(DA,F)"
] | Value(LengthOfLine(EF)) | 7/2 | [
"diameter_of_circle_property_length_equal(1,DA,F)",
"radius_of_circle_property_length_equal(1,FE,F)",
"circle_property_length_of_radius_and_diameter(1,F)"
] | {"START": ["diameter_of_circle_property_length_equal(1,DA,F)", "radius_of_circle_property_length_equal(1,FE,F)", "circle_property_length_of_radius_and_diameter(1,F)"]} | |
771 | YimingHe_2023-03-12 | Geometry3k-796 | 1 | 如图所示，VX=75，WV=72，WX=21，VW垂直于XW。求tan(XV)的值。 | As shown in the diagram, VX=75, WV=72, WX=21, VW⊥XW. Find the value of tan(XV). | 771.png | [
"Shape(VW,WX,XV)"
] | [
"Equal(LengthOfLine(VX),75)",
"Equal(LengthOfLine(WV),72)",
"Equal(LengthOfLine(WX),21)",
"PerpendicularBetweenLine(VW,XW)"
] | [
"Equal(LengthOfLine(VX),75)",
"Equal(LengthOfLine(WV),72)",
"Equal(LengthOfLine(WX),21)",
"PerpendicularBetweenLine(VW,XW)"
] | Value(Tan(MeasureOfAngle(XVW))) | 7/24 | [
"cosine_theorem(1,VWX)"
] | {"START": ["cosine_theorem(1,VWX)"]} | |
772 | YimingHe_2023-03-12 | Geometry3k-797 | 7 | 如图所示，QS=14，RS=3，PS垂直于QS，QP⊥RP。求直线PS的长度。 | As shown in the diagram, QS=14, RS=3, PS⊥QS, QP⊥RP. Find the length of line PS. | 772.png | [
"Shape(PR,RS,SP)",
"Shape(PS,SQ,QP)",
"Collinear(RSQ)"
] | [
"Equal(LengthOfLine(QS),14)",
"Equal(LengthOfLine(RS),3)",
"PerpendicularBetweenLine(PS,QS)",
"PerpendicularBetweenLine(QP,RP)"
] | [
"Equal(LengthOfLine(QS),14)",
"Equal(LengthOfLine(RS),3)",
"PerpendicularBetweenLine(PS,QS)",
"PerpendicularBetweenLine(QP,RP)"
] | Value(LengthOfLine(PS)) | sqrt(42) | [
"adjacent_complementary_angle(1,RSP,PSQ)",
"mirror_similar_triangle_judgment_aa(1,PRS,QPR)",
"mirror_similar_triangle_property_line_ratio(1,PRS,QPR)",
"mirror_similar_triangle_property_line_ratio(1,SPR,PRQ)",
"line_addition(1,RS,SQ)",
"right_triangle_judgment_angle(1,RSP)",
"right_triangle_property_pyth... | {"START": ["adjacent_complementary_angle(1,RSP,PSQ)", "line_addition(1,RS,SQ)"], "adjacent_complementary_angle(1,RSP,PSQ)": ["mirror_similar_triangle_judgment_aa(1,PRS,QPR)", "right_triangle_judgment_angle(1,RSP)"], "mirror_similar_triangle_judgment_aa(1,PRS,QPR)": ["mirror_similar_triangle_property_line_ratio(1,PRS,QP... | |
773 | YimingHe_2023-03-12 | Geometry3k-798 | 5 | 如图所示，PQ=6-x，QS=3+x，RQ=6+x，TQ=3，TP∥RS。求x的值。 | As shown in the diagram, PQ=6-x, QS=3+x, RQ=6+x, TQ=3, TP∥RS. Find the value of x. | 773.png | [
"Shape(PT,TQ,QP)",
"Shape(QR,RS,SQ)",
"Collinear(PQR)",
"Collinear(TQS)"
] | [
"Equal(LengthOfLine(PQ),6-x)",
"Equal(LengthOfLine(QS),3+x)",
"Equal(LengthOfLine(RQ),6+x)",
"Equal(LengthOfLine(TQ),3)",
"ParallelBetweenLine(TP,RS)"
] | [
"Equal(LengthOfLine(PQ),6-x)",
"Equal(LengthOfLine(QS),3+x)",
"Equal(LengthOfLine(RQ),6+x)",
"Equal(LengthOfLine(TQ),3)",
"ParallelBetweenLine(TP,RS)"
] | Value(x) | 0 | [
"parallel_property_alternate_interior_angle(1,TP,RS)",
"parallel_property_alternate_interior_angle(2,TP,RS)",
"similar_triangle_judgment_aa(1,QPT,QRS)",
"similar_triangle_property_line_ratio(1,TQP,SQR)",
"similar_triangle_property_line_ratio(1,PTQ,RSQ)"
] | {"START": ["parallel_property_alternate_interior_angle(1,TP,RS)", "parallel_property_alternate_interior_angle(2,TP,RS)"], "parallel_property_alternate_interior_angle(1,TP,RS)": ["similar_triangle_judgment_aa(1,QPT,QRS)"], "parallel_property_alternate_interior_angle(2,TP,RS)": ["similar_triangle_judgment_aa(1,QPT,QRS)"]... | |
774 | YimingHe_2023-03-12 | Geometry3k-799 | 1 | 如图所示，AB=y，AC=x，BC=15，∠BAC=60°，AC⊥BC。求y的值。 | As shown in the diagram, AB=y, AC=x, BC=15, ∠BAC=60°, AC⊥BC. Find the value of y. | 774.png | [
"Shape(CB,BA,AC)"
] | [
"Equal(LengthOfLine(AB),y)",
"Equal(LengthOfLine(AC),x)",
"Equal(LengthOfLine(BC),15)",
"Equal(MeasureOfAngle(BAC),60)",
"PerpendicularBetweenLine(AC,BC)"
] | [
"Equal(LengthOfLine(AB),y)",
"Equal(LengthOfLine(AC),x)",
"Equal(LengthOfLine(BC),15)",
"Equal(MeasureOfAngle(BAC),60)",
"PerpendicularBetweenLine(AC,BC)"
] | Value(y) | 10*sqrt(3) | [
"sine_theorem(1,BAC)"
] | {"START": ["sine_theorem(1,BAC)"]} | |
775 | YimingHe_2023-03-12 | Geometry3k-800 | 0 | 如图所示，RS=TR，RT=3*x+3，SR=4*x-4，ST=12+x。求x的值。 | As shown in the diagram, RS=TR, RT=3*x+3, SR=4*x-4, ST=12+x. Find the value of x. | 775.png | [
"Shape(SR,RT,TS)"
] | [
"Equal(LengthOfLine(RS),LengthOfLine(TR))",
"Equal(LengthOfLine(RT),3*x+3)",
"Equal(LengthOfLine(SR),4*x-4)",
"Equal(LengthOfLine(ST),12+x)"
] | [
"Equal(LengthOfLine(RS),LengthOfLine(TR))",
"Equal(LengthOfLine(RT),3*x+3)",
"Equal(LengthOfLine(SR),4*x-4)",
"Equal(LengthOfLine(ST),12+x)"
] | Value(x) | 7 | [] | {"START": []} | |
776 | YimingHe_2023-03-12 | Geometry3k-801 | 1 | 如图所示，HP=5*x-16，PJ=3*x+8，∠AJP=4*y+23°，∠GMA=4*z+14°，∠MJA=6*y-3°，JN平分∠GJH。求∠GJH的大小。 | As shown in the diagram, HP=5*x-16, PJ=3*x+8, ∠AJP=4*y+23°, ∠GMA=4*z+14°, ∠MJA=6*y-3°, JN is the angle bisector of ∠GJH. Find the measure of ∠GJH. | 776.png | [
"Shape(NG,GB,BN)",
"Shape(BG,GM,MA,AB)",
"Shape(AM,MJ,JA)",
"Shape(AJ,JP,PZ,ZA)",
"Shape(ZP,PH,HZ)",
"Shape(ZH,HN,NB,BZ)",
"Shape(BA,AZ,ZB)",
"Collinear(GNH)",
"Collinear(GMJ)",
"Collinear(HPJ)",
"Collinear(NBAJ)",
"Collinear(MAZH)",
"Collinear(GBZP)"
] | [
"Equal(LengthOfLine(HP),5*x-16)",
"Equal(LengthOfLine(PJ),3*x+8)",
"Equal(MeasureOfAngle(AJP),4*y+23)",
"Equal(MeasureOfAngle(GMA),4*z+14)",
"Equal(MeasureOfAngle(MJA),6*y-3)",
"IsBisectorOfAngle(JN,GJH)"
] | [] | Value(MeasureOfAngle(GJH)) | 150 | [
"angle_addition(1,GJN,NJH)"
] | {"START": ["angle_addition(1,GJN,NJH)"]} | |
777 | JiaZou_2023-04-09 | Geometry3k-802 | 2 | 如图所示，∠JMK=55°，∠JMK=∠PMR，∠MRP=70°，JMLK是矩形，四边形MRPL是菱形。求∠RPM的大小。 | As shown in the diagram, ∠JMK=55°, ∠JMK=∠PMR, ∠MRP=70°, JMLK is a rectangle, MRPL is a rhombus. Find the measure of ∠RPM. | 777.png | [
"Shape(JM,MK,KJ)",
"Shape(ML,LK,KM)",
"Shape(MP,PL,LM)",
"Shape(MR,RP,PM)"
] | [
"Equal(MeasureOfAngle(JMK),55)",
"Equal(MeasureOfAngle(JMK),MeasureOfAngle(PMR))",
"Equal(MeasureOfAngle(MRP),70)",
"Rectangle(JMLK)",
"Rhombus(MRPL)"
] | [
"Equal(MeasureOfAngle(JMK),55)",
"Equal(MeasureOfAngle(JMK),MeasureOfAngle(PMR))",
"Equal(MeasureOfAngle(MRP),70)",
"Rectangle(JMLK)",
"Rhombus(MRPL)"
] | Value(MeasureOfAngle(RPM)) | 55 | [
"isosceles_triangle_judgment_line_equal(1,RPM)",
"isosceles_triangle_property_angle_equal(1,RPM)"
] | {"START": ["isosceles_triangle_judgment_line_equal(1,RPM)"], "isosceles_triangle_judgment_line_equal(1,RPM)": ["isosceles_triangle_property_angle_equal(1,RPM)"]} | |
778 | NaZhu_2023-04-09 | Geometry3k-803 | 1 | 如图所示，ADCB的面积为750，BA=35，CD=25，DF⊥EF，ADCB是梯形。求四边形ADCB的高。 | As shown in the diagram, the area of ADCB is 750, BA=35, CD=25, DF⊥EF, AD and CB are the non-parallel sides (legs) of trapezoid ADCB. Find the height of ADCB. | 778.png | [
"Shape(AD,DF,FE,EA)",
"Shape(EF,FC,CB,BE)",
"Collinear(AEB)",
"Collinear(DFC)"
] | [
"Equal(AreaOfQuadrilateral(ADCB),750)",
"Equal(LengthOfLine(BA),35)",
"Equal(LengthOfLine(CD),25)",
"PerpendicularBetweenLine(DF,EF)",
"Trapezoid(ADCB)"
] | [
"Equal(AreaOfQuadrilateral(ADCB),750)",
"Equal(LengthOfLine(BA),35)",
"Equal(LengthOfLine(CD),25)",
"PerpendicularBetweenLine(DF,EF)"
] | Value(HeightOfQuadrilateral(ADCB)) | 25 | [
"trapezoid_area_formula(1,ADCB)"
] | {"START": ["trapezoid_area_formula(1,ADCB)"]} | |
779 | NaZhu_2023-04-09 | Geometry3k-804 | 4 | 如图所示，FH=8，FH=FL，FK=17，圆F的圆心为F，FL垂直于KL，JH垂直于FH。求直线JH的长度。 | As shown in the diagram, FH=8, FH=FL, FK=17, F is the center of ⊙F, FL is perpendicular to KL, JH is perpendicular to FH. Find the length of line JH. | 779.png | [
"Shape(FJG,GH,HJ)",
"Shape(FMK,KL,LM)",
"Shape(FKJ,JF,FK)",
"Shape(FJ,JH,HF)",
"Shape(KF,FL,LK)",
"Shape(FGM,ML,LF,FH,HG)",
"Collinear(JHG)",
"Collinear(KLM)",
"Collinear(HFL)",
"Cocircular(F,KJGM)"
] | [
"Equal(LengthOfLine(FH),8)",
"Equal(LengthOfLine(FH),LengthOfLine(FL))",
"Equal(LengthOfLine(FK),17)",
"IsCentreOfCircle(F,F)",
"PerpendicularBetweenLine(FL,KL)",
"PerpendicularBetweenLine(JH,FH)"
] | [
"Equal(LengthOfLine(FH),8)",
"IsCentreOfCircle(F,F)",
"PerpendicularBetweenLine(FL,KL)",
"PerpendicularBetweenLine(JH,FH)"
] | Value(LengthOfLine(JH)) | 15 | [
"radius_of_circle_property_length_equal(1,FK,F)",
"radius_of_circle_property_length_equal(1,FJ,F)",
"right_triangle_judgment_angle(1,JHF)",
"right_triangle_property_pythagorean(1,JHF)"
] | {"START": ["radius_of_circle_property_length_equal(1,FK,F)", "radius_of_circle_property_length_equal(1,FJ,F)", "right_triangle_judgment_angle(1,JHF)"], "right_triangle_judgment_angle(1,JHF)": ["right_triangle_property_pythagorean(1,JHF)"]} | |
780 | NaZhu_2023-04-09 | Geometry3k-805 | 2 | 如图所示，EK=y，JQ=2*x+6，KM=3/5*y+2，RJ=20-5*x，RJ=JQ，JK平行于QM，RE平行于JK，RE∥QM。求y的值。 | As shown in the diagram, EK=y, JQ=2*x+6, KM=3/5*y+2, RJ=20-5*x, RJ=JQ, JK∥QM, RE∥JK, RE is parallel to QM. Find the value of y. | 780.png | [
"Shape(RJ,JK,KE,ER)",
"Shape(JQ,QM,MK,KJ)",
"Shape(GR,RB)",
"Shape(BR,RE)",
"Shape(JR,RG)",
"Shape(RE,EA)",
"Shape(AE,EO)",
"Shape(OE,EK)",
"Shape(XQ,QJ)",
"Shape(IQ,QX)",
"Shape(MQ,QI)",
"Shape(KM,MH)",
"Shape(HM,MY)",
"Shape(YM,MQ)",
"Shape(PJ,JR)",
"Shape(QJ,JP)",
"Shape(EK,KP)",
... | [
"Equal(LengthOfLine(EK),y)",
"Equal(LengthOfLine(JQ),2*x+6)",
"Equal(LengthOfLine(KM),3/5*y+2)",
"Equal(LengthOfLine(RJ),20-5*x)",
"Equal(LengthOfLine(RJ),LengthOfLine(JQ))",
"ParallelBetweenLine(JK,QM)",
"ParallelBetweenLine(RE,JK)",
"ParallelBetweenLine(RE,QM)"
] | [
"Equal(LengthOfLine(EK),y)",
"Equal(LengthOfLine(JQ),2*x+6)",
"Equal(LengthOfLine(KM),3/5*y+2)",
"Equal(LengthOfLine(RJ),20-5*x)",
"Equal(LengthOfLine(RJ),LengthOfLine(JQ))",
"ParallelBetweenLine(JK,QM)",
"ParallelBetweenLine(RE,JK)",
"ParallelBetweenLine(RE,QM)"
] | Value(y) | 5 | [
"trapezoid_judgment_parallel(1,RQME)",
"midsegment_of_quadrilateral_judgment_parallel(1,JK,RQME)"
] | {"START": ["trapezoid_judgment_parallel(1,RQME)"], "trapezoid_judgment_parallel(1,RQME)": ["midsegment_of_quadrilateral_judgment_parallel(1,JK,RQME)"]} | |
781 | YimingHe_2023-03-12 | Geometry3k-806 | 1 | 如图所示，三角形RVS全等于三角形TSV，RS=2*y-1，ST=24.5，VT=24，VS垂直于RS。求y的值。 | As shown in the diagram, △RVS is congruent to △TSV, RS=2*y-1, ST=24.5, VT=24, VS is perpendicular to RS. Find the value of y. | 781.png | [
"Shape(RV,VS,SR)",
"Shape(SV,VT,TS)"
] | [
"CongruentBetweenTriangle(RVS,TSV)",
"Equal(LengthOfLine(RS),2*y-1)",
"Equal(LengthOfLine(ST),24.5)",
"Equal(LengthOfLine(VT),24)",
"PerpendicularBetweenLine(VS,RS)"
] | [
"CongruentBetweenTriangle(RVS,TSV)",
"Equal(LengthOfLine(RS),2*y-1)",
"Equal(LengthOfLine(ST),24.5)",
"Equal(LengthOfLine(VT),24)",
"PerpendicularBetweenLine(VS,RS)"
] | Value(y) | 25/2 | [
"congruent_triangle_property_line_equal(1,VSR,SVT)"
] | {"START": ["congruent_triangle_property_line_equal(1,VSR,SVT)"]} | |
782 | NaZhu_2023-04-09 | Geometry3k-807 | 1 | 如图所示，BK=8，KC=12，KF=16。求直线JK的长度。 | As shown in the diagram, BK=8, KC=12, KF=16. Find the length of line JK. | 782.png | [
"Shape(DAB,BA)",
"Shape(DBJ,JK,KB)",
"Shape(BK,KM,MA,AB)",
"Shape(AM,MF,DFA)",
"Shape(DFA,FE,EA)",
"Shape(DJC,CK,KJ)",
"Shape(MK,KC,CD,DM)",
"Shape(MD,DF,FM)",
"Shape(DC,DCH,HD)",
"Shape(DH,DHF,FD)",
"Shape(DHF,HG,GF)",
"Collinear(JKMF)",
"Collinear(BKC)",
"Collinear(AMDC)",
"Collinear(D... | [
"Equal(LengthOfLine(BK),8)",
"Equal(LengthOfLine(KC),12)",
"Equal(LengthOfLine(KF),16)"
] | [] | Value(LengthOfLine(JK)) | 6 | [
"circle_property_circular_power_chord_and_chord(1,BKC,JKF,D)"
] | {"START": ["circle_property_circular_power_chord_and_chord(1,BKC,JKF,D)"]} | |
783 | NaZhu_2023-04-09 | Geometry3k-808 | 2 | 如图所示，AB=6*y+1/2*x，AD=21，BC=3*x+3*y，DC=2*x+4*y，DC和AB是平行四边形DABC的一组对边。求x的值。 | As shown in the diagram, AB=6*y+1/2*x, AD=21, BC=3*x+3*y, DC=2*x+4*y, DABC is a parallelogram. Find the value of x. | 783.png | [
"Shape(DA,AB,BC,CD)"
] | [
"Equal(LengthOfLine(AB),6*y+1/2*x)",
"Equal(LengthOfLine(AD),21)",
"Equal(LengthOfLine(BC),3*x+3*y)",
"Equal(LengthOfLine(DC),2*x+4*y)",
"Parallelogram(DABC)"
] | [
"Equal(LengthOfLine(AB),6*y+1/2*x)",
"Equal(LengthOfLine(AD),21)",
"Equal(LengthOfLine(BC),3*x+3*y)",
"Equal(LengthOfLine(DC),2*x+4*y)"
] | Value(x) | 4 | [
"parallelogram_property_opposite_line_equal(1,DABC)",
"parallelogram_property_opposite_line_equal(1,ABCD)"
] | {"START": ["parallelogram_property_opposite_line_equal(1,DABC)", "parallelogram_property_opposite_line_equal(1,ABCD)"]} | |
784 | YimingHe_2023-03-12 | Geometry3k-809 | 3 | 如图所示，JH=4*x+7，JK=25，KH=6*x-2，NQ=12，PN=8，PQ=20，∠JHK=∠QNP，∠KJH=∠PQN。求直线HJ的长度。 | As shown in the diagram, JH=4*x+7, JK=25, KH=6*x-2, NQ=12, PN=8, PQ=20, ∠JHK=∠QNP, ∠KJH=∠PQN. Find the length of line HJ. | 784.png | [
"Shape(JH,HK,KJ)",
"Shape(PQ,QN,NP)"
] | [
"Equal(LengthOfLine(JH),4*x+7)",
"Equal(LengthOfLine(JK),25)",
"Equal(LengthOfLine(KH),6*x-2)",
"Equal(LengthOfLine(NQ),12)",
"Equal(LengthOfLine(PN),8)",
"Equal(LengthOfLine(PQ),20)",
"Equal(MeasureOfAngle(JHK),MeasureOfAngle(QNP))",
"Equal(MeasureOfAngle(KJH),MeasureOfAngle(PQN))"
] | [
"Equal(LengthOfLine(JH),4*x+7)",
"Equal(LengthOfLine(JK),25)",
"Equal(LengthOfLine(KH),6*x-2)",
"Equal(LengthOfLine(NQ),12)",
"Equal(LengthOfLine(PN),8)",
"Equal(LengthOfLine(PQ),20)",
"Equal(MeasureOfAngle(JHK),MeasureOfAngle(QNP))",
"Equal(MeasureOfAngle(KJH),MeasureOfAngle(PQN))"
] | Value(LengthOfLine(HJ)) | 15 | [
"similar_triangle_judgment_aa(1,KJH,PQN)",
"similar_triangle_property_line_ratio(1,KJH,PQN)",
"similar_triangle_property_line_ratio(1,HKJ,NPQ)"
] | {"START": ["similar_triangle_judgment_aa(1,KJH,PQN)"], "similar_triangle_judgment_aa(1,KJH,PQN)": ["similar_triangle_property_line_ratio(1,KJH,PQN)", "similar_triangle_property_line_ratio(1,HKJ,NPQ)"]} | |
785 | YimingHe_2023-03-12 | Geometry3k-810 | 1 | 如图所示，PR=8，QR=17，RQ=15，QR⊥PR。求cos(PQ)的值。 | As shown in the diagram, PR=8, QR=17, RQ=15, QR⊥PR. Find the value of cos(PQ). | 785.png | [
"Shape(QR,RP,PQ)"
] | [
"Equal(LengthOfLine(PR),8)",
"Equal(LengthOfLine(QP),17)",
"Equal(LengthOfLine(RQ),15)",
"PerpendicularBetweenLine(QR,PR)"
] | [
"Equal(LengthOfLine(PR),8)",
"Equal(LengthOfLine(QP),17)",
"Equal(LengthOfLine(RQ),15)",
"PerpendicularBetweenLine(QR,PR)"
] | Value(Cos(MeasureOfAngle(PQR))) | 15/17 | [
"cosine_theorem(1,QRP)"
] | {"START": ["cosine_theorem(1,QRP)"]} | |
786 | NaZhu_2023-04-09 | Geometry3k-811 | 3 | 如图所示，WP=6，XP=8，YP=24，ZP=8，YZ和YX是风筝形WZYX的一组临边。求直线ZY的长度。 | As shown in the diagram, WP=6, XP=8, YP=24, ZP=8, WZYX is a kite. Find the length of line ZY. | 786.png | [
"Shape(XW,WP,PX)",
"Shape(WZ,ZP,PW)",
"Shape(XP,PY,YX)",
"Shape(PZ,ZY,YP)",
"Collinear(XPZ)",
"Collinear(WPY)"
] | [
"Equal(LengthOfLine(WP),6)",
"Equal(LengthOfLine(XP),8)",
"Equal(LengthOfLine(YP),24)",
"Equal(LengthOfLine(ZP),8)",
"Kite(WZYX)"
] | [
"Equal(LengthOfLine(WP),6)",
"Equal(LengthOfLine(XP),8)",
"Equal(LengthOfLine(YP),24)",
"Equal(LengthOfLine(ZP),8)"
] | Value(LengthOfLine(ZY)) | 8*sqrt(10) | [
"kite_property_diagonal_perpendicular_bisection(1,YXWZ,P)",
"right_triangle_judgment_angle(1,YPZ)",
"right_triangle_property_pythagorean(1,YPZ)"
] | {"START": ["kite_property_diagonal_perpendicular_bisection(1,YXWZ,P)"], "kite_property_diagonal_perpendicular_bisection(1,YXWZ,P)": ["right_triangle_judgment_angle(1,YPZ)"], "right_triangle_judgment_angle(1,YPZ)": ["right_triangle_property_pythagorean(1,YPZ)"]} | |
787 | YimingHe_2023-03-12 | Geometry3k-812 | 3 | 如图所示，CA=x，CB=24，∠CAD=32°，AC⊥CC，BC垂直于AC。求x的值。 | As shown in the diagram, CA=x, CB=24, ∠CAD=32°, AC is perpendicular to CC, BC⊥AC. Find the value of x. | 787.png | [
"Shape(AD,DC,CA)",
"Shape(CD,DB,BC)",
"Collinear(ADB)"
] | [
"Equal(LengthOfLine(CA),x)",
"Equal(LengthOfLine(CB),24)",
"Equal(MeasureOfAngle(CAD),32)",
"PerpendicularBetweenLine(AC,CD)",
"PerpendicularBetweenLine(BC,AC)"
] | [
"Equal(LengthOfLine(CA),x)",
"Equal(LengthOfLine(CB),24)",
"Equal(MeasureOfAngle(CAD),32)",
"PerpendicularBetweenLine(AC,CD)",
"PerpendicularBetweenLine(BC,AC)"
] | Value(x) | 24*sqrt(1-sin(8*pi/45)**2)/sin(8*pi/45) | [
"sine_theorem(1,BCA)",
"right_triangle_judgment_angle(1,BCA)",
"right_triangle_property_pythagorean(1,BCA)"
] | {"START": ["sine_theorem(1,BCA)", "right_triangle_judgment_angle(1,BCA)"], "right_triangle_judgment_angle(1,BCA)": ["right_triangle_property_pythagorean(1,BCA)"]} | |
788 | XiaokaiZhang_2023-03-19 | Geometry3k-813 | 3 | 如图所示，LM=7*x+1，LP=10*x-5，PN=NM，LN⊥MN。求直线LP的长度。 | As shown in the diagram, LM=7*x+1, LP=10*x-5, PN=NM, LN is perpendicular to MN. Find the length of line LP. | 788.png | [
"Shape(LP,PN,NL)",
"Shape(LN,NM,ML)",
"Collinear(PNM)"
] | [
"Equal(LengthOfLine(LM),7*x+1)",
"Equal(LengthOfLine(LP),10*x-5)",
"Equal(LengthOfLine(PN),LengthOfLine(NM))",
"PerpendicularBetweenLine(LN,MN)"
] | [
"Equal(LengthOfLine(LM),7*x+1)",
"Equal(LengthOfLine(LP),10*x-5)",
"Equal(LengthOfLine(PN),LengthOfLine(NM))",
"PerpendicularBetweenLine(LN,MN)"
] | Value(LengthOfLine(LP)) | 15 | [
"adjacent_complementary_angle(1,PNL,LNM)",
"perpendicular_bisector_judgment_per_and_mid(1,LN,PM)",
"perpendicular_bisector_property_distance_equal(1,LN,PM)"
] | {"START": ["adjacent_complementary_angle(1,PNL,LNM)"], "adjacent_complementary_angle(1,PNL,LNM)": ["perpendicular_bisector_judgment_per_and_mid(1,LN,PM)"], "perpendicular_bisector_judgment_per_and_mid(1,LN,PM)": ["perpendicular_bisector_property_distance_equal(1,LN,PM)"]} | |
789 | NaZhu_2023-04-09 | Geometry3k-814 | 1 | 如图所示，∠TWV=3*x-4°，∠UTW=x°，∠VUT=3*x-4°，∠WVU=x°。求∠WVU的大小。 | As shown in the diagram, ∠TWV=3*x-4°, ∠UTW=x°, ∠VUT=3*x-4°, ∠WVU=x°. Find the measure of ∠WVU. | 789.png | [
"Shape(UT,TW,WV,VU)"
] | [
"Equal(MeasureOfAngle(TWV),3*x-4)",
"Equal(MeasureOfAngle(UTW),x)",
"Equal(MeasureOfAngle(VUT),3*x-4)",
"Equal(MeasureOfAngle(WVU),x)"
] | [
"Equal(MeasureOfAngle(TWV),3*x-4)",
"Equal(MeasureOfAngle(UTW),x)",
"Equal(MeasureOfAngle(VUT),3*x-4)",
"Equal(MeasureOfAngle(WVU),x)"
] | Value(MeasureOfAngle(WVU)) | 46 | [
"quadrilateral_property_angle_sum(1,UTWV)"
] | {"START": ["quadrilateral_property_angle_sum(1,UTWV)"]} | |
790 | NaZhu_2023-04-09 | Geometry3k-815 | 1 | 如图所示，AC=4*y-8，AD=x+4，CB=2*x-4，DB=3*y-2，BCAD是平行四边形。求x的值。 | As shown in the diagram, AC=4*y-8, AD=x+4, CB=2*x-4, DB=3*y-2, BD and CA are opposite sides of the ▱ BCAD. Find the value of x. | 790.png | [
"Shape(BC,CA,AD,DB)"
] | [
"Equal(LengthOfLine(AC),4*y-8)",
"Equal(LengthOfLine(AD),x+4)",
"Equal(LengthOfLine(CB),2*x-4)",
"Equal(LengthOfLine(DB),3*y-2)",
"Parallelogram(BCAD)"
] | [
"Equal(LengthOfLine(AC),4*y-8)",
"Equal(LengthOfLine(AD),x+4)",
"Equal(LengthOfLine(CB),2*x-4)",
"Equal(LengthOfLine(DB),3*y-2)"
] | Value(x) | 8 | [
"parallelogram_property_opposite_line_equal(1,BCAD)"
] | {"START": ["parallelogram_property_opposite_line_equal(1,BCAD)"]} | |
791 | NaZhu_2023-04-09 | Geometry3k-817 | 2 | 如图所示，∠CFD=7*x-38°，∠EHI=178-3*x°，BH∥DF。求x的值。 | As shown in the diagram, ∠CFD=7*x-38°, ∠EHI=178-3*x°, BH∥DF. Find the value of x. | 791.png | [
"Shape(EH,HI)",
"Shape(BH,HE)",
"Shape(FH,HB)",
"Shape(IH,HF)",
"Shape(DF,FH)",
"Shape(HF,FG)",
"Shape(CF,FD)",
"Shape(GF,FC)",
"Collinear(BHI)",
"Collinear(DFG)",
"Collinear(EHFC)"
] | [
"Equal(MeasureOfAngle(CFD),7*x-38)",
"Equal(MeasureOfAngle(EHI),178-3*x)",
"ParallelBetweenLine(BH,DF)"
] | [
"Equal(MeasureOfAngle(CFD),7*x-38)",
"Equal(MeasureOfAngle(EHI),178-3*x)"
] | Value(x) | 108/5 | [
"parallel_property_corresponding_angle(1,FD,HB,C)",
"vertical_angle(1,EHI,FHB)"
] | {"START": ["parallel_property_corresponding_angle(1,FD,HB,C)", "vertical_angle(1,EHI,FHB)"]} | |
792 | XiaokaiZhang_2023-03-19 | Geometry3k-818 | 1 | 如图所示，∠AEF=148°，∠FAE=18°，∠XYZ=3*x+y°，∠XYZ=∠EFA，∠YZX=5*x-y°，∠ZXY=∠AEF。求x的值。 | As shown in the diagram, ∠AEF=148°, ∠FAE=18°, ∠XYZ=3*x+y°, ∠XYZ=∠EFA, ∠YZX=5*x-y°, ∠ZXY=∠AEF. Find the value of x. | 792.png | [
"Shape(EF,FA,AE)",
"Shape(ZX,XY,YZ)"
] | [
"Equal(MeasureOfAngle(AEF),148)",
"Equal(MeasureOfAngle(FAE),18)",
"Equal(MeasureOfAngle(XYZ),3*x+y)",
"Equal(MeasureOfAngle(XYZ),MeasureOfAngle(EFA))",
"Equal(MeasureOfAngle(YZX),5*x-y)",
"Equal(MeasureOfAngle(ZXY),MeasureOfAngle(AEF))"
] | [
"Equal(MeasureOfAngle(AEF),148)",
"Equal(MeasureOfAngle(FAE),18)",
"Equal(MeasureOfAngle(XYZ),3*x+y)",
"Equal(MeasureOfAngle(XYZ),MeasureOfAngle(EFA))",
"Equal(MeasureOfAngle(YZX),5*x-y)",
"Equal(MeasureOfAngle(ZXY),MeasureOfAngle(AEF))"
] | Value(x) | 4 | [
"triangle_property_angle_sum(1,ZXY)"
] | {"START": ["triangle_property_angle_sum(1,ZXY)"]} | |
793 | XiaokaiZhang_2023-03-19 | Geometry3k-819 | 0 | 如图所示，RS=3*x-5，RS=RT，TR=2*x+7，TS=22。求直线RT的长度。 | As shown in the diagram, RS=3*x-5, RS=RT, TR=2*x+7, TS=22. Find the length of line RT. | 793.png | [
"Shape(RS,ST,TR)"
] | [
"Equal(LengthOfLine(RS),3*x-5)",
"Equal(LengthOfLine(RS),LengthOfLine(RT))",
"Equal(LengthOfLine(TR),2*x+7)",
"Equal(LengthOfLine(TS),22)"
] | [
"Equal(LengthOfLine(RS),3*x-5)",
"Equal(LengthOfLine(RS),LengthOfLine(RT))",
"Equal(LengthOfLine(TR),2*x+7)",
"Equal(LengthOfLine(TS),22)"
] | Value(LengthOfLine(RT)) | 31 | [] | {"START": []} | |
794 | NaZhu_2023-04-09 | Geometry3k-820 | 1 | 如图所示，∠AZB=104°，⌒ZCB的角度为94，Z是⊙Z的圆心，Z是四边形ADCB的内心，AB∥DC。求弧ZBA的角度。 | As shown in the diagram, ∠AZB=104°, the measure of arc ZCB is 94, Z is the center of circle Z, the incenter of quadrilateral ADCB is Z, AB is parallel to DC. Find the measure of ⌒ZBA. | 794.png | [
"Shape(ZCB,BC)",
"Shape(ZBA,AB)",
"Shape(ZAD,DA)",
"Shape(ZDC,CD)",
"Shape(EC,CB,BE)",
"Shape(DC,CE,ED)",
"Shape(ZB,BA,AZ)",
"Shape(EA,AD,DE)",
"Shape(EB,BZ,ZA,AE)",
"Collinear(BED)",
"Collinear(AEC)",
"Cocircular(Z,CBAD)"
] | [
"Equal(MeasureOfAngle(AZB),104)",
"Equal(MeasureOfArc(ZCB),94)",
"IsCentreOfCircle(Z,Z)",
"IsIncenterOfQuadrilateral(Z,ADCB)",
"ParallelBetweenLine(AB,DC)"
] | [
"IsCentreOfCircle(Z,Z)"
] | Value(MeasureOfArc(ZBA)) | 104 | [
"arc_property_center_angle(1,ZBA,Z)"
] | {"START": ["arc_property_center_angle(1,ZBA,Z)"]} | |
795 | NaZhu_2023-04-09 | Geometry3k-821 | 2 | 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°，RM和PN是平行四边形MRPN的一组对边。求∠MQN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°, quadrilateral MRPN is a parallelogram. Find the measure of ∠MQN. | 795.png | [
"Shape(MR,RQ,QM)",
"Shape(QR,RP,PQ)",
"Shape(MQ,QN,NM)",
"Shape(NQ,QP,PN)",
"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(MQN)) | 97 | [
"flat_angle(1,MQP)",
"angle_addition(1,MQN,NQP)"
] | {"START": ["flat_angle(1,MQP)", "angle_addition(1,MQN,NQP)"]} | |
796 | XiaokaiZhang_2023-03-19 | Geometry3k-822 | 1 | 如图所示，∠DHK=120°，∠IKH=54°，∠JKI=36°，JI平行于KH。求∠KIJ的大小。 | As shown in the diagram, ∠DHK=120°, ∠IKH=54°, ∠JKI=36°, JI is parallel to KH. Find the measure of ∠KIJ. | 796.png | [
"Shape(KH,HI,IK)",
"Shape(KI,IJ,JK)",
"Shape(DH,HK)",
"Collinear(DHI)"
] | [
"Equal(MeasureOfAngle(DHK),120)",
"Equal(MeasureOfAngle(IKH),54)",
"Equal(MeasureOfAngle(JKI),36)",
"ParallelBetweenLine(JI,KH)"
] | [
"Equal(MeasureOfAngle(DHK),120)",
"Equal(MeasureOfAngle(IKH),54)",
"Equal(MeasureOfAngle(JKI),36)",
"ParallelBetweenLine(JI,KH)"
] | Value(MeasureOfAngle(KIJ)) | 54 | [
"parallel_property_alternate_interior_angle(2,JI,KH)"
] | {"START": ["parallel_property_alternate_interior_angle(2,JI,KH)"]} | |
797 | XiaokaiZhang_2023-03-19 | Geometry3k-823 | 1 | 如图所示，RQ=21，SQ=33，SR=53，∠QRS=x°。求x的值。 | As shown in the diagram, RQ=21, SQ=33, SR=53, ∠QRS=x°. Find the value of x. | 797.png | [
"Shape(QR,RS,SQ)"
] | [
"Equal(LengthOfLine(RQ),21)",
"Equal(LengthOfLine(SQ),33)",
"Equal(LengthOfLine(SR),53)",
"Equal(MeasureOfAngle(QRS),x)"
] | [
"Equal(LengthOfLine(RQ),21)",
"Equal(LengthOfLine(SQ),33)",
"Equal(LengthOfLine(SR),53)",
"Equal(MeasureOfAngle(QRS),x)"
] | Value(x) | 180*acos(2161/2226)/pi | [
"cosine_theorem(1,RSQ)"
] | {"START": ["cosine_theorem(1,RSQ)"]} | |
798 | NaZhu_2023-04-09 | Geometry3k-824 | 2 | 如图所示，∠FHM=94°，DH平行于EC。求∠ICE的大小。 | As shown in the diagram, ∠FHM=94°, DH∥EC. Find the measure of ∠ICE. | 798.png | [
"Shape(FH,HM)",
"Shape(MH,HC)",
"Shape(HC,CA)",
"Shape(AC,CI)",
"Shape(IC,CE)",
"Shape(EC,CH)",
"Shape(CH,HD)",
"Shape(DH,HF)",
"Collinear(FHCI)",
"Collinear(MHD)",
"Collinear(ACE)"
] | [
"Equal(MeasureOfAngle(FHM),94)",
"ParallelBetweenLine(DH,EC)"
] | [
"Equal(MeasureOfAngle(FHM),94)",
"ParallelBetweenLine(DH,EC)"
] | Value(MeasureOfAngle(ICE)) | 94 | [
"vertical_angle(1,FHM,CHD)",
"parallel_property_corresponding_angle(1,CE,HD,I)"
] | {"START": ["vertical_angle(1,FHM,CHD)", "parallel_property_corresponding_angle(1,CE,HD,I)"]} | |
799 | XiaokaiZhang_2023-03-19 | Geometry3k-825 | 0 | 如图所示，BD=4*x+9，CD=7*x-6，∠CDA=2*y-6°，AD是三角形ACB的中线。求x的值。 | As shown in the diagram, BD=4*x+9, CD=7*x-6, ∠CDA=2*y-6°, AD is the median of triangle ACB. Find the value of x. | 799.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)",
"IsMedianOfTriangle(AD,ACB)"
] | [
"Equal(LengthOfLine(BD),4*x+9)",
"Equal(LengthOfLine(CD),7*x-6)",
"Equal(MeasureOfAngle(CDA),2*y-6)",
"IsMedianOfTriangle(AD,ACB)"
] | Value(x) | 5 | [] | {"START": []} | |
800 | XiaokaiZhang_2023-03-19 | Geometry3k-826 | 8 | 如图所示，AB=x，CA=z，CB=12，PA=y，PB=8，AP垂直于CP，CA垂直于BA。求x的值。 | As shown in the diagram, AB=x, CA=z, CB=12, PA=y, PB=8, AP⊥CP, CA is perpendicular to BA. Find the value of x. | 800.png | [
"Shape(CA,AP,PC)",
"Shape(PA,AB,BP)",
"Collinear(CPB)"
] | [
"Equal(LengthOfLine(AB),x)",
"Equal(LengthOfLine(CA),z)",
"Equal(LengthOfLine(CB),12)",
"Equal(LengthOfLine(PA),y)",
"Equal(LengthOfLine(PB),8)",
"PerpendicularBetweenLine(AP,CP)",
"PerpendicularBetweenLine(CA,BA)"
] | [
"Equal(LengthOfLine(AB),x)",
"Equal(LengthOfLine(CA),z)",
"Equal(LengthOfLine(CB),12)",
"Equal(LengthOfLine(PA),y)",
"Equal(LengthOfLine(PB),8)",
"PerpendicularBetweenLine(AP,CP)",
"PerpendicularBetweenLine(CA,BA)"
] | Value(x) | 4*sqrt(6) | [
"adjacent_complementary_angle(1,BPA,APC)",
"right_triangle_judgment_angle(1,APC)",
"right_triangle_judgment_angle(1,CAB)",
"right_triangle_judgment_angle(1,BPA)",
"line_addition(1,CP,PB)",
"right_triangle_property_pythagorean(1,APC)",
"right_triangle_property_pythagorean(1,CAB)",
"right_triangle_prope... | {"START": ["adjacent_complementary_angle(1,BPA,APC)", "right_triangle_judgment_angle(1,APC)", "right_triangle_judgment_angle(1,CAB)", "line_addition(1,CP,PB)"], "adjacent_complementary_angle(1,BPA,APC)": ["right_triangle_judgment_angle(1,BPA)"], "right_triangle_judgment_angle(1,APC)": ["right_triangle_property_pythagor... |
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