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<image>The Caption of this geometric diagram is:As shown in the diagram, MN=3*x-4, NQ=15, PN=2*y+5, PQ=12, RM=18, RP=20, RQ=3*z-3, ∠MRQ=38°, ∠NQP=83°, ∠QNM=33°, MN and RP are opposite sides of the ▱ MRPN. Find the value of y. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
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consCDL:['Shape(MR,RQ,QM)', 'Shape(QR,RP,PQ)', 'Shape(MQ,QN,NM)', 'Shape(QP,PN,NQ)', 'Collinear(MQP)', 'Collinear(RQN)'], imgCDL:['Equal(LengthOfLine(MN),3*x-4)', 'Equal(LengthOfLine(NQ),15)', 'Equal(LengthOfLine(PN),2*y+5)', 'Equal(LengthOfLine(PQ),12)', 'Equal(LengthOfLine(RM),18)', 'Equal(LengthOfLine(RP),20)', 'Equal(LengthOfLine(RQ),3*z-3)', 'Equal(MeasureOfAngle(MRQ),38)', 'Equal(MeasureOfAngle(NQP),83)', 'Equal(MeasureOfAngle(QNM),33)'], textCDL:['Equal(LengthOfLine(MN),3*x-4)', 'Equal(LengthOfLine(NQ),15)', 'Equal(LengthOfLine(PN),2*y+5)', 'Equal(LengthOfLine(PQ),12)', 'Equal(LengthOfLine(RM),18)', 'Equal(LengthOfLine(RP),20)', 'Equal(LengthOfLine(RQ),3*z-3)', 'Equal(MeasureOfAngle(MRQ),38)', 'Equal(MeasureOfAngle(NQP),83)', 'Equal(MeasureOfAngle(QNM),33)', 'Parallelogram(MRPN)'].
|
2
|
Find the value of y.
|
13/2
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, AB=30, CD=30, ∠XCZ=40°, X is the center of circle X, AM⊥YM, DN is perpendicular to ZN. Find the measure of arc XBA. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
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consCDL:['Shape(XBY,YM,MB)', 'Shape(XYA,AM,MY)', 'Shape(XM,MA,XAC,CN,NX)', 'Shape(NC,XCZ,ZN)', 'Shape(NZ,XZD,DN)', 'Shape(MX,XN,ND,XDB,BM)', 'Collinear(AMB)', 'Collinear(YMX)', 'Collinear(XNZ)', 'Collinear(CND)', 'Cocircular(X,ACZDBY)'], imgCDL:['Equal(LengthOfLine(AB),30)', 'Equal(LengthOfLine(CD),30)', 'Equal(MeasureOfArc(XCZ),40)', 'PerpendicularBetweenLine(AM,YM)', 'PerpendicularBetweenLine(DN,ZN)'], textCDL:['Equal(LengthOfLine(AB),30)', 'Equal(LengthOfLine(CD),30)', 'Equal(MeasureOfArc(XCZ),40)', 'IsCentreOfCircle(X,X)', 'PerpendicularBetweenLine(AM,YM)', 'PerpendicularBetweenLine(DN,ZN)'].
|
12
|
Find the measure of arc XBA.
|
80
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, IB=1/2*x-7, JI=1/4*x+5, LD=66-2/3*y, NL=1/3*y-6, NL=LD, CJ is perpendicular to NJ, IB⊥DB, JI⊥LI. Find the value of x. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
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consCDL:['Shape(JI,IL,LN,NJ)', 'Shape(IB,BD,DL,LI)', 'Shape(CJ,JN)', 'Collinear(CJIB)', 'Collinear(NLD)'], imgCDL:['Equal(LengthOfLine(IB),1/2*x-7)', 'Equal(LengthOfLine(JI),1/4*x+5)', 'Equal(LengthOfLine(LD),66-2/3*y)', 'Equal(LengthOfLine(NL),1/3*y-6)', 'Equal(LengthOfLine(NL),LengthOfLine(LD))', 'PerpendicularBetweenLine(CJ,NJ)', 'PerpendicularBetweenLine(IB,DB)', 'PerpendicularBetweenLine(JI,LI)'], textCDL:['Equal(LengthOfLine(IB),1/2*x-7)', 'Equal(LengthOfLine(JI),1/4*x+5)', 'Equal(LengthOfLine(LD),66-2/3*y)', 'Equal(LengthOfLine(NL),1/3*y-6)', 'Equal(LengthOfLine(NL),LengthOfLine(LD))', 'PerpendicularBetweenLine(CJ,NJ)', 'PerpendicularBetweenLine(IB,DB)', 'PerpendicularBetweenLine(JI,LI)'].
|
15
|
Find the value of x.
|
48
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, AE=BE, BA=8, BC=8, BE=CE, DA=10, DC=10, ∠ADE=x°, DE is perpendicular to AE. Find sin(x). Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
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consCDL:['Shape(AD,DE,EA)', 'Shape(AE,EB,BA)', 'Shape(ED,DC,CE)', 'Shape(BE,EC,CB)', 'Collinear(DEB)', 'Collinear(AEC)'], imgCDL:['Equal(LengthOfLine(AE),LengthOfLine(BE))', 'Equal(LengthOfLine(BA),8)', 'Equal(LengthOfLine(BC),8)', 'Equal(LengthOfLine(BE),LengthOfLine(CE))', 'Equal(LengthOfLine(DA),10)', 'Equal(LengthOfLine(DC),10)', 'Equal(MeasureOfAngle(ADE),x)', 'PerpendicularBetweenLine(DE,AE)'], textCDL:['Equal(LengthOfLine(AE),LengthOfLine(BE))', 'Equal(LengthOfLine(BA),8)', 'Equal(LengthOfLine(BC),8)', 'Equal(LengthOfLine(BE),LengthOfLine(CE))', 'Equal(LengthOfLine(DA),10)', 'Equal(LengthOfLine(DC),10)', 'Equal(MeasureOfAngle(ADE),x)', 'PerpendicularBetweenLine(DE,AE)'].
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20
|
Find sin(x).
|
2*sqrt(2)/5
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠NJK=101°, JA∥NF. Find ∠HNJ. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
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consCDL:['Shape(KJ,JE)', 'Shape(EJ,JA)', 'Shape(AJ,JN)', 'Shape(NJ,JK)', 'Shape(HN,NJ)', 'Shape(JN,NF)', 'Shape(FN,NI)', 'Shape(IN,NH)', 'Collinear(KJA)', 'Collinear(HNF)', 'Collinear(EJNI)'], imgCDL:['Equal(MeasureOfAngle(NJK),101)', 'ParallelBetweenLine(JA,NF)'], textCDL:['Equal(MeasureOfAngle(NJK),101)', 'ParallelBetweenLine(JA,NF)'].
|
22
|
Find ∠HNJ.
|
79
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠CHE=9*x-11°, ∠GDF=8*x+4°, BD∥EH. Find the value of x. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
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consCDL:['Shape(GD,DF)', 'Shape(FD,DH)', 'Shape(DH,HA)', 'Shape(AH,HC)', 'Shape(CH,HE)', 'Shape(EH,HD)', 'Shape(HD,DB)', 'Shape(BD,DG)', 'Collinear(GDHC)', 'Collinear(FDB)', 'Collinear(AHE)'], imgCDL:['Equal(MeasureOfAngle(CHE),9*x-11)', 'Equal(MeasureOfAngle(GDF),8*x+4)', 'ParallelBetweenLine(BD,EH)'], textCDL:['Equal(MeasureOfAngle(CHE),9*x-11)', 'Equal(MeasureOfAngle(GDF),8*x+4)', 'ParallelBetweenLine(BD,EH)'].
|
28
|
Find the value of x.
|
15
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠ABD=130°, ∠CBA=x°, ∠DBC=95°. Find the value of x. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
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consCDL:['Shape(BAC,CB,BA)', 'Shape(BDA,AB,BD)', 'Shape(BCD,DB,BC)'], imgCDL:['Equal(MeasureOfAngle(ABD),130)', 'Equal(MeasureOfAngle(CBA),x)', 'Equal(MeasureOfAngle(DBC),95)'], textCDL:['Equal(MeasureOfAngle(ABD),130)', 'Equal(MeasureOfAngle(CBA),x)', 'Equal(MeasureOfAngle(DBC),95)'].
|
36
|
Find the value of x.
|
135
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠LWX=3*a+40°, ∠WXE=2*a+25°, ∠XZK=5*b-26°, WL∥XE, XN is parallel to ZK. Find the value of a. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
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consCDL:['Shape(GW,WL)', 'Shape(LW,WX)', 'Shape(WX,XE)', 'Shape(EX,XN)', 'Shape(NX,XZ)', 'Shape(XZ,ZK)', 'Shape(KZ,ZH)', 'Shape(HZ,ZY)', 'Shape(ZY,YM)', 'Shape(MY,YI)', 'Shape(IY,YW)', 'Shape(YW,WG)', 'Shape(WY,YZ,ZX,XW)', 'Collinear(GWXN)', 'Collinear(IYZK)', 'Collinear(LWYM)', 'Collinear(EXZH)'], imgCDL:['Equal(MeasureOfAngle(LWX),3*a+40)', 'Equal(MeasureOfAngle(WXE),2*a+25)', 'Equal(MeasureOfAngle(XZK),5*b-26)', 'ParallelBetweenLine(WL,XE)', 'ParallelBetweenLine(XN,ZK)'], textCDL:['Equal(MeasureOfAngle(LWX),3*a+40)', 'Equal(MeasureOfAngle(WXE),2*a+25)', 'Equal(MeasureOfAngle(XZK),5*b-26)', 'ParallelBetweenLine(WL,XE)', 'ParallelBetweenLine(XN,ZK)'].
|
51
|
Find the value of a.
|
23
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠BCE=∠EBC, ∠DAG=136°, ∠DEA=47°, ∠EFB=63°, ∠FED=69°. Find ∠EBC. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
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consCDL:['Shape(FB,BE,EF)', 'Shape(DE,EA,AD)', 'Shape(BC,CE,EB)', 'Shape(FE,ED)', 'Shape(FE,EA)', 'Shape(DA,AG)', 'Shape(AE,EC)', 'Collinear(BEAG)', 'Collinear(FEC)'], imgCDL:['Equal(MeasureOfAngle(BCE),MeasureOfAngle(EBC))', 'Equal(MeasureOfAngle(DAG),136)', 'Equal(MeasureOfAngle(DEA),47)', 'Equal(MeasureOfAngle(EFB),63)', 'Equal(MeasureOfAngle(FED),69)'], textCDL:['Equal(MeasureOfAngle(BCE),MeasureOfAngle(EBC))', 'Equal(MeasureOfAngle(DAG),136)', 'Equal(MeasureOfAngle(DEA),47)', 'Equal(MeasureOfAngle(EFB),63)', 'Equal(MeasureOfAngle(FED),69)'].
|
58
|
Find ∠EBC.
|
32
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠LWX=53°, WL is parallel to XE, XN is parallel to ZK. Find ∠XZK. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
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consCDL:['Shape(GW,WL)', 'Shape(LW,WX)', 'Shape(WX,XE)', 'Shape(EX,XN)', 'Shape(NX,XZ)', 'Shape(XZ,ZK)', 'Shape(KZ,ZH)', 'Shape(HZ,ZY)', 'Shape(ZY,YM)', 'Shape(MY,YI)', 'Shape(IY,YW)', 'Shape(YW,WG)', 'Shape(WY,YZ,ZX,XW)', 'Collinear(GWXN)', 'Collinear(IYZK)', 'Collinear(LWYM)', 'Collinear(EXZH)'], imgCDL:['Equal(MeasureOfAngle(LWX),53)', 'ParallelBetweenLine(WL,XE)', 'ParallelBetweenLine(XN,ZK)'], textCDL:['Equal(MeasureOfAngle(LWX),53)', 'ParallelBetweenLine(WL,XE)', 'ParallelBetweenLine(XN,ZK)'].
|
59
|
Find ∠XZK.
|
53
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠AJH=x°, ∠HGB=2*x°, A is the center of ⊙A, GB is perpendicular to HB, JH is perpendicular to GH. Find the measure of ∠BHG. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
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consCDL:['Shape(AGF,FB,BG)', 'Shape(AB,BF,AFJ,JA)', 'Shape(BA,AJ,JH,HB)', 'Shape(AJH,HJ)', 'Shape(BH,HG,GB)', 'Shape(AHG,GH)', 'Collinear(FBH)', 'Collinear(GBAJ)', 'Cocircular(A,GFJH)'], imgCDL:['Equal(MeasureOfAngle(AJH),x)', 'Equal(MeasureOfAngle(HGB),2*x)', 'PerpendicularBetweenLine(GB,HB)', 'PerpendicularBetweenLine(JH,GH)'], textCDL:['Equal(MeasureOfAngle(AJH),x)', 'Equal(MeasureOfAngle(HGB),2*x)', 'IsCentreOfCircle(A,A)', 'PerpendicularBetweenLine(GB,HB)', 'PerpendicularBetweenLine(JH,GH)'].
|
64
|
Find the measure of ∠BHG.
|
30
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠TYZ=52°, ∠ZYX=38°, TY is perpendicular to XY, XW is perpendicular to TW, YX is perpendicular to WX, YZ is perpendicular to TZ. Find ∠WTZ. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
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consCDL:['Shape(TY,YZ,ZT)', 'Shape(TZ,ZW,WT)', 'Shape(ZY,YX,XW,WZ)', 'Collinear(YZW)'], imgCDL:['Equal(MeasureOfAngle(TYZ),52)', 'Equal(MeasureOfAngle(ZYX),38)', 'PerpendicularBetweenLine(TY,XY)', 'PerpendicularBetweenLine(XW,TW)', 'PerpendicularBetweenLine(YX,WX)', 'PerpendicularBetweenLine(YZ,TZ)'], textCDL:['Equal(MeasureOfAngle(TYZ),52)', 'Equal(MeasureOfAngle(ZYX),38)', 'PerpendicularBetweenLine(TY,XY)', 'PerpendicularBetweenLine(XW,TW)', 'PerpendicularBetweenLine(YX,WX)', 'PerpendicularBetweenLine(YZ,TZ)'].
|
72
|
Find ∠WTZ.
|
52
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, AB=32, AD=DC, BC=2*x-3, EF=12, EH=HG, FG=x-5, ∠BCD=∠FGH, ∠DAB=∠HEF. Find the value of x. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
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consCDL:['Shape(EF,FH,HE)', 'Shape(HF,FG,GH)', 'Shape(AB,BD,DA)', 'Shape(DB,BC,CD)', 'Collinear(EHG)', 'Collinear(ADC)'], imgCDL:['Equal(LengthOfLine(AB),32)', 'Equal(LengthOfLine(AD),LengthOfLine(DC))', 'Equal(LengthOfLine(BC),2*x-3)', 'Equal(LengthOfLine(EF),12)', 'Equal(LengthOfLine(EH),LengthOfLine(HG))', 'Equal(LengthOfLine(FG),x-5)', 'Equal(MeasureOfAngle(BCD),MeasureOfAngle(FGH))', 'Equal(MeasureOfAngle(DAB),MeasureOfAngle(HEF))'], textCDL:['Equal(LengthOfLine(AB),32)', 'Equal(LengthOfLine(AD),LengthOfLine(DC))', 'Equal(LengthOfLine(BC),2*x-3)', 'Equal(LengthOfLine(EF),12)', 'Equal(LengthOfLine(EH),LengthOfLine(HG))', 'Equal(LengthOfLine(FG),x-5)', 'Equal(MeasureOfAngle(BCD),MeasureOfAngle(FGH))', 'Equal(MeasureOfAngle(DAB),MeasureOfAngle(HEF))'].
|
84
|
Find the value of x.
|
31/2
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠DBC=170°, the center of circle D is D. Find the measure of ∠CAB. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
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consCDL:['Shape(DCA,AC)', 'Shape(DC,CA,AD)', 'Shape(DA,AB,BD)', 'Shape(DAB,BA)', 'Shape(DB,DBC,CD)', 'Cocircular(D,CAB)'], imgCDL:['Equal(MeasureOfArc(DBC),170)'], textCDL:['Equal(MeasureOfArc(DBC),170)', 'IsCentreOfCircle(D,D)'].
|
94
|
Find the measure of ∠CAB.
|
85
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠PNO=56°, ∠BMN=70°, B is the center of ⊙B. Find the measure of ⌒BOP. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
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consCDL:['Shape(BPM,MP)', 'Shape(BMN,NP,PM)', 'Shape(PN,NO,BOP)', 'Shape(BNO,ON)', 'Cocircular(B,PMNO)'], imgCDL:['Equal(MeasureOfAngle(PNO),56)', 'Equal(MeasureOfArc(BMN),70)'], textCDL:['Equal(MeasureOfAngle(PNO),56)', 'Equal(MeasureOfArc(BMN),70)', 'IsCentreOfCircle(B,B)'].
|
95
|
Find the measure of ⌒BOP.
|
112
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠FOE=118°, ∠LDA=104°, OD∥FI. Find ∠OFI. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
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consCDL:['Shape(LD,DA)', 'Shape(AD,DI)', 'Shape(DI,IB)', 'Shape(BI,IC)', 'Shape(CI,IF)', 'Shape(IF,FJ)', 'Shape(JF,FK)', 'Shape(KF,FO)', 'Shape(FO,OE)', 'Shape(EO,OH)', 'Shape(HO,OD)', 'Shape(ID,DL)', 'Shape(DO,OF,FI,ID)', 'Collinear(LDIC)', 'Collinear(HOFJ)', 'Collinear(ADOE)', 'Collinear(BIFK)'], imgCDL:['Equal(MeasureOfAngle(FOE),118)', 'Equal(MeasureOfAngle(LDA),104)', 'ParallelBetweenLine(OD,FI)'], textCDL:['Equal(MeasureOfAngle(FOE),118)', 'Equal(MeasureOfAngle(LDA),104)', 'ParallelBetweenLine(OD,FI)'].
|
115
|
Find ∠OFI.
|
118
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠GOI=3*y+1°, ∠HBI=3*x+11°, ∠OIE=4*x-5°, GE is parallel to OI, IB is parallel to OH, OI∥HB. Find the value of x. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
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consCDL:['Shape(GO,OI,IE,EG)', 'Shape(OH,HB,BI,IO)', 'Collinear(GOH)', 'Collinear(BIE)'], imgCDL:['Equal(MeasureOfAngle(GOI),3*y+1)', 'Equal(MeasureOfAngle(HBI),3*x+11)', 'Equal(MeasureOfAngle(OIE),4*x-5)', 'ParallelBetweenLine(GE,OI)', 'ParallelBetweenLine(IB,OH)', 'ParallelBetweenLine(OI,HB)'], textCDL:['Equal(MeasureOfAngle(GOI),3*y+1)', 'Equal(MeasureOfAngle(HBI),3*x+11)', 'Equal(MeasureOfAngle(OIE),4*x-5)', 'ParallelBetweenLine(GE,OI)', 'ParallelBetweenLine(IB,OH)', 'ParallelBetweenLine(OI,HB)'].
|
116
|
Find the value of x.
|
16
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, the center of ⊙A is A, DF is the tangent to circle A. Find ∠AFD. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
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consCDL:['Shape(AF,AFB,BA)', 'Shape(AB,ABF,FA)', 'Shape(AF,FD)', 'Collinear(FAB)', 'Cocircular(A,FB)'], imgCDL:[], textCDL:['IsCentreOfCircle(A,A)', 'IsTangentOfCircle(DF,A)'].
|
118
|
Find ∠AFD.
|
90
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠ABH=3*p-10°, ∠CDB=6*r+5°, ∠JAB=4*p+15°, AJ is parallel to BH, CI∥AL. Find the value of r. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
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consCDL:['Shape(LA,AJ)', 'Shape(JA,AB)', 'Shape(AB,BH)', 'Shape(HB,BE)', 'Shape(EB,BD)', 'Shape(BD,DK)', 'Shape(KD,DF)', 'Shape(FD,DC)', 'Shape(DC,CG)', 'Shape(GC,CI)', 'Shape(IC,CA)', 'Shape(CA,AL)', 'Shape(AC,CD,DB,BA)', 'Collinear(LABE)', 'Collinear(ICDK)', 'Collinear(JACG)', 'Collinear(HBDF)'], imgCDL:['Equal(MeasureOfAngle(ABH),3*p-10)', 'Equal(MeasureOfAngle(CDB),6*r+5)', 'Equal(MeasureOfAngle(JAB),4*p+15)', 'ParallelBetweenLine(AJ,BH)', 'ParallelBetweenLine(CI,AL)'], textCDL:['Equal(MeasureOfAngle(ABH),3*p-10)', 'Equal(MeasureOfAngle(CDB),6*r+5)', 'Equal(MeasureOfAngle(JAB),4*p+15)', 'ParallelBetweenLine(AJ,BH)', 'ParallelBetweenLine(CI,AL)'].
|
125
|
Find the value of r.
|
10
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠ADK=96°, ∠HGJ=42°, GA∥HD. Find ∠GHD. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
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consCDL:['Shape(KD,DL)', 'Shape(LD,DH)', 'Shape(DH,HI)', 'Shape(IH,HC)', 'Shape(CH,HG)', 'Shape(HG,GJ)', 'Shape(JG,GF)', 'Shape(FG,GA)', 'Shape(GA,AM)', 'Shape(MA,AF)', 'Shape(FA,AD)', 'Shape(AD,DK)', 'Shape(DA,AG,GH,HD)', 'Collinear(KDHC)', 'Collinear(EAGJ)', 'Collinear(LDAM)', 'Collinear(IHGF)'], imgCDL:['Equal(MeasureOfAngle(ADK),96)', 'Equal(MeasureOfAngle(HGJ),42)', 'ParallelBetweenLine(GA,HD)'], textCDL:['Equal(MeasureOfAngle(ADK),96)', 'Equal(MeasureOfAngle(HGJ),42)', 'ParallelBetweenLine(GA,HD)'].
|
127
|
Find ∠GHD.
|
42
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, AJ=2*x+3, BJ=5*x, JC=8*y-36, JD=4*y, AD and CB are opposite sides of the parallelogram ACBD. Find the value of x. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
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consCDL:['Shape(AC,CJ,JA)', 'Shape(JC,CB,BJ)', 'Shape(JB,BD,DJ)', 'Shape(AJ,JD,DA)', 'Collinear(AJB)', 'Collinear(CJD)'], imgCDL:['Equal(LengthOfLine(AJ),2*x+3)', 'Equal(LengthOfLine(BJ),5*x)', 'Equal(LengthOfLine(JC),8*y-36)', 'Equal(LengthOfLine(JD),4*y)'], textCDL:['Equal(LengthOfLine(AJ),2*x+3)', 'Equal(LengthOfLine(BJ),5*x)', 'Equal(LengthOfLine(JC),8*y-36)', 'Equal(LengthOfLine(JD),4*y)', 'Parallelogram(ACBD)'].
|
132
|
Find the value of x.
|
1
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, BA=5, ∠ABC=46°, B is the center of circle B. Find the area of the sector BCA. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
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consCDL:['Shape(BCA,AB,BC)', 'Shape(BA,BAC,CB)', 'Cocircular(B,CA)'], imgCDL:['Equal(LengthOfLine(BA),5)', 'Equal(MeasureOfAngle(ABC),46)'], textCDL:['Equal(LengthOfLine(BA),5)', 'Equal(MeasureOfAngle(ABC),46)', 'IsCentreOfCircle(B,B)'].
|
146
|
Find the area of the sector BCA.
|
115*pi/36
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠DAF=4*x+5°, ∠FAB=9*x+20°, ∠FBC=4*y+4°, ∠FDA=y**2-1°, quadrilateral ABCD is a rectangle. Find the value of y. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
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consCDL:['Shape(AB,BF,FA)', 'Shape(FB,BC,CF)', 'Shape(FC,CD,DF)', 'Shape(AF,FD,DA)', 'Collinear(AFC)', 'Collinear(BFD)'], imgCDL:['Equal(MeasureOfAngle(DAF),4*x+5)', 'Equal(MeasureOfAngle(FAB),9*x+20)', 'Equal(MeasureOfAngle(FBC),4*y+4)', 'Equal(MeasureOfAngle(FDA),y**2-1)'], textCDL:['Equal(MeasureOfAngle(DAF),4*x+5)', 'Equal(MeasureOfAngle(FAB),9*x+20)', 'Equal(MeasureOfAngle(FBC),4*y+4)', 'Equal(MeasureOfAngle(FDA),y**2-1)', 'Rectangle(ABCD)'].
|
153
|
Find the value of y.
|
5
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, AH=RH, HA=6-x, IJ=4/3*y+1, JE=2*y, RH=2*x+3, HJ is parallel to AE, RI∥HJ. Find the value of y. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
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consCDL:['Shape(RH,HJ,JI,IR)', 'Shape(HA,AE,EJ,JH)', 'Collinear(RHA)', 'Collinear(IJE)'], imgCDL:['Equal(LengthOfLine(AH),LengthOfLine(RH))', 'Equal(LengthOfLine(HA),6-x)', 'Equal(LengthOfLine(IJ),4/3*y+1)', 'Equal(LengthOfLine(JE),2*y)', 'Equal(LengthOfLine(RH),2*x+3)', 'ParallelBetweenLine(HJ,AE)', 'ParallelBetweenLine(RI,HJ)'], textCDL:['Equal(LengthOfLine(AH),LengthOfLine(RH))', 'Equal(LengthOfLine(HA),6-x)', 'Equal(LengthOfLine(IJ),4/3*y+1)', 'Equal(LengthOfLine(JE),2*y)', 'Equal(LengthOfLine(RH),2*x+3)', 'ParallelBetweenLine(HJ,AE)', 'ParallelBetweenLine(RI,HJ)'].
|
154
|
Find the value of y.
|
3/2
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠HPM=4*y°, ∠MPR=68°, ∠PRC=x°, ∠SCR=5*z+2°, MC∥PR, PM∥RC. Find the value of z. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
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consCDL:['Shape(NC,CS)', 'Shape(SC,CR)', 'Shape(CR,RG)', 'Shape(GR,RI)', 'Shape(IR,RP)', 'Shape(RP,PL)', 'Shape(LP,PH)', 'Shape(HP,PM)', 'Shape(PM,ME)', 'Shape(EM,MD)', 'Shape(DM,MC)', 'Shape(MC,CN)', 'Shape(CM,MP,PR,RC)', 'Collinear(NCRI)', 'Collinear(DMPL)', 'Collinear(SCME)', 'Collinear(GRPH)'], imgCDL:['Equal(MeasureOfAngle(HPM),4*y)', 'Equal(MeasureOfAngle(MPR),68)', 'Equal(MeasureOfAngle(PRC),x)', 'Equal(MeasureOfAngle(SCR),5*z+2)', 'ParallelBetweenLine(MC,PR)', 'ParallelBetweenLine(PM,RC)'], textCDL:['Equal(MeasureOfAngle(HPM),4*y)', 'Equal(MeasureOfAngle(MPR),68)', 'Equal(MeasureOfAngle(PRC),x)', 'Equal(MeasureOfAngle(SCR),5*z+2)', 'ParallelBetweenLine(MC,PR)', 'ParallelBetweenLine(PM,RC)'].
|
158
|
Find the value of z.
|
22
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠DCG=3*x°, ∠GBA=x+24°, the center of circle O is O. Find ∠GBA. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
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consCDL:['Shape(OBA,AB)', 'Shape(GB,BA,AG)', 'Shape(OAD,DG,GA)', 'Shape(GD,DC,CG)', 'Shape(ODC,CD)', 'Shape(OCB,BG,GC)', 'Collinear(BGD)', 'Collinear(CGA)', 'Cocircular(O,BADC)'], imgCDL:['Equal(MeasureOfAngle(DCG),3*x)', 'Equal(MeasureOfAngle(GBA),x+24)'], textCDL:['Equal(MeasureOfAngle(DCG),3*x)', 'Equal(MeasureOfAngle(GBA),x+24)', 'IsCentreOfCircle(O,O)'].
|
159
|
Find ∠GBA.
|
36
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, AE=6, DH=6, EF=6, AB⊥FB, DH is perpendicular to BH, EA is perpendicular to BA, FE⊥AE. Find the sum of Area(△DFB) and Area(FEAB). Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
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consCDL:['Shape(DF,FH,HD)', 'Shape(DH,HB,BD)', 'Shape(FE,EA,AB,BH,HF)', 'Collinear(FHB)'], imgCDL:['Equal(LengthOfLine(AE),6)', 'Equal(LengthOfLine(DH),6)', 'Equal(LengthOfLine(EF),6)', 'PerpendicularBetweenLine(AB,FB)', 'PerpendicularBetweenLine(DH,BH)', 'PerpendicularBetweenLine(EA,BA)', 'PerpendicularBetweenLine(FE,AE)'], textCDL:['Equal(LengthOfLine(AE),6)', 'Equal(LengthOfLine(DH),6)', 'Equal(LengthOfLine(EF),6)', 'PerpendicularBetweenLine(AB,FB)', 'PerpendicularBetweenLine(DH,BH)', 'PerpendicularBetweenLine(EA,BA)', 'PerpendicularBetweenLine(FE,AE)'].
|
161
|
Find the sum of Area(△DFB) and Area(FEAB).
|
54
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠CAD=42°, ∠CFG=77°, △CDE is an equilateral △, △CAB is an isosceles △, △CFG is an isosceles △. Find ∠GCF. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
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consCDL:['Shape(CA,AD,DC)', 'Shape(CD,DF,FC)', 'Shape(CF,FG,GC)', 'Shape(CG,GE,EC)', 'Shape(CE,EB,BC)', 'Collinear(ADFGEB)'], imgCDL:['Equal(MeasureOfAngle(CAD),42)', 'Equal(MeasureOfAngle(CFG),77)'], textCDL:['Equal(MeasureOfAngle(CAD),42)', 'Equal(MeasureOfAngle(CFG),77)', 'EquilateralTriangle(CDE)', 'IsoscelesTriangle(CAB)', 'IsoscelesTriangle(CFG)'].
|
164
|
Find ∠GCF.
|
26
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠LWX=53°, WL∥XE, XN∥ZK. Find the measure of ∠XZK. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
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consCDL:['Shape(GW,WL)', 'Shape(LW,WX)', 'Shape(WX,XE)', 'Shape(EX,XN)', 'Shape(NX,XZ)', 'Shape(XZ,ZK)', 'Shape(KZ,ZH)', 'Shape(HZ,ZY)', 'Shape(ZY,YM)', 'Shape(MY,YI)', 'Shape(IY,YW)', 'Shape(YW,WG)', 'Shape(WY,YZ,ZX,XW)', 'Collinear(GWXN)', 'Collinear(IYZK)', 'Collinear(LWYM)', 'Collinear(EXZH)'], imgCDL:['Equal(MeasureOfAngle(LWX),53)', 'ParallelBetweenLine(WL,XE)', 'ParallelBetweenLine(XN,ZK)'], textCDL:['Equal(MeasureOfAngle(LWX),53)', 'ParallelBetweenLine(WL,XE)', 'ParallelBetweenLine(XN,ZK)'].
|
165
|
Find the measure of ∠XZK.
|
53
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠EAD=42°, the center of ⊙A is A. Find ⌒AEC. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
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consCDL:['Shape(AE,AEB,BA)', 'Shape(AB,ABC,CA)', 'Shape(AC,ACD,DA)', 'Shape(AD,ADE,EA)', 'Collinear(BAD)', 'Collinear(CAE)', 'Cocircular(A,BCDE)'], imgCDL:['Equal(MeasureOfAngle(EAD),42)'], textCDL:['Equal(MeasureOfAngle(EAD),42)', 'IsCentreOfCircle(A,A)'].
|
174
|
Find ⌒AEC.
|
180
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, CA=15, CB=x, ∠GBA=30°, C is the center of circle C, the tangent to ⊙C is BA. Find the value of x. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
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consCDL:['Shape(BA,CGA,GB)', 'Shape(AC,CG,CGA)', 'Shape(CA,CAG,GC)', 'Collinear(CGB)', 'Cocircular(C,AG)'], imgCDL:['Equal(LengthOfLine(CA),15)', 'Equal(LengthOfLine(CB),x)', 'Equal(MeasureOfAngle(GBA),30)'], textCDL:['Equal(LengthOfLine(CA),15)', 'Equal(LengthOfLine(CB),x)', 'Equal(MeasureOfAngle(GBA),30)', 'IsCentreOfCircle(C,C)', 'IsTangentOfCircle(BA,C)'].
|
175
|
Find the value of x.
|
30
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠FHM=94°, HM is parallel to CA. Find the measure of ∠HCA. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
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consCDL:['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)'], imgCDL:['Equal(MeasureOfAngle(FHM),94)', 'ParallelBetweenLine(HM,CA)'], textCDL:['Equal(MeasureOfAngle(FHM),94)', 'ParallelBetweenLine(HM,CA)'].
|
180
|
Find the measure of ∠HCA.
|
94
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠YZW=60°, ∠ZWX=95°, V is the center of ⊙V. Find ∠XYZ. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
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consCDL:['Shape(VZW,WZ)', 'Shape(VWX,XW)', 'Shape(WXY,YX)', 'Shape(VYZ,ZY)', 'Shape(ZW,WX,XY,YZ)', 'Cocircular(V,ZWXY)'], imgCDL:['Equal(MeasureOfAngle(YZW),60)', 'Equal(MeasureOfAngle(ZWX),95)'], textCDL:['Equal(MeasureOfAngle(YZW),60)', 'Equal(MeasureOfAngle(ZWX),95)', 'IsCentreOfCircle(V,V)'].
|
181
|
Find ∠XYZ.
|
85
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, the sum of the circumferences of circles A, B, and C is 42*pi, the radius of circle A is twice the radius of circle B, the radius of circle A is 4 times the radius of circle C, A is the center of ⊙A, the center of ⊙B is B, the center of ⊙C is C. Find AC. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
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consCDL:['Shape(BD,BDE,EB)', 'Shape(BE,BED,DB)', 'Shape(CD)', 'Shape(C)', 'Shape(AE)', 'Shape(A)', 'Collinear(CDBEA)', 'Cocircular(C,D)', 'Cocircular(B,DE)', 'Cocircular(A,E)'], imgCDL:[], textCDL:['Equal(Add(PerimeterOfCircle(A),PerimeterOfCircle(B),PerimeterOfCircle(C)),42*pi)', 'Equal(RadiusOfCircle(A),Mul(RadiusOfCircle(B),2))', 'Equal(RadiusOfCircle(A),Mul(RadiusOfCircle(C),4))', 'IsCentreOfCircle(A,A)', 'IsCentreOfCircle(B,B)', 'IsCentreOfCircle(C,C)'].
|
188
|
Find AC.
|
27
|
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<image>The Caption of this geometric diagram is:As shown in the diagram, AE=12, AJ=15, ∠JBE=34°, ∠JCD=32°, J is the center of the inscribed circle of triangle CBA, AF is perpendicular to JF, CD is perpendicular to JD, JE⊥AE. Find ∠JAC. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
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consCDL:['Shape(CD,DJ,JC)', 'Shape(DB,BJ,JD)', 'Shape(JB,BE,EJ)', 'Shape(JE,EA,AJ)', 'Shape(JA,AF,FJ)', 'Shape(JF,FC,CJ)', 'Collinear(CDB)', 'Collinear(BEA)', 'Collinear(AFC)'], imgCDL:['Equal(LengthOfLine(AE),12)', 'Equal(LengthOfLine(AJ),15)', 'Equal(MeasureOfAngle(JBE),34)', 'Equal(MeasureOfAngle(JCD),32)', 'PerpendicularBetweenLine(AF,JF)', 'PerpendicularBetweenLine(CD,JD)', 'PerpendicularBetweenLine(JE,AE)'], textCDL:['Equal(LengthOfLine(AE),12)', 'Equal(LengthOfLine(AJ),15)', 'Equal(MeasureOfAngle(JBE),34)', 'Equal(MeasureOfAngle(JCD),32)', 'IsIncenterOfTriangle(J,CBA)', 'PerpendicularBetweenLine(AF,JF)', 'PerpendicularBetweenLine(CD,JD)', 'PerpendicularBetweenLine(JE,AE)'].
|
189
|
Find ∠JAC.
|
24
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, AB=3, AC=5, AE=y, BE=x, CD=7/2, DE=3, EB is parallel to DC. Find BE. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
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consCDL:['Shape(BA,AE,EB)', 'Shape(BE,ED,DC,CB)', 'Collinear(ABC)', 'Collinear(AED)'], imgCDL:['Equal(LengthOfLine(AB),3)', 'Equal(LengthOfLine(AC),5)', 'Equal(LengthOfLine(AE),y)', 'Equal(LengthOfLine(BE),x)', 'Equal(LengthOfLine(CD),7/2)', 'Equal(LengthOfLine(DE),3)', 'ParallelBetweenLine(EB,DC)'], textCDL:['Equal(LengthOfLine(AB),3)', 'Equal(LengthOfLine(AC),5)', 'Equal(LengthOfLine(AE),y)', 'Equal(LengthOfLine(BE),x)', 'Equal(LengthOfLine(CD),7/2)', 'Equal(LengthOfLine(DE),3)', 'ParallelBetweenLine(EB,DC)'].
|
205
|
Find BE.
|
21/10
|
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<image>The Caption of this geometric diagram is:As shown in the diagram, ∠BRS=103°, B is the center of circle B, TR is the tangent to ⊙B, the tangent to circle B is TS. Find ∠RTS. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
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consCDL:['Shape(BS,BSR,RB)', 'Shape(BR,BRS,SB)', 'Shape(BRS,RT,TS)', 'Cocircular(B,RS)'], imgCDL:['Equal(MeasureOfArc(BRS),103)'], textCDL:['Equal(MeasureOfArc(BRS),103)', 'IsCentreOfCircle(B,B)', 'IsTangentOfCircle(TR,B)', 'IsTangentOfCircle(TS,B)'].
|
212
|
Find ∠RTS.
|
77
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, AB=22, AC=14, BD=14, CD=22, E is the center of circle E, O is the center of circle O, AC is the diameter of circle O, BD is the diameter of circle E, OC⊥DC. Find the area of quadrilateral ACDB minus the sum of the areas of sectors OCA and EBD. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
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consCDL:['Shape(AO,OC,OCA)', 'Shape(OCA,CD,EBD,BA)', 'Shape(EBD,DE,EB)', 'Collinear(AOC)', 'Collinear(BED)', 'Cocircular(O,AC)', 'Cocircular(E,BD)'], imgCDL:['Equal(LengthOfLine(AB),22)', 'Equal(LengthOfLine(AC),14)', 'Equal(LengthOfLine(BD),14)', 'Equal(LengthOfLine(CD),22)', 'PerpendicularBetweenLine(OC,DC)'], textCDL:['Equal(LengthOfLine(AB),22)', 'Equal(LengthOfLine(AC),14)', 'Equal(LengthOfLine(BD),14)', 'Equal(LengthOfLine(CD),22)', 'IsCentreOfCircle(E,E)', 'IsCentreOfCircle(O,O)', 'IsDiameterOfCircle(AC,O)', 'IsDiameterOfCircle(BD,E)', 'PerpendicularBetweenLine(OC,DC)'].
|
217
|
Find the area of quadrilateral ACDB minus the sum of the areas of sectors OCA and EBD.
|
308-49*pi
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, AD=15, PF=6, the centroid of triangle ACE is P. Find AP. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
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consCDL:['Shape(AB,BP,PA)', 'Shape(BC,CP,PB)', 'Shape(PC,CD,DP)', 'Shape(PD,DE,EP)', 'Shape(PE,EF,FP)', 'Shape(PF,FA,AP)', 'Collinear(ABC)', 'Collinear(CDE)', 'Collinear(EFA)', 'Collinear(BPE)', 'Collinear(CPF)', 'Collinear(APD)'], imgCDL:['Equal(LengthOfLine(AD),15)', 'Equal(LengthOfLine(PF),6)'], textCDL:['Equal(LengthOfLine(AD),15)', 'Equal(LengthOfLine(PF),6)', 'IsCentroidOfTriangle(P,ACE)'].
|
220
|
Find AP.
|
10
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠ACB=29°, ∠CBA=x°, ∠DAB=4*x°. Find the value of x. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
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consCDL:['Shape(AC,CB,BA)', 'Shape(DA,AB)', 'Collinear(DAC)'], imgCDL:['Equal(MeasureOfAngle(ACB),29)', 'Equal(MeasureOfAngle(CBA),x)', 'Equal(MeasureOfAngle(DAB),4*x)'], textCDL:['Equal(MeasureOfAngle(ACB),29)', 'Equal(MeasureOfAngle(CBA),x)', 'Equal(MeasureOfAngle(DAB),4*x)'].
|
229
|
Find the value of x.
|
29/3
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠BEC=57°, DF∥HE, FE∥DH. Find ∠IFA. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
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consCDL:['Shape(FD,DH,HE,EF)', 'Shape(BE,EC)', 'Shape(IF,FA)', 'Collinear(AFDL)', 'Collinear(BEHK)', 'Collinear(IFEC)', 'Collinear(GDHJ)'], imgCDL:['Equal(MeasureOfAngle(BEC),57)', 'ParallelBetweenLine(DF,HE)', 'ParallelBetweenLine(FE,DH)'], textCDL:['Equal(MeasureOfAngle(BEC),57)', 'ParallelBetweenLine(DF,HE)', 'ParallelBetweenLine(FE,DH)'].
|
234
|
Find ∠IFA.
|
123
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠NAP=120°, ∠PAQ=100°, the center of circle A is A. Find the measure of ∠QPN. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
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consCDL:['Shape(APN,NP)', 'Shape(AP,PN,NA)', 'Shape(PA,AQ,QP)', 'Shape(AQP,PQ)', 'Shape(ANQ,QA,AN)', 'Cocircular(A,PNQ)'], imgCDL:['Equal(MeasureOfAngle(NAP),120)', 'Equal(MeasureOfAngle(PAQ),100)'], textCDL:['Equal(MeasureOfAngle(NAP),120)', 'Equal(MeasureOfAngle(PAQ),100)', 'IsCentreOfCircle(A,A)'].
|
235
|
Find the measure of ∠QPN.
|
70
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, LR=10, PM=2KP, PR is parallel to KL, KN⊥MN, RM⊥PM. Find RM. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
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consCDL:['Shape(LR,RQ,QN,NL)', 'Shape(RM,MQ,QR)', 'Shape(QM,MP,PQ)', 'Shape(NQ,QP,PK,KN)', 'Collinear(LRM)', 'Collinear(MPK)', 'Collinear(LNK)', 'Collinear(RQP)', 'Collinear(NQM)'], imgCDL:['Equal(LengthOfLine(LR),10)', 'Equal(LengthOfLine(PM),Mul(LengthOfLine(KP),2))', 'ParallelBetweenLine(PR,KL)', 'PerpendicularBetweenLine(KN,MN)', 'PerpendicularBetweenLine(RM,PM)'], textCDL:['Equal(LengthOfLine(LR),10)', 'Equal(LengthOfLine(PM),Mul(LengthOfLine(KP),2))', 'ParallelBetweenLine(PR,KL)', 'PerpendicularBetweenLine(KN,MN)', 'PerpendicularBetweenLine(RM,PM)'].
|
241
|
Find RM.
|
20
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, BC=4, BF=x, ∠ABD=30°, ∠CBE=30°, ∠DBF=30°, ∠EBA=30°, BA⊥EA, BD⊥AD, BE is perpendicular to CE, BF is perpendicular to DF. Find the value of x. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
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consCDL:['Shape(CB,BE,EC)', 'Shape(EB,BA,AE)', 'Shape(AB,BD,DA)', 'Shape(DB,BF,FD)'], imgCDL:['Equal(LengthOfLine(BC),4)', 'Equal(LengthOfLine(BF),x)', 'Equal(MeasureOfAngle(ABD),30)', 'Equal(MeasureOfAngle(CBE),30)', 'Equal(MeasureOfAngle(DBF),30)', 'Equal(MeasureOfAngle(EBA),30)', 'PerpendicularBetweenLine(BA,EA)', 'PerpendicularBetweenLine(BD,AD)', 'PerpendicularBetweenLine(BE,CE)', 'PerpendicularBetweenLine(BF,DF)'], textCDL:['Equal(LengthOfLine(BC),4)', 'Equal(LengthOfLine(BF),x)', 'Equal(MeasureOfAngle(ABD),30)', 'Equal(MeasureOfAngle(CBE),30)', 'Equal(MeasureOfAngle(DBF),30)', 'Equal(MeasureOfAngle(EBA),30)', 'PerpendicularBetweenLine(BA,EA)', 'PerpendicularBetweenLine(BD,AD)', 'PerpendicularBetweenLine(BE,CE)', 'PerpendicularBetweenLine(BF,DF)'].
|
246
|
Find the value of x.
|
9/4
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, AB=2, triangle DBC is an equilateral triangle, A is the center of circle A. Find the area of the ⊙A minus the area of triangle DBC. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
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consCDL:['Shape(ADB,BD)', 'Shape(DB,BA,AD)', 'Shape(AB,BC,CD,DA)', 'Shape(ACD,DC)', 'Shape(ABC,CB)', 'Cocircular(A,DBC)'], imgCDL:['Equal(LengthOfLine(AB),2)'], textCDL:['Equal(LengthOfLine(AB),2)', 'EquilateralTriangle(DBC)', 'IsCentreOfCircle(A,A)'].
|
250
|
Find the area of the ⊙A minus the area of triangle DBC.
|
-3*sqrt(3)+4*pi
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠BDF=47°, ∠CIF=112°, ∠DFB=65°. Find the measure of ∠IAF. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
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consCDL:['Shape(BD,DF,FB)', 'Shape(FI,IA,AF)', 'Shape(DB,BG)', 'Shape(BF,FA)', 'Shape(CI,IF)', 'Collinear(GBFI)', 'Collinear(AFD)', 'Collinear(AIC)'], imgCDL:['Equal(MeasureOfAngle(BDF),47)', 'Equal(MeasureOfAngle(CIF),112)', 'Equal(MeasureOfAngle(DFB),65)'], textCDL:['Equal(MeasureOfAngle(BDF),47)', 'Equal(MeasureOfAngle(CIF),112)', 'Equal(MeasureOfAngle(DFB),65)'].
|
257
|
Find the measure of ∠IAF.
|
47
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠FEC=a°, ∠GDA=b°, DH is perpendicular to EH. Find the value of a+b-90. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(DH,HE,ED)', 'Shape(GD,DA)', 'Shape(FE,EC)', 'Collinear(ADH)', 'Collinear(HEF)', 'Collinear(GDEC)'], imgCDL:['Equal(MeasureOfAngle(FEC),a)', 'Equal(MeasureOfAngle(GDA),b)', 'PerpendicularBetweenLine(DH,EH)'], textCDL:['Equal(MeasureOfAngle(FEC),a)', 'Equal(MeasureOfAngle(GDA),b)', 'PerpendicularBetweenLine(DH,EH)'].
|
271
|
Find the value of a+b-90.
|
0
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠ABG=47°, ∠ACG=136°, ∠BED=63°, ∠DFB=∠BDF, ∠EBA=69°. Find the measure of ∠BCA. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(ED,DB,BE)', 'Shape(BD,DF,FB)', 'Shape(AB,BC,CA)', 'Shape(EB,BA)', 'Shape(AC,CG)', 'Collinear(DBCG)', 'Collinear(EBF)'], imgCDL:['Equal(MeasureOfAngle(ABG),47)', 'Equal(MeasureOfAngle(ACG),136)', 'Equal(MeasureOfAngle(BED),63)', 'Equal(MeasureOfAngle(DFB),MeasureOfAngle(BDF))', 'Equal(MeasureOfAngle(EBA),69)'], textCDL:['Equal(MeasureOfAngle(ABG),47)', 'Equal(MeasureOfAngle(ACG),136)', 'Equal(MeasureOfAngle(BED),63)', 'Equal(MeasureOfAngle(DFB),MeasureOfAngle(BDF))', 'Equal(MeasureOfAngle(EBA),69)'].
|
273
|
Find the measure of ∠BCA.
|
44
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠BGC=100°, ∠DCF=75°. Find ∠GAC. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(GA,AC,CG)', 'Shape(BG,GC)', 'Shape(DC,CF)', 'Collinear(EGCF)', 'Collinear(AGB)', 'Collinear(ACD)'], imgCDL:['Equal(MeasureOfAngle(BGC),100)', 'Equal(MeasureOfAngle(DCF),75)'], textCDL:['Equal(MeasureOfAngle(BGC),100)', 'Equal(MeasureOfAngle(DCF),75)'].
|
289
|
Find ∠GAC.
|
25
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠ACE=∠EAC, ∠DBG=136°, ∠DEB=47°, ∠EFA=63°, ∠FED=69°. Find the measure of ∠FAE. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(FA,AE,EF)', 'Shape(AC,CE,EA)', 'Shape(DE,EB,BD)', 'Shape(FE,ED)', 'Shape(FE,EB)', 'Shape(DB,BG)', 'Collinear(AEBG)', 'Collinear(FEC)'], imgCDL:['Equal(MeasureOfAngle(ACE),MeasureOfAngle(EAC))', 'Equal(MeasureOfAngle(DBG),136)', 'Equal(MeasureOfAngle(DEB),47)', 'Equal(MeasureOfAngle(EFA),63)', 'Equal(MeasureOfAngle(FED),69)'], textCDL:['Equal(MeasureOfAngle(ACE),MeasureOfAngle(EAC))', 'Equal(MeasureOfAngle(DBG),136)', 'Equal(MeasureOfAngle(DEB),47)', 'Equal(MeasureOfAngle(EFA),63)', 'Equal(MeasureOfAngle(FED),69)'].
|
295
|
Find the measure of ∠FAE.
|
53
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, RC=x, ST=20, TC=12, the center of ⊙R is R, TS is the tangent to ⊙R. Find the value of x. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(RSC,CR,RS)', 'Shape(RCS,SR,RC)', 'Shape(RCS,CT,TS)', 'Collinear(RCT)', 'Cocircular(R,SC)'], imgCDL:['Equal(LengthOfLine(RC),x)', 'Equal(LengthOfLine(ST),20)', 'Equal(LengthOfLine(TC),12)'], textCDL:['Equal(LengthOfLine(RC),x)', 'Equal(LengthOfLine(ST),20)', 'Equal(LengthOfLine(TC),12)', 'IsCentreOfCircle(R,R)', 'IsTangentOfCircle(TS,R)'].
|
296
|
Find the value of x.
|
32/3
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠BAD=65°, ∠DAE=110°, ∠EAC=x°, A is the center of ⊙A, CA is perpendicular to BA. Find the value of x. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
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consCDL:['Shape(ABC,CA,AB)', 'Shape(ADB,BA,AD)', 'Shape(ACE,EA,AC)', 'Shape(AED,DA,AE)', 'Cocircular(A,BCED)'], imgCDL:['Equal(MeasureOfAngle(BAD),65)', 'Equal(MeasureOfAngle(DAE),110)', 'Equal(MeasureOfAngle(EAC),x)', 'PerpendicularBetweenLine(CA,BA)'], textCDL:['Equal(MeasureOfAngle(BAD),65)', 'Equal(MeasureOfAngle(DAE),110)', 'Equal(MeasureOfAngle(EAC),x)', 'IsCentreOfCircle(A,A)', 'PerpendicularBetweenLine(CA,BA)'].
|
299
|
Find the value of x.
|
95
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, ML=3, PJ=x, HP is the midsegment of △ MLK, JH is the midsegment of triangle LKM, PJ is the midsegment of triangle KML. Find the value of x. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
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consCDL:['Shape(KP,PJ,JK)', 'Shape(JP,PH,HJ)', 'Shape(PM,MH,HP)', 'Shape(JH,HL,LJ)', 'Collinear(KPM)', 'Collinear(MHL)', 'Collinear(KJL)'], imgCDL:['Equal(LengthOfLine(ML),3)', 'Equal(LengthOfLine(PJ),x)'], textCDL:['Equal(LengthOfLine(ML),3)', 'Equal(LengthOfLine(PJ),x)', 'IsMidsegmentOfTriangle(HP,MLK)', 'IsMidsegmentOfTriangle(JH,LKM)', 'IsMidsegmentOfTriangle(PJ,KML)'].
|
300
|
Find the value of x.
|
3/2
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, QP=24, RT=16, ST=9, PQ is parallel to TR. Find PS. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
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consCDL:['Shape(RQ,QP,PT,TR)', 'Shape(SR,RT,TS)', 'Collinear(PTS)', 'Collinear(QRS)'], imgCDL:['Equal(LengthOfLine(QP),24)', 'Equal(LengthOfLine(RT),16)', 'Equal(LengthOfLine(ST),9)', 'ParallelBetweenLine(PQ,TR)'], textCDL:['Equal(LengthOfLine(QP),24)', 'Equal(LengthOfLine(RT),16)', 'Equal(LengthOfLine(ST),9)', 'ParallelBetweenLine(PQ,TR)'].
|
301
|
Find PS.
|
27/2
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, ⌒SRT is 8, ∠TSR=70°, S is the center of ⊙S. Find the circumference of the circle S. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
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consCDL:['Shape(STR,RS,ST)', 'Shape(SRT,TS,SR)', 'Cocircular(S,TR)'], imgCDL:['Equal(LengthOfArc(SRT),8)', 'Equal(MeasureOfAngle(TSR),70)'], textCDL:['Equal(LengthOfArc(SRT),8)', 'Equal(MeasureOfAngle(TSR),70)', 'IsCentreOfCircle(S,S)'].
|
306
|
Find the circumference of the circle S.
|
288/7
|
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<image>The Caption of this geometric diagram is:As shown in the diagram, AH=y, DA=8, DH=x, HF=6, ∠DAH=30°, ∠FBC=45°, DC is parallel to HF, AH is perpendicular to DH, CF⊥BF. Find the value of y. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
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consCDL:['Shape(DA,AH,HD)', 'Shape(DH,HF,FC,CD)', 'Shape(CF,FB,BC)', 'Collinear(AHFB)'], imgCDL:['Equal(LengthOfLine(AH),y)', 'Equal(LengthOfLine(DA),8)', 'Equal(LengthOfLine(DH),x)', 'Equal(LengthOfLine(HF),6)', 'Equal(MeasureOfAngle(DAH),30)', 'Equal(MeasureOfAngle(FBC),45)', 'ParallelBetweenLine(DC,HF)', 'PerpendicularBetweenLine(AH,DH)', 'PerpendicularBetweenLine(CF,BF)'], textCDL:['Equal(LengthOfLine(AH),y)', 'Equal(LengthOfLine(DA),8)', 'Equal(LengthOfLine(DH),x)', 'Equal(LengthOfLine(HF),6)', 'Equal(MeasureOfAngle(DAH),30)', 'Equal(MeasureOfAngle(FBC),45)', 'ParallelBetweenLine(DC,HF)', 'PerpendicularBetweenLine(AH,DH)', 'PerpendicularBetweenLine(CF,BF)'].
|
316
|
Find the value of y.
|
4*sqrt(3)
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|
<image>The Caption of this geometric diagram is:As shown in the diagram, BG=10, EG=10, the radius of circle G is 26, G is the center of ⊙G, CB is perpendicular to GB, FE⊥GE. Find DE. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
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consCDL:['Shape(GAF,FG,GA)', 'Shape(GF,FE,EG)', 'Shape(AG,GB,BA)', 'Shape(GFD,DE,EF)', 'Shape(GCA,AB,BC)', 'Shape(GE,ED,GDC,CB,BG)', 'Collinear(FED)', 'Collinear(ABC)', 'Cocircular(G,AFDC)'], imgCDL:['Equal(LengthOfLine(BG),10)', 'Equal(LengthOfLine(EG),10)', 'PerpendicularBetweenLine(CB,GB)', 'PerpendicularBetweenLine(FE,GE)'], textCDL:['Equal(LengthOfLine(BG),10)', 'Equal(LengthOfLine(EG),10)', 'Equal(RadiusOfCircle(G),26)', 'IsCentreOfCircle(G,G)', 'PerpendicularBetweenLine(CB,GB)', 'PerpendicularBetweenLine(FE,GE)'].
|
317
|
Find DE.
|
24
|
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<image>The Caption of this geometric diagram is:As shown in the diagram, ∠AGB=30°, G is the center of circle G, CG⊥DG. Find the measure of arc GBA. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
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consCDL:['Shape(GBA,AG,GB)', 'Shape(GCB,BG,GC)', 'Shape(GDC,CG,GD)', 'Shape(GFD,DG,GF)', 'Shape(GAF,FG,GA)', 'Collinear(AGD)', 'Collinear(BGF)', 'Cocircular(G,CBAFD)'], imgCDL:['Equal(MeasureOfAngle(AGB),30)', 'PerpendicularBetweenLine(CG,DG)'], textCDL:['Equal(MeasureOfAngle(AGB),30)', 'IsCentreOfCircle(G,G)', 'PerpendicularBetweenLine(CG,DG)'].
|
322
|
Find the measure of arc GBA.
|
30
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, NC=10, ND=2, the center of ⊙M is M, NC is the tangent to circle M. Find the perimeter of △MNC. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
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consCDL:['Shape(MCD,DM,MC)', 'Shape(MDC,CM,MD)', 'Shape(MDC,DN,NC)', 'Collinear(NDM)', 'Cocircular(M,DC)'], imgCDL:['Equal(LengthOfLine(NC),10)', 'Equal(LengthOfLine(ND),2)'], textCDL:['Equal(LengthOfLine(NC),10)', 'Equal(LengthOfLine(ND),2)', 'IsCentreOfCircle(M,M)', 'IsTangentOfCircle(NC,M)'].
|
324
|
Find the perimeter of △MNC.
|
60
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠FOE=118°, ∠LDA=104°, OD∥FI. Find ∠IFJ. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
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consCDL:['Shape(LD,DA)', 'Shape(FO,OE)', 'Shape(IF,FJ)', 'Shape(JF,FK)', 'Collinear(LDIC)', 'Collinear(HOFJ)', 'Collinear(ADOE)', 'Collinear(BIFK)'], imgCDL:['Equal(MeasureOfAngle(FOE),118)', 'Equal(MeasureOfAngle(LDA),104)', 'ParallelBetweenLine(OD,FI)'], textCDL:['Equal(MeasureOfAngle(FOE),118)', 'Equal(MeasureOfAngle(LDA),104)', 'ParallelBetweenLine(OD,FI)'].
|
329
|
Find ∠IFJ.
|
62
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠GOI=3*y+1°, ∠HBI=3*x+11°, ∠OIE=4*x-5°, GE is parallel to OI, HG∥BE, OI∥HB. Find the value of y. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
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consCDL:['Shape(GO,OI,IE,EG)', 'Shape(OH,HB,BI,IO)', 'Collinear(GOH)', 'Collinear(EIB)'], imgCDL:['Equal(MeasureOfAngle(GOI),3*y+1)', 'Equal(MeasureOfAngle(HBI),3*x+11)', 'Equal(MeasureOfAngle(OIE),4*x-5)', 'ParallelBetweenLine(GE,OI)', 'ParallelBetweenLine(HG,BE)', 'ParallelBetweenLine(OI,HB)'], textCDL:['Equal(MeasureOfAngle(GOI),3*y+1)', 'Equal(MeasureOfAngle(HBI),3*x+11)', 'Equal(MeasureOfAngle(OIE),4*x-5)', 'ParallelBetweenLine(GE,OI)', 'ParallelBetweenLine(HG,BE)', 'ParallelBetweenLine(OI,HB)'].
|
344
|
Find the value of y.
|
40
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, AF=10*z-40, CF=18-6*x, DA=2*z, DB=12*y-4, EB=4*y, EC=3*x, the center of ⊙G is G, AD is the tangent to ⊙G, the tangent to ⊙G is AF, BD is the tangent to ⊙G, BE is the tangent to ⊙G, CE is the tangent to circle G, CF is the tangent to ⊙G. Find the perimeter of △ABC. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
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consCDL:['Shape(GFD,FA,AD)', 'Shape(GDE,DB,BE)', 'Shape(GEF,EC,CF)', 'Shape(G)', 'Collinear(AFC)', 'Collinear(CEB)', 'Collinear(BDA)', 'Cocircular(G,FDE)'], imgCDL:['Equal(LengthOfLine(AF),10*z-40)', 'Equal(LengthOfLine(CF),18-6*x)', 'Equal(LengthOfLine(DA),2*z)', 'Equal(LengthOfLine(DB),12*y-4)', 'Equal(LengthOfLine(EB),4*y)', 'Equal(LengthOfLine(EC),3*x)'], textCDL:['Equal(LengthOfLine(AF),10*z-40)', 'Equal(LengthOfLine(CF),18-6*x)', 'Equal(LengthOfLine(DA),2*z)', 'Equal(LengthOfLine(DB),12*y-4)', 'Equal(LengthOfLine(EB),4*y)', 'Equal(LengthOfLine(EC),3*x)', 'IsCentreOfCircle(G,G)', 'IsTangentOfCircle(AD,G)', 'IsTangentOfCircle(AF,G)', 'IsTangentOfCircle(BD,G)', 'IsTangentOfCircle(BE,G)', 'IsTangentOfCircle(CE,G)', 'IsTangentOfCircle(CF,G)'].
|
349
|
Find the perimeter of △ABC.
|
36
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠CEB=40°, ∠EFD=2*x°, ∠EFD=∠FDE. Find the value of x. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
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consCDL:['Shape(FD,DE,EF)', 'Shape(EB,BC,CE)', 'Collinear(DEC)', 'Collinear(FEB)'], imgCDL:['Equal(MeasureOfAngle(CEB),40)', 'Equal(MeasureOfAngle(EFD),2*x)', 'Equal(MeasureOfAngle(EFD),MeasureOfAngle(FDE))'], textCDL:['Equal(MeasureOfAngle(CEB),40)', 'Equal(MeasureOfAngle(EFD),2*x)', 'Equal(MeasureOfAngle(EFD),MeasureOfAngle(FDE))'].
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351
|
Find the value of x.
|
35
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, FD=25, the center of ⊙O is O, the diameter of circle O is EH, DH is the tangent to circle O, the tangent to circle O is FE, EF is perpendicular to NF, HA is perpendicular to KA, KG is perpendicular to EG, ND⊥HD. Find the circumference of the ⊙O. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
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consCDL:['Shape(KG,GE,OKE)', 'Shape(EF,FN,OEN)', 'Shape(ND,DH,ONH)', 'Shape(HA,AK,OHK)', 'Shape(EO,OH,OHK,OKE)', 'Shape(HO,OE,OEN,ONH)', 'Shape(OHK,OKE,OEN,ONH)', 'Collinear(GKA)', 'Collinear(GEF)', 'Collinear(FND)', 'Collinear(AHD)', 'Collinear(EOH)', 'Cocircular(O,KENH)'], imgCDL:['Equal(LengthOfLine(FD),25)', 'PerpendicularBetweenLine(EF,NF)', 'PerpendicularBetweenLine(HA,KA)', 'PerpendicularBetweenLine(KG,EG)', 'PerpendicularBetweenLine(ND,HD)'], textCDL:['Equal(LengthOfLine(FD),25)', 'IsCentreOfCircle(O,O)', 'IsDiameterOfCircle(EH,O)', 'IsTangentOfCircle(DH,O)', 'IsTangentOfCircle(FE,O)', 'PerpendicularBetweenLine(EF,NF)', 'PerpendicularBetweenLine(HA,KA)', 'PerpendicularBetweenLine(KG,EG)', 'PerpendicularBetweenLine(ND,HD)'].
|
353
|
Find the circumference of the ⊙O.
|
25*pi
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, CB=23, DE=5, ∠EDB=45°, AC and DB are opposite sides of the parallelogram CADB, AE is perpendicular to BE. Find Perimeter(CADB). Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
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consCDL:['Shape(CA,AE,EB,BC)', 'Shape(BE,ED,DB)', 'Collinear(AED)'], imgCDL:['Equal(LengthOfLine(CB),23)', 'Equal(LengthOfLine(DE),5)', 'Equal(MeasureOfAngle(EDB),45)', 'PerpendicularBetweenLine(AE,BE)'], textCDL:['Equal(LengthOfLine(CB),23)', 'Equal(LengthOfLine(DE),5)', 'Equal(MeasureOfAngle(EDB),45)', 'Parallelogram(CADB)', 'PerpendicularBetweenLine(AE,BE)'].
|
361
|
Find Perimeter(CADB).
|
10*sqrt(2)+46
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠BFC=6*x°, ∠CFD=3*x°, ∠EFA=12*y-10°, EF is perpendicular to AF. Find the value of x. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
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consCDL:['Shape(AF,FB)', 'Shape(BF,FC)', 'Shape(CF,FD)', 'Shape(DF,FE)', 'Shape(EF,FA)', 'Collinear(AFD)', 'Collinear(BFE)'], imgCDL:['Equal(MeasureOfAngle(BFC),6*x)', 'Equal(MeasureOfAngle(CFD),3*x)', 'Equal(MeasureOfAngle(EFA),12*y-10)', 'PerpendicularBetweenLine(EF,AF)'], textCDL:['Equal(MeasureOfAngle(BFC),6*x)', 'Equal(MeasureOfAngle(CFD),3*x)', 'Equal(MeasureOfAngle(EFA),12*y-10)', 'PerpendicularBetweenLine(EF,AF)'].
|
362
|
Find the value of x.
|
10
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, AB=y, AD=z, BD=4, CB=x, CD=10, AB⊥CB, DC is perpendicular to AC. Find the value of z. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
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consCDL:['Shape(CA,AB,BC)', 'Shape(CB,BD,DC)', 'Collinear(ABD)'], imgCDL:['Equal(LengthOfLine(AB),y)', 'Equal(LengthOfLine(AD),z)', 'Equal(LengthOfLine(BD),4)', 'Equal(LengthOfLine(CB),x)', 'Equal(LengthOfLine(CD),10)', 'PerpendicularBetweenLine(AB,CB)', 'PerpendicularBetweenLine(DC,AC)'], textCDL:['Equal(LengthOfLine(AB),y)', 'Equal(LengthOfLine(AD),z)', 'Equal(LengthOfLine(BD),4)', 'Equal(LengthOfLine(CB),x)', 'Equal(LengthOfLine(CD),10)', 'PerpendicularBetweenLine(AB,CB)', 'PerpendicularBetweenLine(DC,AC)'].
|
365
|
Find the value of z.
|
25
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, PQ=6, PS=x, RP=15, TP=4, the center of ⊙A is A. Find the value of x. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
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consCDL:['Shape(TP,PQ,AQT)', 'Shape(SP,PT,ATS)', 'Shape(RP,PS,ASR)', 'Shape(QP,PR,ARQ)', 'Collinear(QPS)', 'Collinear(TPR)', 'Cocircular(A,RQTS)'], imgCDL:['Equal(LengthOfLine(PQ),6)', 'Equal(LengthOfLine(PS),x)', 'Equal(LengthOfLine(RP),15)', 'Equal(LengthOfLine(TP),4)'], textCDL:['Equal(LengthOfLine(PQ),6)', 'Equal(LengthOfLine(PS),x)', 'Equal(LengthOfLine(RP),15)', 'Equal(LengthOfLine(TP),4)', 'IsCentreOfCircle(A,A)'].
|
369
|
Find the value of x.
|
10
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, AD=7, AE=14, BD=x, the center of circle O is O, the tangent to ⊙O is AE. Find the value of x. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
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consCDL:['Shape(EA,AD,OED)', 'Shape(OED,DB,OBE)', 'Shape(BD,ODB)', 'Shape(CE)', 'Collinear(ADB)', 'Collinear(AEC)', 'Cocircular(O,EDB)'], imgCDL:['Equal(LengthOfLine(AD),7)', 'Equal(LengthOfLine(AE),14)', 'Equal(LengthOfLine(BD),x)'], textCDL:['Equal(LengthOfLine(AD),7)', 'Equal(LengthOfLine(AE),14)', 'Equal(LengthOfLine(BD),x)', 'IsCentreOfCircle(O,O)', 'IsTangentOfCircle(AE,O)'].
|
371
|
Find the value of x.
|
21
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, AB=26, AD=12, DG=9/2, EF=8, GF=14, ∠AGF=108°, AGFE is similar to ADCB. Find the perimeter of AGFE. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
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consCDL:['Shape(AG,GF,FE,EA)', 'Shape(GD,DC,CB,BE,EF,FG)', 'Collinear(AEB)', 'Collinear(AGD)'], imgCDL:['Equal(LengthOfLine(AB),26)', 'Equal(LengthOfLine(AD),12)', 'Equal(LengthOfLine(DG),9/2)', 'Equal(LengthOfLine(EF),8)', 'Equal(LengthOfLine(GF),14)', 'Equal(MeasureOfAngle(AGF),108)'], textCDL:['Equal(LengthOfLine(AB),26)', 'Equal(LengthOfLine(AD),12)', 'Equal(LengthOfLine(DG),9/2)', 'Equal(LengthOfLine(EF),8)', 'Equal(LengthOfLine(GF),14)', 'Equal(MeasureOfAngle(AGF),108)', 'SimilarBetweenQuadrilateral(AGFE,ADCB)'].
|
372
|
Find the perimeter of AGFE.
|
183/4
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, AE=x, BC=4, BE=3, CD=2, the center of circle X is X. Find the value of x. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
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consCDL:['Shape(DC,XCD)', 'Shape(EB,BC,XEC)', 'Shape(AE,XEC,CD,XDA)', 'Shape(EA,XAE)', 'Collinear(DCB)', 'Collinear(AEB)', 'Cocircular(X,AECD)'], imgCDL:['Equal(LengthOfLine(AE),x)', 'Equal(LengthOfLine(BC),4)', 'Equal(LengthOfLine(BE),3)', 'Equal(LengthOfLine(CD),2)'], textCDL:['Equal(LengthOfLine(AE),x)', 'Equal(LengthOfLine(BC),4)', 'Equal(LengthOfLine(BE),3)', 'Equal(LengthOfLine(CD),2)', 'IsCentreOfCircle(X,X)'].
|
376
|
Find the value of x.
|
5
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, PT=8, SR=3, TQ=3, ST is parallel to RQ. Find the length of line PS. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
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consCDL:['Shape(PS,ST,TP)', 'Shape(SR,RQ,QT,TS)', 'Collinear(PSR)', 'Collinear(PTQ)'], imgCDL:['Equal(LengthOfLine(PT),8)', 'Equal(LengthOfLine(SR),3)', 'Equal(LengthOfLine(TQ),3)', 'ParallelBetweenLine(ST,RQ)'], textCDL:['Equal(LengthOfLine(PT),8)', 'Equal(LengthOfLine(SR),3)', 'Equal(LengthOfLine(TQ),3)', 'ParallelBetweenLine(ST,RQ)'].
|
381
|
Find the length of line PS.
|
8
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠EAH=38°, ∠GEB=52°, AH is perpendicular to EH. Find ∠CHA. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
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consCDL:['Shape(IA,AF)', 'Shape(FA,AE)', 'Shape(AE,EG)', 'Shape(GE,EB)', 'Shape(CH,HA)', 'Shape(HA,AI)', 'Shape(DH,HC)', 'Shape(BE,EH)', 'Shape(EH,HD)', 'Shape(AH,HE,EA)', 'Collinear(IAEB)', 'Collinear(FAHD)', 'Collinear(CHEG)'], imgCDL:['Equal(MeasureOfAngle(EAH),38)', 'Equal(MeasureOfAngle(GEB),52)', 'PerpendicularBetweenLine(AH,EH)'], textCDL:['Equal(MeasureOfAngle(EAH),38)', 'Equal(MeasureOfAngle(GEB),52)', 'PerpendicularBetweenLine(AH,EH)'].
|
383
|
Find ∠CHA.
|
90
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, AD=10, BC=15, BE=6, EC=12, ED=3*x-2, ∠ADE=∠CBE. Find the value of x. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
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consCDL:['Shape(AD,DE,EA)', 'Shape(BE,EC,CB)', 'Collinear(AEC)', 'Collinear(BED)'], imgCDL:['Equal(LengthOfLine(AD),10)', 'Equal(LengthOfLine(BC),15)', 'Equal(LengthOfLine(BE),6)', 'Equal(LengthOfLine(EC),12)', 'Equal(LengthOfLine(ED),3*x-2)', 'Equal(MeasureOfAngle(ADE),MeasureOfAngle(CBE))'], textCDL:['Equal(LengthOfLine(AD),10)', 'Equal(LengthOfLine(BC),15)', 'Equal(LengthOfLine(BE),6)', 'Equal(LengthOfLine(EC),12)', 'Equal(LengthOfLine(ED),3*x-2)', 'Equal(MeasureOfAngle(ADE),MeasureOfAngle(CBE))'].
|
384
|
Find the value of x.
|
2
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, the diameter of circle A is 8, Diameter(⊙B) is 18, the diameter of ⊙C is 11, the center of circle A is A, the center of circle B is B, C is the center of ⊙C. Find the length of line FB. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
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consCDL:['Shape(AF,AFI,BIA)', 'Shape(FA,BAJ,AJF)', 'Shape(BIJ,AIJ)', 'Shape(FB,BM,CKM,BKI,AFI)', 'Shape(MB,BF,AJF,BJL,CML)', 'Shape(MG,BGK,CKM)', 'Shape(GM,CML,BLG)', 'Shape(BLG,BGK,CLK)', 'Collinear(AFBMGC)', 'Cocircular(A,JFI)', 'Cocircular(B,IAJLGK)', 'Cocircular(C,KML)'], imgCDL:[], textCDL:['Equal(DiameterOfCircle(A),8)', 'Equal(DiameterOfCircle(B),18)', 'Equal(DiameterOfCircle(C),11)', 'IsCentreOfCircle(A,A)', 'IsCentreOfCircle(B,B)', 'IsCentreOfCircle(C,C)'].
|
385
|
Find the length of line FB.
|
5
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠ADK=96°, ∠HGJ=42°, DH is parallel to AG. Find the measure of ∠EAD. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
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consCDL:['Shape(KD,DL)', 'Shape(LD,DH)', 'Shape(DH,HI)', 'Shape(IH,HC)', 'Shape(AD,DK)', 'Shape(HD,DA)', 'Shape(GH,HD)', 'Shape(CH,HG)', 'Shape(EA,AD)', 'Shape(DA,AG)', 'Shape(AG,GH)', 'Shape(HG,GJ)', 'Shape(MA,AE)', 'Shape(GA,AM)', 'Shape(FG,GA)', 'Shape(JG,GF)', 'Collinear(KDHC)', 'Collinear(EAGJ)', 'Collinear(LDAM)', 'Collinear(IHGF)'], imgCDL:['Equal(MeasureOfAngle(ADK),96)', 'Equal(MeasureOfAngle(HGJ),42)', 'ParallelBetweenLine(DH,AG)'], textCDL:['Equal(MeasureOfAngle(ADK),96)', 'Equal(MeasureOfAngle(HGJ),42)', 'ParallelBetweenLine(DH,AG)'].
|
387
|
Find the measure of ∠EAD.
|
84
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, AB=15, PB=12, ∠PBA=24°, quadrilateral ADCB is a rhombus. Find AP. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
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consCDL:['Shape(AD,DP,PA)', 'Shape(PD,DC,CP)', 'Shape(PC,CB,BP)', 'Shape(PB,BA,AP)', 'Collinear(APC)', 'Collinear(DPB)'], imgCDL:['Equal(LengthOfLine(AB),15)', 'Equal(LengthOfLine(PB),12)', 'Equal(MeasureOfAngle(PBA),24)'], textCDL:['Equal(LengthOfLine(AB),15)', 'Equal(LengthOfLine(PB),12)', 'Equal(MeasureOfAngle(PBA),24)', 'Rhombus(ADCB)'].
|
390
|
Find AP.
|
9
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, YW=18, ZY=18, ∠OYW=143°, ∠OZY=2*x-1°, O is the center of circle O. Find the value of x. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(WY,OYW)', 'Shape(ZY,YW,OWZ)', 'Shape(YZ,OZY)', 'Cocircular(O,YWZ)'], imgCDL:['Equal(LengthOfLine(YW),18)', 'Equal(LengthOfLine(ZY),18)', 'Equal(MeasureOfArc(OYW),143)', 'Equal(MeasureOfArc(OZY),2*x-1)'], textCDL:['Equal(LengthOfLine(YW),18)', 'Equal(LengthOfLine(ZY),18)', 'Equal(MeasureOfArc(OYW),143)', 'Equal(MeasureOfArc(OZY),2*x-1)', 'IsCentreOfCircle(O,O)'].
|
402
|
Find the value of x.
|
72
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠JQR=131°, QR∥TS, TQ is parallel to SR. Find the measure of ∠STC. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(JQ,QR)', 'Shape(QR,RH)', 'Shape(QT,TS,SR,RQ)', 'Shape(ST,TC)', 'Shape(BS,ST)', 'Collinear(JQTC)', 'Collinear(HRSB)'], imgCDL:['Equal(MeasureOfAngle(JQR),131)', 'ParallelBetweenLine(QR,TS)', 'ParallelBetweenLine(TQ,SR)'], textCDL:['Equal(MeasureOfAngle(JQR),131)', 'ParallelBetweenLine(QR,TS)', 'ParallelBetweenLine(TQ,SR)'].
|
404
|
Find the measure of ∠STC.
|
49
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠DQS=238°, D is the center of circle D, the tangent to ⊙D is RQ. Find ∠RQS. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(QS,DSQ)', 'Shape(SQ,QD,DS)', 'Shape(SD,DQ,DQT,DTS)', 'Shape(RQ,QS)', 'Cocircular(D,SQT)'], imgCDL:['Equal(MeasureOfArc(DQS),238)'], textCDL:['Equal(MeasureOfArc(DQS),238)', 'IsCentreOfCircle(D,D)', 'IsTangentOfCircle(RQ,D)'].
|
408
|
Find ∠RQS.
|
61
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, RD=3, SA=3, TA=x, UC=x, Perimeter(TSRU) is 18, the center of circle J is J, the tangent to ⊙J is RC, RD is the tangent to ⊙J, the tangent to circle J is SA, SD is the tangent to circle J, TA is the tangent to ⊙J, TB is the tangent to circle J, UB is the tangent to ⊙J, the tangent to ⊙J is UC. Find the value of x. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(BT,TA,JBA)', 'Shape(AS,SD,JAD)', 'Shape(DR,RC,JDC)', 'Shape(CU,UB,JCB)', 'Shape(JAD,JDC,JCB,JBA)', 'Shape(J)', 'Collinear(TBU)', 'Collinear(TAS)', 'Collinear(SDR)', 'Collinear(UCR)', 'Cocircular(J,BADC)'], imgCDL:['Equal(LengthOfLine(RD),3)', 'Equal(LengthOfLine(SA),3)', 'Equal(LengthOfLine(TA),x)', 'Equal(LengthOfLine(UC),x)'], textCDL:['Equal(LengthOfLine(RD),3)', 'Equal(LengthOfLine(SA),3)', 'Equal(LengthOfLine(TA),x)', 'Equal(LengthOfLine(UC),x)', 'Equal(PerimeterOfQuadrilateral(TSRU),18)', 'IsCentreOfCircle(J,J)', 'IsTangentOfCircle(RC,J)', 'IsTangentOfCircle(RD,J)', 'IsTangentOfCircle(SA,J)', 'IsTangentOfCircle(SD,J)', 'IsTangentOfCircle(TA,J)', 'IsTangentOfCircle(TB,J)', 'IsTangentOfCircle(UB,J)', 'IsTangentOfCircle(UC,J)'].
|
419
|
Find the value of x.
|
3/2
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, PT=6, QR=12, SP=4, PT∥QR. Find the length of line SQ. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(SP,PT,TS)', 'Shape(PQ,QR,RT,TP)', 'Collinear(SPQ)', 'Collinear(STR)'], imgCDL:['Equal(LengthOfLine(PT),6)', 'Equal(LengthOfLine(QR),12)', 'Equal(LengthOfLine(SP),4)', 'ParallelBetweenLine(PT,QR)'], textCDL:['Equal(LengthOfLine(PT),6)', 'Equal(LengthOfLine(QR),12)', 'Equal(LengthOfLine(SP),4)', 'ParallelBetweenLine(PT,QR)'].
|
425
|
Find the length of line SQ.
|
8
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, AC=12, AR=x, BC=9, RB=7, RD=6, DC is perpendicular to BC, DR is perpendicular to AR. Find the length of line AR. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(AD,DR,RA)', 'Shape(BR,RD,DC,CB)', 'Collinear(ADC)', 'Collinear(ARB)'], imgCDL:['Equal(LengthOfLine(AC),12)', 'Equal(LengthOfLine(AR),x)', 'Equal(LengthOfLine(BC),9)', 'Equal(LengthOfLine(RB),7)', 'Equal(LengthOfLine(RD),6)', 'PerpendicularBetweenLine(DC,BC)', 'PerpendicularBetweenLine(DR,AR)'], textCDL:['Equal(LengthOfLine(AC),12)', 'Equal(LengthOfLine(AR),x)', 'Equal(LengthOfLine(BC),9)', 'Equal(LengthOfLine(RB),7)', 'Equal(LengthOfLine(RD),6)', 'PerpendicularBetweenLine(DC,BC)', 'PerpendicularBetweenLine(DR,AR)'].
|
431
|
Find the length of line AR.
|
8
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, AD=x+2, BD=3*y-9, BD=DY, CA=AY, CB=3/2*x+11, DY=2*y+6. Find the value of x. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(AY,YD,DA)', 'Shape(BC,CA,AD,DB)', 'Collinear(CAY)', 'Collinear(BDY)'], imgCDL:['Equal(LengthOfLine(AD),x+2)', 'Equal(LengthOfLine(BD),3*y-9)', 'Equal(LengthOfLine(BD),LengthOfLine(DY))', 'Equal(LengthOfLine(CA),LengthOfLine(AY))', 'Equal(LengthOfLine(CB),3/2*x+11)', 'Equal(LengthOfLine(DY),2*y+6)'], textCDL:['Equal(LengthOfLine(AD),x+2)', 'Equal(LengthOfLine(BD),3*y-9)', 'Equal(LengthOfLine(BD),LengthOfLine(DY))', 'Equal(LengthOfLine(CA),LengthOfLine(AY))', 'Equal(LengthOfLine(CB),3/2*x+11)', 'Equal(LengthOfLine(DY),2*y+6)'].
|
434
|
Find the value of x.
|
14
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠ACD=x°, ∠BCA=130°, ∠DCB=60°, C is the center of ⊙C. Find the value of x. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(DC,CB,CBD)', 'Shape(AC,CD,CDA)', 'Shape(BC,CA,CAB)', 'Cocircular(C,BDA)'], imgCDL:['Equal(MeasureOfAngle(ACD),x)', 'Equal(MeasureOfAngle(BCA),130)', 'Equal(MeasureOfAngle(DCB),60)'], textCDL:['Equal(MeasureOfAngle(ACD),x)', 'Equal(MeasureOfAngle(BCA),130)', 'Equal(MeasureOfAngle(DCB),60)', 'IsCentreOfCircle(C,C)'].
|
443
|
Find the value of x.
|
170
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠MPG=89°, ∠PNE=66°, the center of circle P is P. Find ∠MNG. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(GE,PEG)', 'Shape(MG,PGM)', 'Shape(NM,PMN)', 'Shape(EN,PNE)', 'Shape(GP,PB,BE,EG)', 'Shape(GM,MP,PG)', 'Shape(PM,MB,BP)', 'Shape(BM,MN,NB)', 'Shape(BN,NE,EB)', 'Collinear(GPBN)', 'Collinear(MBE)', 'Cocircular(P,GMNE)'], imgCDL:['Equal(MeasureOfAngle(MPG),89)', 'Equal(MeasureOfArc(PNE),66)'], textCDL:['Equal(MeasureOfAngle(MPG),89)', 'Equal(MeasureOfArc(PNE),66)', 'IsCentreOfCircle(P,P)'].
|
444
|
Find ∠MNG.
|
89/2
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠AGE=55°, ∠BGA=x°, ∠GBH=y°, BD is parallel to GA. Find the value of y. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(HB,BF)', 'Shape(CG,GB)', 'Shape(GB,BH)', 'Shape(EG,GC)', 'Shape(AG,GE)', 'Shape(DB,BG)', 'Shape(BG,GA)', 'Shape(FB,BD)', 'Collinear(HBD)', 'Collinear(CGA)', 'Collinear(FBGE)'], imgCDL:['Equal(MeasureOfAngle(AGE),55)', 'Equal(MeasureOfAngle(BGA),x)', 'Equal(MeasureOfAngle(GBH),y)', 'ParallelBetweenLine(BD,GA)'], textCDL:['Equal(MeasureOfAngle(AGE),55)', 'Equal(MeasureOfAngle(BGA),x)', 'Equal(MeasureOfAngle(GBH),y)', 'ParallelBetweenLine(BD,GA)'].
|
458
|
Find the value of y.
|
125
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, AB=35, CD=19, the perimeter of DBAC is 74, DB and AC are the non-parallel sides of isosceles trapezoid DBAC, CF⊥AF, DE is perpendicular to AE. Find the area of quadrilateral DBAC. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(DB,BE,ED)', 'Shape(DE,EF,FC,CD)', 'Shape(CF,FA,AC)', 'Collinear(BEFA)'], imgCDL:['Equal(LengthOfLine(AB),35)', 'Equal(LengthOfLine(CD),19)', 'PerpendicularBetweenLine(CF,AF)', 'PerpendicularBetweenLine(DE,AE)'], textCDL:['Equal(LengthOfLine(AB),35)', 'Equal(LengthOfLine(CD),19)', 'Equal(PerimeterOfQuadrilateral(DBAC),74)', 'IsoscelesTrapezoid(DBAC)', 'PerpendicularBetweenLine(CF,AF)', 'PerpendicularBetweenLine(DE,AE)'].
|
462
|
Find the area of quadrilateral DBAC.
|
162
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠RST=63°, the center of circle A is A. Find the measure of ⌒ATR. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(SR,ARS)', 'Shape(TS,AST)', 'Shape(AT,ATR,RA)', 'Shape(ST,TA,AR,RS)', 'Cocircular(A,RST)'], imgCDL:['Equal(MeasureOfAngle(RST),63)'], textCDL:['Equal(MeasureOfAngle(RST),63)', 'IsCentreOfCircle(A,A)'].
|
463
|
Find the measure of ⌒ATR.
|
126
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠FYD=4*y+10°, EH is parallel to BY, YH is perpendicular to EH. Find the value of y. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(EH,HJ)', 'Shape(JH,HA)', 'Shape(YH,HE)', 'Shape(BY,YH)', 'Shape(DY,YB)', 'Shape(FY,YD)', 'Shape(HY,YF)', 'Shape(AH,HY)', 'Collinear(JHYD)', 'Collinear(EHA)', 'Collinear(BYF)'], imgCDL:['Equal(MeasureOfAngle(FYD),4*y+10)', 'ParallelBetweenLine(EH,BY)', 'PerpendicularBetweenLine(YH,EH)'], textCDL:['Equal(MeasureOfAngle(FYD),4*y+10)', 'ParallelBetweenLine(EH,BY)', 'PerpendicularBetweenLine(YH,EH)'].
|
465
|
Find the value of y.
|
20
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠AQT=32°, ∠QSR=5*x+4°, ∠QTR=6*x-2°, the center of ⊙C is C. Find ∠SRT. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(CSR,RS)', 'Shape(AS,SR,RA)', 'Shape(AR,CRQ,QA)', 'Shape(AQ,QT,TA)', 'Shape(CQT,TQ)', 'Shape(AT,CTS,SA)', 'Collinear(RAT)', 'Collinear(QAS)', 'Cocircular(C,RQTS)'], imgCDL:['Equal(MeasureOfAngle(AQT),32)', 'Equal(MeasureOfAngle(QSR),5*x+4)', 'Equal(MeasureOfAngle(QTR),6*x-2)'], textCDL:['Equal(MeasureOfAngle(AQT),32)', 'Equal(MeasureOfAngle(QSR),5*x+4)', 'Equal(MeasureOfAngle(QTR),6*x-2)', 'IsCentreOfCircle(C,C)'].
|
470
|
Find ∠SRT.
|
32
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, BG=7, DC=14, the center of ⊙B is B, quadrilateral ADCE is a square. Find the area of ADCE minus the area of the ⊙B. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(AF,BIF,IA)', 'Shape(FD,DG,BFG)', 'Shape(GC,CH,BGH)', 'Shape(HE,EI,BHI)', 'Shape(BIF,BFG,BGH,BHI)', 'Shape(BG)', 'Collinear(AFD)', 'Collinear(DGC)', 'Collinear(CHE)', 'Collinear(AIE)', 'Cocircular(B,FGHI)'], imgCDL:['Equal(LengthOfLine(BG),7)', 'Equal(LengthOfLine(DC),14)'], textCDL:['Equal(LengthOfLine(BG),7)', 'Equal(LengthOfLine(DC),14)', 'IsCentreOfCircle(B,B)', 'Square(ADCE)'].
|
474
|
Find the area of ADCE minus the area of the ⊙B.
|
196-49*pi
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠FEI=2*x+70°, ∠HGL=2*y-20°, ∠RFN=3*x+40°, FN∥EI, GF is parallel to HE. Find the value of x. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(LG,GQ)', 'Shape(HG,GL)', 'Shape(PH,HG)', 'Shape(MH,HP)', 'Shape(EH,HM)', 'Shape(QG,GF)', 'Shape(OE,EH)', 'Shape(GF,FR)', 'Shape(HE,EF,FG,GH)', 'Shape(RF,FN)', 'Shape(NF,FE)', 'Shape(FE,EI)', 'Shape(IE,EO)', 'Collinear(QGHM)', 'Collinear(RFEO)', 'Collinear(LGFN)', 'Collinear(PHEI)'], imgCDL:['Equal(MeasureOfAngle(FEI),2*x+70)', 'Equal(MeasureOfAngle(HGL),2*y-20)', 'Equal(MeasureOfAngle(RFN),3*x+40)', 'ParallelBetweenLine(FN,EI)', 'ParallelBetweenLine(GF,HE)'], textCDL:['Equal(MeasureOfAngle(FEI),2*x+70)', 'Equal(MeasureOfAngle(HGL),2*y-20)', 'Equal(MeasureOfAngle(RFN),3*x+40)', 'ParallelBetweenLine(FN,EI)', 'ParallelBetweenLine(GF,HE)'].
|
483
|
Find the value of x.
|
30
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠JKL=62°, the center of circle A is A. Find the measure of arc AJK. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(AL,ALJ,JA)', 'Shape(AJ,JK,KA)', 'Shape(AJK,KJ)', 'Shape(AK,AKL,LA)', 'Collinear(LAK)', 'Cocircular(A,LJK)'], imgCDL:['Equal(MeasureOfAngle(JKL),62)'], textCDL:['Equal(MeasureOfAngle(JKL),62)', 'IsCentreOfCircle(A,A)'].
|
491
|
Find the measure of arc AJK.
|
56
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠AHD=14*x+9°, ∠FEG=5*x+90°, HD is parallel to EB. Find the value of x. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(CH,HA)', 'Shape(AH,HD)', 'Shape(EH,HC)', 'Shape(DH,HE)', 'Shape(GE,EH)', 'Shape(HE,EB)', 'Shape(FE,EG)', 'Shape(BE,EF)', 'Collinear(CHD)', 'Collinear(GEB)', 'Collinear(AHEF)'], imgCDL:['Equal(MeasureOfAngle(AHD),14*x+9)', 'Equal(MeasureOfAngle(FEG),5*x+90)', 'ParallelBetweenLine(HD,EB)'], textCDL:['Equal(MeasureOfAngle(AHD),14*x+9)', 'Equal(MeasureOfAngle(FEG),5*x+90)', 'ParallelBetweenLine(HD,EB)'].
|
494
|
Find the value of x.
|
9
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, BF=2*y+4, DG=3/2*x+8, DG=FG, EB=3*y-6, FG=1/2*x+12. Find FD. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(FG,GB,BF)', 'Shape(BG,GD,DE,EB)', 'Collinear(FGD)', 'Collinear(FBE)'], imgCDL:['Equal(LengthOfLine(BF),2*y+4)', 'Equal(LengthOfLine(DG),3/2*x+8)', 'Equal(LengthOfLine(DG),LengthOfLine(FG))', 'Equal(LengthOfLine(EB),3*y-6)', 'Equal(LengthOfLine(FG),1/2*x+12)'], textCDL:['Equal(LengthOfLine(BF),2*y+4)', 'Equal(LengthOfLine(DG),3/2*x+8)', 'Equal(LengthOfLine(DG),LengthOfLine(FG))', 'Equal(LengthOfLine(EB),3*y-6)', 'Equal(LengthOfLine(FG),1/2*x+12)'].
|
496
|
Find FD.
|
28
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, AC=x+7, CB=4, CE=12-x, DC=6, AB is perpendicular to CB, ED⊥CD, △ABC is similar to △EDC.. Find CE. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(AB,BC,CA)', 'Shape(ED,DC,CE)', 'Collinear(DCB)', 'Collinear(ACE)'], imgCDL:['Equal(LengthOfLine(AC),x+7)', 'Equal(LengthOfLine(CB),4)', 'Equal(LengthOfLine(CE),12-x)', 'Equal(LengthOfLine(DC),6)', 'PerpendicularBetweenLine(AB,CB)', 'PerpendicularBetweenLine(ED,CD)'], textCDL:['Equal(LengthOfLine(AC),x+7)', 'Equal(LengthOfLine(CB),4)', 'Equal(LengthOfLine(CE),12-x)', 'Equal(LengthOfLine(DC),6)', 'PerpendicularBetweenLine(AB,CB)', 'PerpendicularBetweenLine(ED,CD)', 'SimilarBetweenTriangle(ABC,EDC)'].
|
501
|
Find CE.
|
57/5
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, PQ=21, PT=8, TR=15, PQ is parallel to TR. Find the length of line TS. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(QP,PT,TR,RQ)', 'Shape(RT,TS,SR)', 'Collinear(QRS)', 'Collinear(PTS)'], imgCDL:['Equal(LengthOfLine(PQ),21)', 'Equal(LengthOfLine(PT),8)', 'Equal(LengthOfLine(TR),15)', 'ParallelBetweenLine(PQ,TR)'], textCDL:['Equal(LengthOfLine(PQ),21)', 'Equal(LengthOfLine(PT),8)', 'Equal(LengthOfLine(TR),15)', 'ParallelBetweenLine(PQ,TR)'].
|
503
|
Find the length of line TS.
|
20
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠AGC=40°, ∠DGF=53°, CB is perpendicular to GB, FG⊥CG, GF is perpendicular to DF. Find the measure of ∠GCB. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(DG,GF,FD)', 'Shape(GA,AF,FG)', 'Shape(GC,CB,BG)', 'Shape(CA,AB,BC)', 'Collinear(DFA)', 'Collinear(GBA)'], imgCDL:['Equal(MeasureOfAngle(AGC),40)', 'Equal(MeasureOfAngle(DGF),53)', 'PerpendicularBetweenLine(CB,GB)', 'PerpendicularBetweenLine(FG,CG)', 'PerpendicularBetweenLine(GF,DF)'], textCDL:['Equal(MeasureOfAngle(AGC),40)', 'Equal(MeasureOfAngle(DGF),53)', 'PerpendicularBetweenLine(CB,GB)', 'PerpendicularBetweenLine(FG,CG)', 'PerpendicularBetweenLine(GF,DF)'].
|
506
|
Find the measure of ∠GCB.
|
50
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, AC=2/3*x-4, AD=1/3*x+2, AD=AC, DE=5*y, EB=7/3*y+8, ED=EB. Find the length of line DB. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(DA,AE,ED)', 'Shape(EA,AC,CB,BE)', 'Collinear(DAC)', 'Collinear(DEB)'], imgCDL:['Equal(LengthOfLine(AC),2/3*x-4)', 'Equal(LengthOfLine(AD),1/3*x+2)', 'Equal(LengthOfLine(AD),LengthOfLine(AC))', 'Equal(LengthOfLine(DE),5*y)', 'Equal(LengthOfLine(EB),7/3*y+8)', 'Equal(LengthOfLine(ED),LengthOfLine(EB))'], textCDL:['Equal(LengthOfLine(AC),2/3*x-4)', 'Equal(LengthOfLine(AD),1/3*x+2)', 'Equal(LengthOfLine(AD),LengthOfLine(AC))', 'Equal(LengthOfLine(DE),5*y)', 'Equal(LengthOfLine(EB),7/3*y+8)', 'Equal(LengthOfLine(ED),LengthOfLine(EB))'].
|
507
|
Find the length of line DB.
|
30
|
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