images images listlengths 1 1 | problem stringlengths 310 675 | answer stringlengths 114 1.18k | proID stringlengths 1 4 |
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<image>The Caption of this geometric diagram is:As shown in the diagram, JH=5, JH=y+2, LV=2*x+6, ML=20-5*x, ML=LV, MN=4, QO=3, Q is the midpoint of segment BU, MB and VU are the parallel sides of trapezoid MVUB. Prove that LQ is the midsegment of quadrilateral MVUB. Please provide the consCDL and imgCDL based on this g... | consCDL:['Shape(GM,MN)', 'Shape(NM,MB)', 'Shape(MB,BA)', 'Shape(AB,BP)', 'Shape(GM,ML)', 'Shape(PB,BQ)', 'Shape(CL,LM)', 'Shape(BQ,QO)', 'Shape(CL,LV)', 'Shape(OQ,QU)', 'Shape(JV,VL)', 'Shape(QU,UH)', 'Shape(JV,VS)', 'Shape(SV,VU)', 'Shape(VU,UY)', 'Shape(YU,UH)', 'Shape(ML,LQ,QB,BM)', 'Shape(QL,LV,VU,UQ)', 'Collinear(... | 293 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠GJI=∠LON, ∠GJI=y+30°, ∠HGJ=87°, ∠IHG=98°, ∠IHG=∠NML, ∠JIH=∠ONM, ∠LON=60°, ∠MLO=x-4°, quadrilateral HGJI is similar to quadrilateral MLON. Find the value of x. Please provide the consCDL and imgCDL based on this given geometric diagram and provide... | consCDL:['Shape(IH,HG,GJ,JI)', 'Shape(NM,ML,LO,ON)'], imgCDL:['Equal(MeasureOfAngle(GJI),MeasureOfAngle(LON))', 'Equal(MeasureOfAngle(GJI),y+30)', 'Equal(MeasureOfAngle(HGJ),87)', 'Equal(MeasureOfAngle(IHG),98)', 'Equal(MeasureOfAngle(IHG),MeasureOfAngle(NML))', 'Equal(MeasureOfAngle(JIH),MeasureOfAngle(ONM))', 'Equal(... | 294 | |
<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. You first think within <think></think> tags and... | consCDL:['Shape(FA,AE,EF)', 'Shape(AC,CE,EA)', 'Shape(DE,EB,BD)', 'Shape(FE,ED)', 'Shape(CE,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(Mea... | 295 | |
<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. You first think within <think></thin... | 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)', 'IsCentreOfCircl... | 296 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, AB=x, AC=11, BC=9, ∠BCA=28°. 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. You first think within <think></think> tags and then provide all CDLs withi... | consCDL:['Shape(AB,BC,CA)'], imgCDL:['Equal(LengthOfLine(AB),x)', 'Equal(LengthOfLine(AC),11)', 'Equal(LengthOfLine(BC),9)', 'Equal(MeasureOfAngle(BCA),28)'], textCDL:['Equal(LengthOfLine(AB),x)', 'Equal(LengthOfLine(AC),11)', 'Equal(LengthOfLine(BC),9)', 'Equal(MeasureOfAngle(BCA),28)']. | 297 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, AC=5*y, AY=2*x-5, CB=3*x-18, YB=2*y+12, quadrilateral AYBC is a parallelogram. 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. You first think within <t... | consCDL:['Shape(AY,YB,BC,CA)'], imgCDL:['Equal(LengthOfLine(AC),5*y)', 'Equal(LengthOfLine(AY),2*x-5)', 'Equal(LengthOfLine(CB),3*x-18)', 'Equal(LengthOfLine(YB),2*y+12)'], textCDL:['Equal(LengthOfLine(AC),5*y)', 'Equal(LengthOfLine(AY),2*x-5)', 'Equal(LengthOfLine(CB),3*x-18)', 'Equal(LengthOfLine(YB),2*y+12)', 'Paral... | 298 | |
<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. You first think within <... | 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(D... | 299 | |
<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 o... | 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)', 'IsMidsegmen... | 300 | |
<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. You first think within <think></think> tags and then provide all CDLs with... | 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)', 'Parall... | 301 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, AB=10, ∠OBA=60°, Radius(⊙O) is 10, the center of circle O is O, BX⊥OX. Find the length of line AX. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <th... | consCDL:['Shape(OBY,YX,XB)', 'Shape(OYA,AX,XY)', 'Shape(OAB,BX,XA)', 'Shape(BX,XO)', 'Shape(OX,XA)', 'Collinear(AXB)', 'Collinear(YXO)', 'Cocircular(O,BYA)'], imgCDL:['Equal(LengthOfLine(AB),10)', 'Equal(MeasureOfArc(OBA),60)', 'PerpendicularBetweenLine(BX,OX)'], textCDL:['Equal(LengthOfLine(AB),10)', 'Equal(MeasureOfA... | 302 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, PM=20, QR=6*x, TS=2*x, M is the midpoint of segment RS, P bisects segment QT, QR and TS are the parallel sides of trapezoid QTSR. Find the value of x. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the text... | consCDL:['Shape(QP,PM,MR,RQ)', 'Shape(PT,TS,SM,MP)', 'Collinear(QPT)', 'Collinear(RMS)'], imgCDL:['Equal(LengthOfLine(PM),20)', 'Equal(LengthOfLine(QR),6*x)', 'Equal(LengthOfLine(TS),2*x)'], textCDL:['Equal(LengthOfLine(PM),20)', 'Equal(LengthOfLine(QR),6*x)', 'Equal(LengthOfLine(TS),2*x)', 'IsMidpointOfLine(M,RS)', 'I... | 303 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠GCH=2*x°, ∠HCD=6*x+28°, the center of ⊙C is C, FC⊥GC. Find the measure of ⌒CFE. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags ... | consCDL:['Shape(CHG,GC,CH)', 'Shape(CGF,FC,CG)', 'Shape(CFE,EC,CF)', 'Shape(CED,DC,CE)', 'Shape(CDH,HC,CD)', 'Collinear(HCE)', 'Collinear(GCD)', 'Cocircular(C,HGFED)'], imgCDL:['Equal(MeasureOfAngle(GCH),2*x)', 'Equal(MeasureOfAngle(HCD),6*x+28)', 'PerpendicularBetweenLine(FC,GC)'], textCDL:['Equal(MeasureOfAngle(GCH),... | 304 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, RT=x, ST=7, ∠RTS=30°, ∠TSR=120°. 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. You first think within <think></think> tags and then provide all CDLs w... | consCDL:['Shape(SR,RT,TS)'], imgCDL:['Equal(LengthOfLine(RT),x)', 'Equal(LengthOfLine(ST),7)', 'Equal(MeasureOfAngle(RTS),30)', 'Equal(MeasureOfAngle(TSR),120)'], textCDL:['Equal(LengthOfLine(RT),x)', 'Equal(LengthOfLine(ST),7)', 'Equal(MeasureOfAngle(RTS),30)', 'Equal(MeasureOfAngle(TSR),120)']. | 305 | |
<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. You first think within <think></think> ta... | 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 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, AB=5*x-11, AD=3*x+5, BC=15, CD=15, AC is perpendicular to DC. Find the length of line AB. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></thi... | consCDL:['Shape(AB,BC,CA)', 'Shape(AC,CD,DA)', 'Collinear(BCD)'], imgCDL:['Equal(LengthOfLine(AB),5*x-11)', 'Equal(LengthOfLine(AD),3*x+5)', 'Equal(LengthOfLine(BC),15)', 'Equal(LengthOfLine(CD),15)', 'PerpendicularBetweenLine(AC,DC)'], textCDL:['Equal(LengthOfLine(AB),5*x-11)', 'Equal(LengthOfLine(AD),3*x+5)', 'Equal(... | 309 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, BE=x, DE=x+10, EA=x+1, EC=x+3, the center of circle F is F. 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. You first think within <think></think> tags ... | consCDL:['Shape(FBA,AE,EB)', 'Shape(FAD,DF,FE,EA)', 'Shape(FDC,CE,EF,FD)', 'Shape(FCB,BE,EC)', 'Collinear(BEFD)', 'Collinear(AEC)', 'Cocircular(F,CBAD)'], imgCDL:['Equal(LengthOfLine(BE),x)', 'Equal(LengthOfLine(DE),x+10)', 'Equal(LengthOfLine(EA),x+1)', 'Equal(LengthOfLine(EC),x+3)'], textCDL:['Equal(LengthOfLine(BE),... | 310 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, AB=x, BC=5, DE=x-4, FE=3, ∠ABC=∠FED, ∠CAB=∠EDF. Find DE. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDL... | consCDL:['Shape(AB,BC,CA)', 'Shape(DF,FE,ED)'], imgCDL:['Equal(LengthOfLine(AB),x)', 'Equal(LengthOfLine(BC),5)', 'Equal(LengthOfLine(DE),x-4)', 'Equal(LengthOfLine(FE),3)', 'Equal(MeasureOfAngle(ABC),MeasureOfAngle(FED))', 'Equal(MeasureOfAngle(CAB),MeasureOfAngle(EDF))'], textCDL:['Equal(LengthOfLine(AB),x)', 'Equal(... | 312 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, AC=x, BA=7, BC=19, BA⊥CA. 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. You first think within <think></think> tags and then provide all CDLs within <... | consCDL:['Shape(BA,AC,CB)'], imgCDL:['Equal(LengthOfLine(AC),x)', 'Equal(LengthOfLine(BA),7)', 'Equal(LengthOfLine(BC),19)', 'PerpendicularBetweenLine(BA,CA)'], textCDL:['Equal(LengthOfLine(AC),x)', 'Equal(LengthOfLine(BA),7)', 'Equal(LengthOfLine(BC),19)', 'PerpendicularBetweenLine(BA,CA)']. | 313 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, RP=y+4, RS=27, TP=2*y-5, TQ=5*x, ∠PQT=95°, ∠RQP=33°, ∠TSP=3*z°, QTSR is a parallelogram. 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. You first think... | consCDL:['Shape(QT,TP,PQ)', 'Shape(PT,TS,SP)', 'Shape(QP,PR,RQ)', 'Shape(RP,PS,SR)', 'Collinear(QPS)', 'Collinear(TPR)'], imgCDL:['Equal(LengthOfLine(RP),y+4)', 'Equal(LengthOfLine(RS),27)', 'Equal(LengthOfLine(TP),2*y-5)', 'Equal(LengthOfLine(TQ),5*x)', 'Equal(MeasureOfAngle(PQT),95)', 'Equal(MeasureOfAngle(RQP),33)',... | 314 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, EN=3, triangle DCB is an equilateral triangle, the center of circle N is N, N is the centroid of triangle DCB, N is the incenter of △DCB, the tangent to ⊙N is BG, CF is the tangent to circle N, DE is the tangent to ⊙N. Find the area of △DCB minus ... | consCDL:['Shape(NQG,NGE,EN,NQ)', 'Shape(NEF,NFQ,QN,NE)', 'Shape(NGE,GD,DE)', 'Shape(NEF,EC,CF)', 'Shape(NFQ,FB,BQ)', 'Shape(NQG,QB,BG)', 'Collinear(ENQB)', 'Collinear(DGB)', 'Collinear(CFB)', 'Collinear(DEC)', 'Cocircular(N,GEFQ)'], imgCDL:['Equal(LengthOfLine(EN),3)'], textCDL:['Equal(LengthOfLine(EN),3)', 'Equilatera... | 315 | |
<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. You ... | 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)', 'Perpendicu... | 316 | |
<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. You first think... | 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... | 317 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, AE=x+7, BE=4, EC=9, EF=x, the center of ⊙D is D. 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. You first think within <think></think> tags and then pr... | consCDL:['Shape(DAC,CE,EA)', 'Shape(DCB,BE,EC)', 'Shape(DBF,FE,EB)', 'Shape(DFA,AE,EF)', 'Collinear(AEB)', 'Collinear(CEF)', 'Cocircular(D,ACBF)'], imgCDL:['Equal(LengthOfLine(AE),x+7)', 'Equal(LengthOfLine(BE),4)', 'Equal(LengthOfLine(EC),9)', 'Equal(LengthOfLine(EF),x)'], textCDL:['Equal(LengthOfLine(AE),x+7)', 'Equa... | 319 | |
<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. You first think within <think></think> tags and th... | 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)', 'Perpen... | 322 | |
<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. You first think within <think>... | 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 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, NM=39, PM=36, PN=15, MP⊥NP. Find the value of Cos(NMP). Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs... | consCDL:['Shape(PN,NM,MP)'], imgCDL:['Equal(LengthOfLine(NM),39)', 'Equal(LengthOfLine(PM),36)', 'Equal(LengthOfLine(PN),15)', 'PerpendicularBetweenLine(MP,NP)'], textCDL:['Equal(LengthOfLine(NM),39)', 'Equal(LengthOfLine(PM),36)', 'Equal(LengthOfLine(PN),15)', 'PerpendicularBetweenLine(MP,NP)']. | 326 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, AE=2, BE=x, DE=4, EC=5, X is the center of circle 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. You first think within <think></think> tags and the... | consCDL:['Shape(XAD,DE,EA)', 'Shape(XDB,BE,ED)', 'Shape(XBC,CE,EB)', 'Shape(XCA,AE,EC)', 'Collinear(AEB)', 'Collinear(DEC)', 'Cocircular(X,CADB)'], imgCDL:['Equal(LengthOfLine(AE),2)', 'Equal(LengthOfLine(BE),x)', 'Equal(LengthOfLine(DE),4)', 'Equal(LengthOfLine(EC),5)'], textCDL:['Equal(LengthOfLine(AE),2)', 'Equal(Le... | 327 | |
<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. You first think within <think></think> tags and then provide all CDLs within <CDL></C... | consCDL:['Shape(LD,DA)', 'Shape(AD,DI)', 'Shape(BI,ID)', 'Shape(BI,IC)', 'Shape(LD,DO)', 'Shape(CI,IF)', 'Shape(IF,FJ)', 'Shape(HO,OD)', 'Shape(EO,OF)', 'Shape(HO,OE)', 'Shape(OF,FK)', 'Shape(JF,FK)', 'Shape(DI,IF,FO,OD)', 'Collinear(LDIC)', 'Collinear(HOFJ)', 'Collinear(ADOE)', 'Collinear(BIFK)'], imgCDL:['Equal(Measu... | 329 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, DC=DA, ∠ACD=66°, ∠DBA=24°. Find the measure of ∠DAC. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs wi... | consCDL:['Shape(DB,BA,AD)', 'Shape(CD,DA,AC)', 'Collinear(BDC)'], imgCDL:['Equal(LengthOfLine(DC),LengthOfLine(DA))', 'Equal(MeasureOfAngle(ACD),66)', 'Equal(MeasureOfAngle(DBA),24)'], textCDL:['Equal(LengthOfLine(DC),LengthOfLine(DA))', 'Equal(MeasureOfAngle(ACD),66)', 'Equal(MeasureOfAngle(DBA),24)']. | 330 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, SR=5, ST=4, TR=3, ST⊥RT. Find the value of Tan(SRT). Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs wi... | consCDL:['Shape(TS,SR,RT)'], imgCDL:['Equal(LengthOfLine(SR),5)', 'Equal(LengthOfLine(ST),4)', 'Equal(LengthOfLine(TR),3)', 'PerpendicularBetweenLine(ST,RT)'], textCDL:['Equal(LengthOfLine(SR),5)', 'Equal(LengthOfLine(ST),4)', 'Equal(LengthOfLine(TR),3)', 'PerpendicularBetweenLine(ST,RT)']. | 333 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, CE=24, DE=24, EA=12, EB=x, the center of ⊙F is F. Find the length of line AB. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and... | consCDL:['Shape(FAD,DE,EA)', 'Shape(FCA,AE,EC)', 'Shape(FDB,BF,FE,ED)', 'Shape(FBC,CE,EF,FB)', 'Collinear(DEC)', 'Collinear(AEFB)', 'Cocircular(F,ADBC)'], imgCDL:['Equal(LengthOfLine(CE),24)', 'Equal(LengthOfLine(DE),24)', 'Equal(LengthOfLine(EA),12)', 'Equal(LengthOfLine(EB),x)'], textCDL:['Equal(LengthOfLine(CE),24)'... | 335 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, RS=x, RT=y+3, TS=49, VU=21, WU=29, WV=20, ∠RST=∠UWV, ∠STR=∠WVU, ∠TRS=∠VUW. 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. You first think within <think... | consCDL:['Shape(RS,ST,TR)', 'Shape(UW,WV,VU)'], imgCDL:['Equal(LengthOfLine(RS),x)', 'Equal(LengthOfLine(RT),y+3)', 'Equal(LengthOfLine(TS),49)', 'Equal(LengthOfLine(VU),21)', 'Equal(LengthOfLine(WU),29)', 'Equal(LengthOfLine(WV),20)', 'Equal(MeasureOfAngle(RST),MeasureOfAngle(UWV))', 'Equal(MeasureOfAngle(STR),Measure... | 336 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, BD=7, FE=6, OE=9, quadrilateral FBOD is a kite. Find the area of FBOD. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then p... | consCDL:['Shape(FB,BE,EF)', 'Shape(FE,ED,DF)', 'Shape(BO,OE,EB)', 'Shape(EO,OD,DE)', 'Collinear(FEO)', 'Collinear(BED)'], imgCDL:['Equal(LengthOfLine(BD),7)', 'Equal(LengthOfLine(FE),6)', 'Equal(LengthOfLine(OE),9)'], textCDL:['Equal(LengthOfLine(BD),7)', 'Equal(LengthOfLine(FE),6)', 'Equal(LengthOfLine(OE),9)', 'Kite(... | 338 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠KGL=x°, ∠AJH=47°, ∠ALK=116°, A is the center of circle 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. You first think within <think></think> tags a... | consCDL:['Shape(LG,GH,AHL)', 'Shape(HG,GJ,AJH)', 'Shape(KG,GL,ALK)', 'Shape(JG,GK,AKJ)', 'Collinear(LGJ)', 'Collinear(HGK)', 'Cocircular(A,HLKJ)'], imgCDL:['Equal(MeasureOfAngle(KGL),x)', 'Equal(MeasureOfArc(AJH),47)', 'Equal(MeasureOfArc(ALK),116)'], textCDL:['Equal(MeasureOfAngle(KGL),x)', 'Equal(MeasureOfArc(AJH),47... | 339 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, AZ=y, QZ=z, RQ=12, RS=10, RZ=x, ∠AQR=30°, ∠SPA=45°, SR∥AZ, PA is perpendicular to SA, RZ is perpendicular to QZ. Find the value of y. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its ... | consCDL:['Shape(SP,PA,AS)', 'Shape(SA,AZ,ZR,RS)', 'Shape(RZ,ZQ,QR)', 'Collinear(PAZQ)'], imgCDL:['Equal(LengthOfLine(AZ),y)', 'Equal(LengthOfLine(QZ),z)', 'Equal(LengthOfLine(RQ),12)', 'Equal(LengthOfLine(RS),10)', 'Equal(LengthOfLine(RZ),x)', 'Equal(MeasureOfAngle(AQR),30)', 'Equal(MeasureOfAngle(SPA),45)', 'ParallelB... | 341 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, AC=x-3, BA=2*x-7, BC=4*x-15, triangleABC is an isosceles triangle. Prove that triangle ABC is an equilateral triangle. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You fi... | consCDL:['Shape(AB,BC,CA)'], imgCDL:['Equal(LengthOfLine(AC),x-3)', 'Equal(LengthOfLine(BA),2*x-7)', 'Equal(LengthOfLine(BC),4*x-15)'], textCDL:['Equal(LengthOfLine(AC),x-3)', 'Equal(LengthOfLine(BA),2*x-7)', 'Equal(LengthOfLine(BC),4*x-15)', 'IsoscelesTriangle(ABC)']. | 342 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, BC=z, BX=6*x, CA=y, CX=36, XA=x, AC is perpendicular to BC, BX is perpendicular to CX. 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. You first think w... | consCDL:['Shape(CB,BX,XC)', 'Shape(CX,XA,AC)', 'Collinear(BXA)'], imgCDL:['Equal(LengthOfLine(BC),z)', 'Equal(LengthOfLine(BX),6*x)', 'Equal(LengthOfLine(CA),y)', 'Equal(LengthOfLine(CX),36)', 'Equal(LengthOfLine(XA),x)', 'PerpendicularBetweenLine(AC,BC)', 'PerpendicularBetweenLine(BX,CX)'], textCDL:['Equal(LengthOfLin... | 343 | |
<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. You first think within <thin... | 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(Measur... | 344 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠EAB=40°, AB⊥DB, quadrilateral ABDC is a rectangle. Find the measure of ∠DEB. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and... | consCDL:['Shape(AE,EC,CA)', 'Shape(BE,EA,AB)', 'Shape(EB,BD,DE)', 'Shape(CE,ED,DC)', 'Collinear(AED)', 'Collinear(BEC)'], imgCDL:['Equal(MeasureOfAngle(EAB),40)', 'PerpendicularBetweenLine(AB,DB)'], textCDL:['Equal(MeasureOfAngle(EAB),40)', 'PerpendicularBetweenLine(AB,DB)', 'Rectangle(ABDC)']. | 345 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, AB=x, BC=y, CA=14, ∠CAB=30°, AB⊥CB. 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. You first think within <think></think> tags and then provide all CDL... | consCDL:['Shape(CA,AB,BC)'], imgCDL:['Equal(LengthOfLine(AB),x)', 'Equal(LengthOfLine(BC),y)', 'Equal(LengthOfLine(CA),14)', 'Equal(MeasureOfAngle(CAB),30)', 'PerpendicularBetweenLine(AB,CB)'], textCDL:['Equal(LengthOfLine(AB),x)', 'Equal(LengthOfLine(BC),y)', 'Equal(LengthOfLine(CA),14)', 'Equal(MeasureOfAngle(CAB),30... | 347 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠BCF=120°, ∠DBC=5*y°, ∠DFE=108°, ∠FDB=2*x°, BD is parallel to CE. 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. You first think within <think></think>... | consCDL:['Shape(BC,CF,FD,DB)', 'Shape(DF,FE)', 'Collinear(CFE)'], imgCDL:['Equal(MeasureOfAngle(BCF),120)', 'Equal(MeasureOfAngle(DBC),5*y)', 'Equal(MeasureOfAngle(DFE),108)', 'Equal(MeasureOfAngle(FDB),2*x)', 'ParallelBetweenLine(BD,CE)'], textCDL:['Equal(MeasureOfAngle(BCF),120)', 'Equal(MeasureOfAngle(DBC),5*y)', 'E... | 348 | |
<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 p... | 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(E... | 349 | |
<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. You first think within <think></think> tags and then provide all CDLs wi... | 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),Measure... | 351 | |
<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. P... | 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)', 'Collinear(GKA)', 'Collinear(GEF)', 'Collinear(FND)', 'Collinear(AHD)', 'Collinear(EOH)', 'Cocircular(O,KENH)'], imgCDL:['Equal(LengthOfLine(FD),25)', 'PerpendicularBetweenLine(EF,NF)... | 353 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, AC=x, AD=8, CB=y, DB=25, DC=z, AC is perpendicular to BC, BD is perpendicular to CD. 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. You first think wit... | consCDL:['Shape(AC,CD,DA)', 'Shape(DC,CB,BD)', 'Collinear(ADB)'], imgCDL:['Equal(LengthOfLine(AC),x)', 'Equal(LengthOfLine(AD),8)', 'Equal(LengthOfLine(CB),y)', 'Equal(LengthOfLine(DB),25)', 'Equal(LengthOfLine(DC),z)', 'PerpendicularBetweenLine(AC,BC)', 'PerpendicularBetweenLine(BD,CD)'], textCDL:['Equal(LengthOfLine(... | 354 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠BCJ=105°, ∠CIE=x°, ∠KEF=125°, BD is parallel to FH. 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. You first think within <think></think> tags and the... | consCDL:['Shape(BC,CJ)', 'Shape(JC,CD)', 'Shape(EI,IC)', 'Shape(FE,EI)', 'Shape(IE,EH)', 'Shape(KE,EF)', 'Shape(HE,EK)', 'Shape(IC,CB)', 'Shape(DC,CI)', 'Collinear(BCD)', 'Collinear(JCI)', 'Collinear(IEK)', 'Collinear(FEH)'], imgCDL:['Equal(MeasureOfAngle(BCJ),105)', 'Equal(MeasureOfAngle(CIE),x)', 'Equal(MeasureOfAngl... | 355 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, AB=26, AC=24, CB=10, BC is perpendicular to AC. Find the value of Sin(ABC). Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and t... | consCDL:['Shape(CA,AB,BC)'], imgCDL:['Equal(LengthOfLine(AB),26)', 'Equal(LengthOfLine(AC),24)', 'Equal(LengthOfLine(CB),10)', 'PerpendicularBetweenLine(BC,AC)'], textCDL:['Equal(LengthOfLine(AB),26)', 'Equal(LengthOfLine(AC),24)', 'Equal(LengthOfLine(CB),10)', 'PerpendicularBetweenLine(BC,AC)']. | 356 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, BA=h, CA=3, ∠BAC=45°, AC is perpendicular to BC. Find the value of h. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then pr... | consCDL:['Shape(CB,BA,AC)'], imgCDL:['Equal(LengthOfLine(BA),h)', 'Equal(LengthOfLine(CA),3)', 'Equal(MeasureOfAngle(BAC),45)', 'PerpendicularBetweenLine(AC,BC)'], textCDL:['Equal(LengthOfLine(BA),h)', 'Equal(LengthOfLine(CA),3)', 'Equal(MeasureOfAngle(BAC),45)', 'PerpendicularBetweenLine(AC,BC)']. | 358 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, AB=2, AE=x-1, CD=5, ED=x+5, BA is parallel to DC. Find the length of line AE. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and... | consCDL:['Shape(AB,BE,EA)', 'Shape(ED,DC,CE)', 'Collinear(BEC)', 'Collinear(AED)'], imgCDL:['Equal(LengthOfLine(AB),2)', 'Equal(LengthOfLine(AE),x-1)', 'Equal(LengthOfLine(CD),5)', 'Equal(LengthOfLine(ED),x+5)', 'ParallelBetweenLine(BA,DC)'], textCDL:['Equal(LengthOfLine(AB),2)', 'Equal(LengthOfLine(AE),x-1)', 'Equal(L... | 359 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, AB=26, AC=24, CB=10, BC⊥AC. Find the value of Tan(ABC). Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs... | consCDL:['Shape(CA,AB,BC)'], imgCDL:['Equal(LengthOfLine(AB),26)', 'Equal(LengthOfLine(AC),24)', 'Equal(LengthOfLine(CB),10)', 'PerpendicularBetweenLine(BC,AC)'], textCDL:['Equal(LengthOfLine(AB),26)', 'Equal(LengthOfLine(AC),24)', 'Equal(LengthOfLine(CB),10)', 'PerpendicularBetweenLine(BC,AC)']. | 360 | |
<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 captio... | 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... | 361 | |
<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. You first think within <think></think> t... | 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)', '... | 362 | |
<image>The Caption of this geometric diagram is: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°, RM and PN are opposite sides of the ▱ MRPN. Find the measure of ∠RQM. Please provide the consCDL and imgCDL based on this given geometric diagram and pro... | consCDL:['Shape(MQ,QN,NM)', 'Shape(MR,RQ,QM)', 'Shape(QR,RP,PQ)', 'Shape(QP,PN,NQ)', 'Collinear(MQP)', 'Collinear(RQN)'], imgCDL:['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)'... | 363 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, AG=1/5*x+3, CJ=2*y+1, CJ=JE, EG=4*x-35, JE=5*y-8, AC∥GJ. 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. You first think within <think></think> tags and... | consCDL:['Shape(AG,GJ,JC,CA)', 'Shape(GE,EJ,JG)', 'Collinear(AGE)', 'Collinear(EJC)'], imgCDL:['Equal(LengthOfLine(AG),1/5*x+3)', 'Equal(LengthOfLine(CJ),2*y+1)', 'Equal(LengthOfLine(CJ),LengthOfLine(JE))', 'Equal(LengthOfLine(EG),4*x-35)', 'Equal(LengthOfLine(JE),5*y-8)', 'ParallelBetweenLine(AC,GJ)'], textCDL:['Equal... | 364 | |
<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. You first think within <think></think> ... | 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(... | 365 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, AC=20, BA=48, BC=x, CA⊥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. You first think within <think></think> tags and then provide all CDLs within ... | consCDL:['Shape(BC,CA,AB)'], imgCDL:['Equal(LengthOfLine(AC),20)', 'Equal(LengthOfLine(BA),48)', 'Equal(LengthOfLine(BC),x)', 'PerpendicularBetweenLine(CA,BA)'], textCDL:['Equal(LengthOfLine(AC),20)', 'Equal(LengthOfLine(BA),48)', 'Equal(LengthOfLine(BC),x)', 'PerpendicularBetweenLine(CA,BA)']. | 366 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, BA=18, BC=x, ∠BAC=45°, AC is perpendicular to BC. 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. You first think within <think></think> tags and then p... | consCDL:['Shape(BA,AC,CB)'], imgCDL:['Equal(LengthOfLine(BA),18)', 'Equal(LengthOfLine(BC),x)', 'Equal(MeasureOfAngle(BAC),45)', 'PerpendicularBetweenLine(AC,BC)'], textCDL:['Equal(LengthOfLine(BA),18)', 'Equal(LengthOfLine(BC),x)', 'Equal(MeasureOfAngle(BAC),45)', 'PerpendicularBetweenLine(AC,BC)']. | 367 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, JM=MK, ∠JLM=6*x+8°, ∠MLK=9*x-4°, LK⊥MK, MJ is perpendicular to LJ. Find ∠MLK. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and... | consCDL:['Shape(JL,LM,MJ)', 'Shape(ML,LK,KM)'], imgCDL:['Equal(LengthOfLine(JM),LengthOfLine(MK))', 'Equal(MeasureOfAngle(JLM),6*x+8)', 'Equal(MeasureOfAngle(MLK),9*x-4)', 'PerpendicularBetweenLine(LK,MK)', 'PerpendicularBetweenLine(MJ,LJ)'], textCDL:['Equal(LengthOfLine(JM),LengthOfLine(MK))', 'Equal(MeasureOfAngle(JL... | 368 | |
<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. You first think within <think></think> tags and then pro... | 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(L... | 369 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, WY=6*x+3, WY=XY, XW=9*x, XW=WY, XY=4*x+5. Prove that triangle XWY is an equilateral triangle. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think><... | consCDL:['Shape(XW,WY,YX)'], imgCDL:['Equal(LengthOfLine(WY),6*x+3)', 'Equal(LengthOfLine(WY),LengthOfLine(XY))', 'Equal(LengthOfLine(XW),9*x)', 'Equal(LengthOfLine(XW),LengthOfLine(WY))', 'Equal(LengthOfLine(XY),4*x+5)'], textCDL:['Equal(LengthOfLine(WY),6*x+3)', 'Equal(LengthOfLine(WY),LengthOfLine(XY))', 'Equal(Leng... | 370 | |
<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. You first think within <think><... | 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(LengthOfLi... | 371 | |
<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. You first think within <th... | 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... | 372 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, BA=5, CB=8, CD=12, NE=5, BA is perpendicular to DA, NE is perpendicular to BE. Find the sum of the area of triangle NCB and the area of triangle BCD. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textC... | consCDL:['Shape(NE,EB,BN)', 'Shape(NC,CE,EN)', 'Shape(BC,CA,AB)', 'Shape(BA,AD,DB)', 'Collinear(CEB)', 'Collinear(CAD)'], imgCDL:['Equal(LengthOfLine(BA),5)', 'Equal(LengthOfLine(CB),8)', 'Equal(LengthOfLine(CD),12)', 'Equal(LengthOfLine(NE),5)', 'PerpendicularBetweenLine(BA,DA)', 'PerpendicularBetweenLine(NE,BE)'], te... | 374 | |
<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. You first think within <think></think> tags and the... | 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(Leng... | 376 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, BA=c, BC=a, BE=x, CA=b, EA=y, ∠CAE=30°, ∠EBC=60°, x=7*sqrt(3), AE is perpendicular to CE, BC is perpendicular to AC. Find the value of y. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on ... | consCDL:['Shape(BC,CE,EB)', 'Shape(EC,CA,AE)', 'Collinear(BEA)'], imgCDL:['Equal(LengthOfLine(BA),c)', 'Equal(LengthOfLine(BC),a)', 'Equal(LengthOfLine(BE),x)', 'Equal(LengthOfLine(CA),b)', 'Equal(LengthOfLine(EA),y)', 'Equal(MeasureOfAngle(CAE),30)', 'Equal(MeasureOfAngle(EBC),60)', 'PerpendicularBetweenLine(AE,CE)', ... | 379 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, AB=26, AD=10, CB=16, DC=8, AD is the altitude of triangle ACB. Find the area of △ACB. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> ... | consCDL:['Shape(AD,DC,CA)', 'Shape(AC,CB,BA)', 'Collinear(DCB)'], imgCDL:['Equal(LengthOfLine(AB),26)', 'Equal(LengthOfLine(AD),10)', 'Equal(LengthOfLine(CB),16)', 'Equal(LengthOfLine(DC),8)'], textCDL:['Equal(LengthOfLine(AB),26)', 'Equal(LengthOfLine(AD),10)', 'Equal(LengthOfLine(CB),16)', 'Equal(LengthOfLine(DC),8)'... | 380 | |
<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. You first think within <think></think> tags and then prov... | 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)', 'ParallelBe... | 381 | |
<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. You first think within <think></think> tags and then provide all CD... | 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)', 'PerpendicularBe... | 383 | |
<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. You first think within <think></think> tags and then pro... | 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(LengthOfL... | 384 | |
<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 geo... | 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... | 385 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, AP=3*y+11, HP=7*y-5, ∠HWQ=4*x-16°, ∠HWX=x+12°, ∠QAP=3*x-2°, WX bisects ∠HWQ, WP is the median of triangle WAH. Find the length of line HA. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on... | consCDL:['Shape(HW,WX,XH)', 'Shape(HX,XP,PH)', 'Shape(XW,WQ,QX)', 'Shape(PX,XQ,QA,AP)', 'Collinear(HXQ)', 'Collinear(WXP)', 'Collinear(HPA)', 'Collinear(WQA)'], imgCDL:['Equal(LengthOfLine(AP),3*y+11)', 'Equal(LengthOfLine(HP),7*y-5)', 'Equal(MeasureOfAngle(HWQ),4*x-16)', 'Equal(MeasureOfAngle(HWX),x+12)', 'Equal(Measu... | 386 | |
<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. You first think within <think></think> tags and then prov... | consCDL:['Shape(KD,DL)', 'Shape(LD,DH)', 'Shape(DH,HI)', 'Shape(IH,HC)', 'Shape(AD,DK)', 'Shape(CH,HG)', 'Shape(EA,AD)', 'Shape(DA,AG,GH,HD)', '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(Measu... | 387 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, AC=13, CD=6, DB=29, CD⊥AD. Find the area of △ADB. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs withi... | consCDL:['Shape(AC,CD,DA)', 'Shape(AD,DB,BA)', 'Collinear(CDB)'], imgCDL:['Equal(LengthOfLine(AC),13)', 'Equal(LengthOfLine(CD),6)', 'Equal(LengthOfLine(DB),29)', 'PerpendicularBetweenLine(CD,AD)'], textCDL:['Equal(LengthOfLine(AC),13)', 'Equal(LengthOfLine(CD),6)', 'Equal(LengthOfLine(DB),29)', 'PerpendicularBetweenLi... | 388 | |
<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. You first think within <think></think> tags and then provid... | 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),... | 390 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, GK=14, MF=8, arc FKG=142°, F is the center of circle F, HI⊥KI. Find the measure of arc FMK. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></t... | consCDL:['Shape(GI,IH,FHG)', 'Shape(HI,IK,FKH)', 'Shape(FI,IG,GF)', 'Shape(MF,FG,FGM)', 'Shape(IF,FK,KI)', 'Shape(KF,FM,FMK)', 'Collinear(GIK)', 'Collinear(MFIH)', 'Cocircular(F,GMKH)'], imgCDL:['Equal(LengthOfLine(GK),14)', 'Equal(LengthOfLine(MF),8)', 'Equal(MeasureOfArc(FKG),142)', 'PerpendicularBetweenLine(HI,KI)']... | 392 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, AB=2*sqrt(3), AY=x, YC=y, ∠BAY=30°, ∠YCB=60°, AY is perpendicular to BY, CB⊥AB. 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. You first think within <... | consCDL:['Shape(AY,YB,BA)', 'Shape(BY,YC,CB)', 'Collinear(AYC)'], imgCDL:['Equal(LengthOfLine(AB),2*sqrt(3))', 'Equal(LengthOfLine(AY),x)', 'Equal(LengthOfLine(YC),y)', 'Equal(MeasureOfAngle(BAY),30)', 'Equal(MeasureOfAngle(YCB),60)', 'PerpendicularBetweenLine(AY,BY)', 'PerpendicularBetweenLine(CB,AB)'], textCDL:['Equa... | 393 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, AB=x+1, CD=x-1, FE=8, HG=5, ∠ADC=∠EHG, ∠BAD=∠FEH, ∠CBA=∠GFE, ∠DCB=∠HGF, quadrilateral BADC is similar to quadrilateral FEHG. Find the length of line CD. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the te... | consCDL:['Shape(BA,AD,DC,CB)', 'Shape(EH,HG,GF,FE)'], imgCDL:['Equal(LengthOfLine(AB),x+1)', 'Equal(LengthOfLine(CD),x-1)', 'Equal(LengthOfLine(FE),8)', 'Equal(LengthOfLine(HG),5)', 'Equal(MeasureOfAngle(ADC),MeasureOfAngle(EHG))', 'Equal(MeasureOfAngle(BAD),MeasureOfAngle(FEH))', 'Equal(MeasureOfAngle(CBA),MeasureOfAn... | 394 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, KJ=11, KL=11, ML=5.5, ∠KJM=60°, KM is perpendicular to LM. Find the measure of ∠LKJ. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> t... | consCDL:['Shape(KJ,JM,MK)', 'Shape(KM,ML,LK)', 'Collinear(JML)'], imgCDL:['Equal(LengthOfLine(KJ),11)', 'Equal(LengthOfLine(KL),11)', 'Equal(LengthOfLine(ML),5.5)', 'Equal(MeasureOfAngle(KJM),60)', 'PerpendicularBetweenLine(KM,LM)'], textCDL:['Equal(LengthOfLine(KJ),11)', 'Equal(LengthOfLine(KL),11)', 'Equal(LengthOfLi... | 396 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, PQ=UQ, ∠QPU=32°. Find ∠PUQ. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags. | consCDL:['Shape(RQ,QS,SR)', 'Shape(QP,PU,UQ)', 'Shape(QU,US,SQ)', 'Shape(SU,UT,TS)', 'Collinear(RQP)', 'Collinear(RST)', 'Collinear(PUT)'], imgCDL:['Equal(LengthOfLine(PQ),LengthOfLine(UQ))', 'Equal(MeasureOfAngle(QPU),32)'], textCDL:['Equal(LengthOfLine(PQ),LengthOfLine(UQ))', 'Equal(MeasureOfAngle(QPU),32)']. | 400 | |
<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. You first think within <think></think... | 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)',... | 402 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, AC=12, BA=13, BC=15. Find the measure of ∠ACB. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <... | consCDL:['Shape(BA,AC,CB)'], imgCDL:['Equal(LengthOfLine(AC),12)', 'Equal(LengthOfLine(BA),13)', 'Equal(LengthOfLine(BC),15)'], textCDL:['Equal(LengthOfLine(AC),12)', 'Equal(LengthOfLine(BA),13)', 'Equal(LengthOfLine(BC),15)']. | 403 | |
<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. You first think within <think></think> tags and then provid... | 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)', 'ParallelB... | 404 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, CA=10, CD=2, CE=t-2, EB=t+1, AB∥DE. Find the value of t. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDL... | consCDL:['Shape(AD,DE,EB,BA)', 'Shape(DC,CE,ED)', 'Collinear(ADC)', 'Collinear(CEB)'], imgCDL:['Equal(LengthOfLine(CA),10)', 'Equal(LengthOfLine(CD),2)', 'Equal(LengthOfLine(CE),t-2)', 'Equal(LengthOfLine(EB),t+1)', 'ParallelBetweenLine(AB,DE)'], textCDL:['Equal(LengthOfLine(CA),10)', 'Equal(LengthOfLine(CD),2)', 'Equa... | 406 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, AC=CB, AD=DC, ∠ADC=92°. Find ∠DCA. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> t... | consCDL:['Shape(AD,DC,CA)', 'Shape(AC,CB,BA)', 'Collinear(DCB)'], imgCDL:['Equal(LengthOfLine(AC),LengthOfLine(CB))', 'Equal(LengthOfLine(AD),LengthOfLine(DC))', 'Equal(MeasureOfAngle(ADC),92)'], textCDL:['Equal(LengthOfLine(AC),LengthOfLine(CB))', 'Equal(LengthOfLine(AD),LengthOfLine(DC))', 'Equal(MeasureOfAngle(ADC),... | 407 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, arc 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. You first think within <think></think> tags an... | consCDL:['Shape(QS,DSQ)', 'Shape(SQ,DQS)', 'Shape(RQ,QS)', 'Cocircular(D,SQ)'], imgCDL:['Equal(MeasureOfArc(DQS),238)'], textCDL:['Equal(MeasureOfArc(DQS),238)', 'IsCentreOfCircle(D,D)', 'IsTangentOfCircle(RQ,D)']. | 408 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, AC=5, BA=12, CB=x, ∠BAC=60°. 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. You first think within <think></think> tags and then provide all CDLs withi... | consCDL:['Shape(CB,BA,AC)'], imgCDL:['Equal(LengthOfLine(AC),5)', 'Equal(LengthOfLine(BA),12)', 'Equal(LengthOfLine(CB),x)', 'Equal(MeasureOfAngle(BAC),60)'], textCDL:['Equal(LengthOfLine(AC),5)', 'Equal(LengthOfLine(BA),12)', 'Equal(LengthOfLine(CB),x)', 'Equal(MeasureOfAngle(BAC),60)']. | 409 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, BA=y, BF=x, FA=z, LA=sqrt(3), LF=2*sqrt(3), FB is perpendicular to AB, LA⊥FA. 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. You first think within <th... | consCDL:['Shape(FB,BA,AF)', 'Shape(BL,LA,AB)', 'Collinear(LBF)'], imgCDL:['Equal(LengthOfLine(BA),y)', 'Equal(LengthOfLine(BF),x)', 'Equal(LengthOfLine(FA),z)', 'Equal(LengthOfLine(LA),sqrt(3))', 'Equal(LengthOfLine(LF),2*sqrt(3))', 'PerpendicularBetweenLine(FB,AB)', 'PerpendicularBetweenLine(LA,FA)'], textCDL:['Equal(... | 410 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠POM=43°, FB is parallel to QM, KC∥GJ. Find the measure of ∠BPO. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide... | consCDL:['Shape(KP,PB)', 'Shape(BP,PO)', 'Shape(PO,OM)', 'Shape(MO,OC)', 'Shape(KP,PH)', 'Shape(GH,HP)', 'Shape(PH,HN,NO,OP)', 'Shape(CO,ON)', 'Shape(ON,NJ)', 'Shape(FH,HG)', 'Shape(NH,HF)', 'Shape(QN,NH)', 'Shape(JN,NQ)', 'Collinear(KPOC)', 'Collinear(GHNJ)', 'Collinear(BPHF)', 'Collinear(MONQ)'], imgCDL:['Equal(Measu... | 412 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, YX=24, ZY=28, ∠XWZ=105°, WX and ZY are opposite sides of the ▱ WZYX. Find WZ. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and... | consCDL:['Shape(WZ,ZY,YX,XW)'], imgCDL:['Equal(LengthOfLine(YX),24)', 'Equal(LengthOfLine(ZY),28)', 'Equal(MeasureOfAngle(XWZ),105)'], textCDL:['Equal(LengthOfLine(YX),24)', 'Equal(LengthOfLine(ZY),28)', 'Equal(MeasureOfAngle(XWZ),105)', 'Parallelogram(WZYX)']. | 413 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, BC=4*x-17, DF=2*x-1, ∠CBF=3*y+5°, ∠DFB=5*y-13°, BDFC is a parallelogram. 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. You first think within <think><... | consCDL:['Shape(BD,DF,FB)', 'Shape(FC,CB,BF)'], imgCDL:['Equal(LengthOfLine(BC),4*x-17)', 'Equal(LengthOfLine(DF),2*x-1)', 'Equal(MeasureOfAngle(CBF),3*y+5)', 'Equal(MeasureOfAngle(DFB),5*y-13)'], textCDL:['Equal(LengthOfLine(BC),4*x-17)', 'Equal(LengthOfLine(DF),2*x-1)', 'Equal(MeasureOfAngle(CBF),3*y+5)', 'Equal(Meas... | 414 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, AC=21, AD=17, DE=8, BCAD is a parallelogram, CA is perpendicular to EA, DE is perpendicular to AE. Find the area of quadrilateral BCAD. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on it... | consCDL:['Shape(BC,CA,AE,EB)', 'Shape(EA,AD,DE)', 'Collinear(BED)'], imgCDL:['Equal(LengthOfLine(AC),21)', 'Equal(LengthOfLine(AD),17)', 'Equal(LengthOfLine(DE),8)', 'PerpendicularBetweenLine(CA,EA)', 'PerpendicularBetweenLine(DE,AE)'], textCDL:['Equal(LengthOfLine(AC),21)', 'Equal(LengthOfLine(AD),17)', 'Equal(LengthO... | 415 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, AN=21, BL=6, BN=18, SC=4, BL⊥NL, SC is perpendicular to NC. Find the sum of the area of triangle SBN and Area(△NBA). Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You firs... | consCDL:['Shape(BA,AL,LB)', 'Shape(BL,LN,NB)', 'Shape(SB,BC,CS)', 'Shape(SC,CN,NS)', 'Collinear(ALN)', 'Collinear(BCN)'], imgCDL:['Equal(LengthOfLine(AN),21)', 'Equal(LengthOfLine(BL),6)', 'Equal(LengthOfLine(BN),18)', 'Equal(LengthOfLine(SC),4)', 'PerpendicularBetweenLine(BL,NL)', 'PerpendicularBetweenLine(SC,NC)'], t... | 418 | |
<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 ... | 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)', 'Eq... | 419 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, AB=3, the center of ⊙B is B. Find the circumference of the ⊙B. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide a... | consCDL:['Shape(BA)', 'Cocircular(B,A)'], imgCDL:['Equal(LengthOfLine(AB),3)'], textCDL:['Equal(LengthOfLine(AB),3)', 'IsCentreOfCircle(B,B)']. | 421 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, AC=x, BA=18, ∠ABC=25°, CA⊥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. You first think within <think></think> tags and then provide all CDLs with... | consCDL:['Shape(AB,BC,CA)'], imgCDL:['Equal(LengthOfLine(AC),x)', 'Equal(LengthOfLine(BA),18)', 'Equal(MeasureOfAngle(ABC),25)', 'PerpendicularBetweenLine(CA,BA)'], textCDL:['Equal(LengthOfLine(AC),x)', 'Equal(LengthOfLine(BA),18)', 'Equal(MeasureOfAngle(ABC),25)', 'PerpendicularBetweenLine(CA,BA)']. | 422 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, EH=9, HG=15, ∠EHD=45°, quadrilateral EHGF is a ▱, ED is perpendicular to GD. Find the area of quadrilateral EHGF. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first t... | consCDL:['Shape(EH,HD,DE)', 'Shape(ED,DG,GF,FE)', 'Collinear(HDG)'], imgCDL:['Equal(LengthOfLine(EH),9)', 'Equal(LengthOfLine(HG),15)', 'Equal(MeasureOfAngle(EHD),45)', 'PerpendicularBetweenLine(ED,GD)'], textCDL:['Equal(LengthOfLine(EH),9)', 'Equal(LengthOfLine(HG),15)', 'Equal(MeasureOfAngle(EHD),45)', 'Parallelogram... | 423 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠ADG=36°, ∠AGF=104°, ∠EFC=40°, AB is perpendicular to CB. Find ∠BCF. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then pro... | consCDL:['Shape(AD,DG,GA)', 'Shape(FG,GB,BF)', 'Shape(FB,BC,CF)', 'Shape(AG,GF)', 'Shape(EF,FC)', 'Shape(BG,GD)', 'Shape(EF,FG)', 'Collinear(DGFC)', 'Collinear(AGB)', 'Collinear(BFE)'], imgCDL:['Equal(MeasureOfAngle(ADG),36)', 'Equal(MeasureOfAngle(AGF),104)', 'Equal(MeasureOfAngle(EFC),40)', 'PerpendicularBetweenLine(... | 424 | |
<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. You first think within <think></think> tags and then provide all CDLs w... | 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)', 'Parallel... | 425 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠BEC=2*x°, ∠BFA=3*x-15°, ∠ECB=y**2°, ∠FAE=68°, BE is parallel to FA. 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. You first think within <think></thi... | consCDL:['Shape(FA,AE,EB,BF)', 'Shape(BE,EC,CB)', 'Collinear(FBC)', 'Collinear(AEC)'], imgCDL:['Equal(MeasureOfAngle(BEC),2*x)', 'Equal(MeasureOfAngle(BFA),3*x-15)', 'Equal(MeasureOfAngle(ECB),y**2)', 'Equal(MeasureOfAngle(FAE),68)', 'ParallelBetweenLine(BE,FA)'], textCDL:['Equal(MeasureOfAngle(BEC),2*x)', 'Equal(Measu... | 426 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, the sum of the circumferences of circles A, J, and H is 42*pi, CJ=2*x, HA=x, HC=x, KA=4*x, H is the center of ⊙H, the center of ⊙J is J, K is the center of circle K. Find the length of line KJ. Please provide the consCDL and imgCDL based on this g... | consCDL:['Shape(KA,KAB,BK)', 'Shape(AK,KB,KBA)', 'Shape(KBA,JBC,HCA)', 'Shape(CH,HA,HAC)', 'Shape(HC,HCA,AH)', 'Shape(BJ,JC,JCB)', 'Shape(CJ,JB,JBC)', 'Collinear(KAH)', 'Collinear(HCJ)', 'Collinear(KBJ)', 'Cocircular(K,BA)', 'Cocircular(J,CB)', 'Cocircular(H,AC)'], imgCDL:['Equal(LengthOfLine(CJ),2*x)', 'Equal(LengthOf... | 429 |
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