images images listlengths 1 1 | caption stringlengths 215 580 | cdl stringlengths 116 1.18k | proID stringlengths 1 4 | question stringlengths 8 110 | answer stringclasses 724
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<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. | 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 | Find the value of x. | sqrt(202-198*cos(7*pi/45)) | |
<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. | 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 | Find the value of y. | 4 | |
<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. | 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 | 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 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 | 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. | 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 | Find PS. | 27/2 | |
<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. | 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 | Find the length of line AX. | 5 | |
<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 | Find the value of x. | 5 | |
<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. | 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 | Find the measure of ⌒CFE. | 52 | |
<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. | 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 | Find the value of x. | 7*sqrt(3) | |
<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. | 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 | |
<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. | 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 | Find the length of line AB. | 29 | |
<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. | 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 | Find the value of x. | 1/2 | |
<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. | 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 | Find DE. | 6 | |
<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. | 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 | Find the value of x. | 2*sqrt(78) | |
<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. | 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 | Find the value of x. | 27/5 | |
<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 | Find the area of △DCB minus the area of the ⊙N. | -9*pi+27*sqrt(3) | |
<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. | 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 | Find the value of y. | 4*sqrt(3) | |
<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. | 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 | Find DE. | 24 | |
<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. | 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 | Find the value of x. | 28/5 | |
<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. | 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 | 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. | 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, 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. | 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 | Find the value of Cos(NMP). | 12/13 | |
<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. | consCDL:['Shape(XAD,DE,EA)', 'Shape(XDB,BX,XE,ED)', 'Shape(XBC,CE,EX,XB)', '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)', 'Eq... | 327 | Find the value of x. | 10 | |
<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. | 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(MeasureOfAngl... | 329 | Find ∠IFJ. | 62 | |
<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. | 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 | Find the measure of ∠DAC. | 66 | |
<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. | 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 | Find the value of Tan(SRT). | 4/3 | |
<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. | 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 | Find the length of line AB. | 60 | |
<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. | 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 | Find the value of x. | 1421/20 | |
<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. | 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 | Find the area of FBOD. | 105/2 | |
<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. | consCDL:['Shape(LG,GH,AHL)', 'Shape(HG,GJ,AJH)', 'Shape(KG,GL,ALK)', 'Shape(JG,GK,KJ)', '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 | Find the value of x. | 163/2 | |
<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 | Find the value of y. | 10 | |
<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. | 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 | Find the value of y. | 6*sqrt(42) | |
<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. | 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 | Find the value of y. | 40 | |
<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. | 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 | Find the measure of ∠DEB. | 80 | |
<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. | 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 | Find the value of x. | 7*sqrt(3) | |
<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. | consCDL:['Shape(BC,CF,FD,DB)', '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)', 'Equal(MeasureOfAn... | 348 | Find the value of y. | 12 | |
<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 | 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. | 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 | 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. 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)', 'Shape(OHK,OKE,OEN,ONH)', 'Collinear(GKA)', 'Collinear(GEF)', 'Collinear(FND)', 'Collinear(AHD)', 'Collinear(EOH)', 'Cocircular(O,KENH)'], imgCDL:['Equal(LengthOfLine(FD),25)', 'Perpe... | 353 | Find the circumference of the ⊙O. | 25*pi | |
<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. | 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 | Find the value of x. | 2*sqrt(66) | |
<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. | consCDL:['Shape(BC,CJ)', 'Shape(JC,CD)', 'Shape(CI,IE,EC)', 'Shape(EI,IC)', 'Shape(FE,EI)', 'Shape(CE,EH)', 'Shape(KE,EF)', 'Shape(HE,EK)', 'Shape(IC,CB)', 'Shape(DC,CE)', 'Collinear(BCD)', 'Collinear(JCI)', 'Collinear(IEK)', 'Collinear(FEH)'], imgCDL:['Equal(MeasureOfAngle(BCJ),105)', 'Equal(MeasureOfAngle(CIE),x)', '... | 355 | Find the value of x. | 130 | |
<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. | 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 | Find the value of Sin(ABC). | 12/13 | |
<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. | 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 | Find the value of h. | 3*sqrt(2) | |
<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. | 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 | Find the length of line AE. | 4 | |
<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. | 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 | Find the value of Tan(ABC). | 12/5 | |
<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 | 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. | 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 | Find the value of x. | 10 | |
<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 | Find the measure of ∠RQM. | 83 | |
<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. | 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 | 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. | 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 | Find the value of z. | 25 | |
<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. | 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 | Find the value of x. | 52 | |
<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. | 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 | Find the value of x. | 9*sqrt(2) | |
<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. | 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 | Find ∠MLK. | 32 | |
<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. | 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 | 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. | 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 | 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. | 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 | Find the perimeter of AGFE. | 183/4 | |
<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 | Find the sum of the area of triangle NCB and the area of triangle BCD. | 50 | |
<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. | 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 | Find the value of x. | 5 | |
<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 | Find the value of y. | 21*sqrt(3) | |
<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. | 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 | Find the area of △ACB. | 80 | |
<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. | 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 | 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. | 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 | 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. | 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 | 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 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 | Find the length of line FB. | 5 | |
<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 | Find the length of line HA. | 46 | |
<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. | 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)'... | 387 | Find the measure of ∠EAD. | 84 | |
<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. | 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 | Find the area of △ADB. | 29*sqrt(133)/2 | |
<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. | 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 | Find AP. | 9 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, GK=14, MF=8, ∠FKG=142°, F is the center of circle F, HJ⊥KJ. 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. | consCDL:['Shape(GJ,JH,FHG)', 'Shape(HJ,JK,FKH)', 'Shape(FJ,JG,GF)', 'Shape(MF,FG,FGM)', 'Shape(JF,FK,KJ)', 'Shape(KF,FM,FMK)', 'Collinear(GJK)', 'Collinear(MFJH)', 'Cocircular(F,GMKH)'], imgCDL:['Equal(LengthOfLine(GK),14)', 'Equal(LengthOfLine(MF),8)', 'Equal(MeasureOfArc(FKG),142)', 'PerpendicularBetweenLine(HJ,KJ)']... | 392 | Find the measure of arc FMK. | 109 | |
<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. | 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 | Find the value of x. | 3 | |
<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 | Find the length of line CD. | 10/3 | |
<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. | 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 | Find the measure of ∠LKJ. | 60 | |
<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. | 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 | Find ∠PUQ. | 32 | |
<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)',... | 402 | Find the value of x. | 72 | |
<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. | 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 | Find the measure of ∠ACB. | 180*acos(5/9)/pi | |
<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)', 'ParallelB... | 404 | Find the measure of ∠STC. | 49 | |
<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. | 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 | Find the value of t. | 3 | |
<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. | 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 | Find ∠DCA. | 44 | |
<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, 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. | 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 | Find the value of x. | sqrt(109) | |
<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. | 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 | Find the value of x. | 3*sqrt(3)/2 | |
<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. | 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 | Find the measure of ∠BPO. | 137 | |
<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. | 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 | Find WZ. | 24 | |
<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. | 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 | Find the value of y. | 9 | |
<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 | Find the area of quadrilateral BCAD. | 315 | |
<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. | 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 | Find the sum of the area of triangle SBN and Area(△NBA). | 99 | |
<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 | Find the value of x. | 3/2 | |
<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. | consCDL:['Shape(BA)', 'Cocircular(B,A)'], imgCDL:['Equal(LengthOfLine(AB),3)'], textCDL:['Equal(LengthOfLine(AB),3)', 'IsCentreOfCircle(B,B)']. | 421 | Find the circumference of the ⊙B. | 6*pi | |
<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. | 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 | Find the value of x. | 18*tan(5*pi/36) | |
<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. | 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 | Find the area of quadrilateral EHGF. | 135*sqrt(2)/2 | |
<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. | consCDL:['Shape(AD,DG,GA)', 'Shape(FG,GB,BF)', 'Shape(FB,BC,CF)', 'Shape(AG,GF)', 'Shape(EF,FC)', 'Shape(BG,GD)', 'Collinear(DGFC)', 'Collinear(AGB)', 'Collinear(BFE)'], imgCDL:['Equal(MeasureOfAngle(ADG),36)', 'Equal(MeasureOfAngle(AGF),104)', 'Equal(MeasureOfAngle(EFC),40)', 'PerpendicularBetweenLine(AB,CB)'], textCD... | 424 | Find ∠BCF. | 14 | |
<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)', 'Parallel... | 425 | Find the length of line SQ. | 8 | |
<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. | 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 | Find the value of x. | 34 | |
<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 | Find the length of line KJ. | 24 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠CBA=17°, ∠DCA=29°, AD⊥CD. Find the measure of ∠BAC. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. | consCDL:['Shape(AD,DC,CA)', 'Shape(AC,CB,BA)', 'Collinear(DCB)'], imgCDL:['Equal(MeasureOfAngle(CBA),17)', 'Equal(MeasureOfAngle(DCA),29)', 'PerpendicularBetweenLine(AD,CD)'], textCDL:['Equal(MeasureOfAngle(CBA),17)', 'Equal(MeasureOfAngle(DCA),29)', 'PerpendicularBetweenLine(AD,CD)']. | 430 | Find the measure of ∠BAC. | 12 | |
<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:... | 431 | Find the length of line AR. | 8 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, AB=15, AC=9, BC=12, BC⊥AC. Find Perimeter(△ABC). 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)'], imgCDL:['Equal(LengthOfLine(AB),15)', 'Equal(LengthOfLine(AC),9)', 'Equal(LengthOfLine(BC),12)', 'PerpendicularBetweenLine(BC,AC)'], textCDL:['Equal(LengthOfLine(AB),15)', 'Equal(LengthOfLine(AC),9)', 'Equal(LengthOfLine(BC),12)', 'PerpendicularBetweenLine(BC,AC)']. | 432 | Find Perimeter(△ABC). | 36 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠AFC=70°, ∠EBF=35°, AD⊥ED, EB⊥CB. Find ∠FEB. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. | consCDL:['Shape(DE,EF,FA,AD)', 'Shape(EB,BF,FE)', 'Shape(FB,BC,CF)', 'Shape(AF,FC)', 'Collinear(DEB)', 'Collinear(AFB)', 'Collinear(EFC)'], imgCDL:['Equal(MeasureOfAngle(AFC),70)', 'Equal(MeasureOfAngle(EBF),35)', 'PerpendicularBetweenLine(AD,ED)', 'PerpendicularBetweenLine(EB,CB)'], textCDL:['Equal(MeasureOfAngle(AFC)... | 433 | Find ∠FEB. | 75 | |
<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)'], tex... | 434 | Find the value of x. | 14 | |
<image>The Caption of this geometric diagram is:As shown in the diagram, BA=6, DA=9, DC=7, ∠BAF=32°, ∠CBF=40°, ∠FAD=20°, quadrilateral ADCB is a ▱. Find ∠BDC. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. | consCDL:['Shape(AD,DF,FA)', 'Shape(FD,DC,CF)', 'Shape(FC,CB,BF)', 'Shape(FB,BA,AF)', 'Collinear(DFB)', 'Collinear(AFC)'], imgCDL:['Equal(LengthOfLine(BA),6)', 'Equal(LengthOfLine(DA),9)', 'Equal(LengthOfLine(DC),7)', 'Equal(MeasureOfAngle(BAF),32)', 'Equal(MeasureOfAngle(CBF),40)', 'Equal(MeasureOfAngle(FAD),20)'], tex... | 436 | Find ∠BDC. | 88 |
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