Datasets:
dle666
/
GeoFocus-test

Dataset card Data Studio Files
xet
 Community
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problem
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answer
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<image>As shown in the diagram, AD=2AB, AE=3, CE bisects ∠BCD, AD and BC are opposite sides of the ▱ ABCD. Find the length of line AB.
3
6516
[ "3", "441.5", "60.61", "465.18" ]
A
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<image>As shown in the diagram, QR=x+3, QT=2*x-6, RS=7, TS=7, TS⊥QS. Find the length of line TQ.
12
2770
[ "12", "5.3", "329.24", "147.44" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAADHpklEQVR4nOzdd3wU1f7/8TMzu5teSC9IFQQREAVRRMR2EVARLIAovYgi0jskhN6LekUCiBRBsCFiQ1DBAqIiUmyASCc9QOruzPz+OD/y5aogJcmWeT3/uA9vEjYnm+zO533mfM5RTNMUAAAAAKxBdfcAAAAAAJQfAgAAAABgIQQAAAAAwEIIAAAAAICFEAAAAAAACyEAAAAAABZCAAAAAAAshAAAAAAAWAgBAAAAALAQAgAAAABgIQQAAAAA...
<image>As shown in the diagram, AD/AE=4, AD is the median of △ ABC, HD∥FB. Find the ratio of the length of line AF to the length of line AC.
1/7
5092
[ "1/7", "371.73", "424.11", "204.79" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAADxHUlEQVR4nOzdd3wVVfo/8DMzt6UXSE8ILQkQQkInvVBFRUWxYUXBtvZde1t0seyyVkRAREVd3UVFFhstHQIhCQTSQxrppPdbZub3x/Pl/rI0KYGb3Pm8//AFMQkn905mnuec5zyHk2WZAQAAAACAMvCWHgAAAAAAAFw5SAAAAAAAABQECQAAAAAAgIIgAQAAAAAAUBAkAAAAAAAACoIEAAAAAABAQZAAAAAAAAAoCBIAAAAAAAAFQQIAAAAA...
<image>As shown in the diagram, AB=AC, ∠ABC=70°, the center of ⊙O is O. Find the measure of ∠CAB.
40
6876
[ "40", "347.85", "299.03", "4.61" ]
A
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<image>As shown in the diagram, ∠DAB=110°, ABCD is a parallelogram. Find the measure of ∠DCE.
70
6833
[ "70", "128.63", "4.44", "60.07" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAACcWUlEQVR4nOzdZ3wUVfvw8TMzu+mE0HtHpIQu0nvvIQEsiAoiduWmSG8iASkq9lssqIBKCCR0pASQKkV6770nQPruzjwvzsP+c6cRQvr8vi/4JJvZ3ZlNlr2uc67rHMUwDAEAAADAHNTsPgEAAAAAWYcEAAAAADAREgAAAADAREgAAAAAABMhAQAAAABMhAQAAAAAMBESAAAAAMBESAAAAAAAEyEBAAAAAEyEBAAAAAAwERIAAAAAwERIAAAA...
<image>As shown in the diagram, AB=4, AD=2, OA=2, OB=2, ∠BPA=90°, PO is the median of △ PAB, quadrilateral ADCB is a rectangle. Find the length of line DP.
2+2*sqrt(2)
6307
[ "2+2*sqrt(2)", "470.61", "12.55", "323.53" ]
A
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<image>As shown in the diagram, AC=14, AD=15, DB=10, BD⊥AD, DA⊥CA, quadrilateral DACB is a trapezoid. Find the area of DACB.
180
2779
[ "180", "443.11", "171.71", "172.46" ]
A
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<image>As shown in the diagram, ∠DHK=120°, ∠IKH=54°, ∠JKI=36°, JI is parallel to KH. Find the measure of ∠KIJ.
54
796
[ "54", "325.87", "469.44", "213.55" ]
A
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<image>As shown in the diagram, AE=3, BA=2, CB=6, ED=2*x-3, EB∥DC. Find the value of x.
6
2407
[ "6", "162.38", "443.22", "128.23" ]
A
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<image>As shown in the diagram, the diameter of circle O is 2, ∠CAO=30°, O is the center of ⊙O, AB is the diameter of ⊙O, the tangent to ⊙O is DC. Find the length of line CD.
sqrt(3)
4808
[ "sqrt(3)", "307.67", "332.81", "133.44" ]
A
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<image>As shown in the diagram, ∠ABD=125°, ∠CBA=x°, ∠DBC=155°, the center of circle B is B. Find the value of x.
80
1073
[ "80", "44.92", "185.07", "458.1" ]
A
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<image>As shown in the diagram, CB/AC=2/3, AC=12, D bisects segment AC, E is the midpoint of segment AB. Find the length of line DE.
4
5097
[ "4", "494.24", "242.33", "87.57" ]
A
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<image>As shown in the diagram, ∠ENB=30°, MG is the angle bisector of ∠NMD, AB∥CD. Find the measure of ∠NMG.
15
3035
[ "15", "69.85", "115.12", "10.61" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAADYU0lEQVR4nOzdZ3wUV572/VMdlCWUESByEGByzhY5CEVwIKdx2PHe88x47A2znt2d4N175p7ZnbDrhI3JwQZFgkDknDHB5CAyEkI5tbq76nlxlt42QQiQ1C3V7/uCj9SqbpVE69T/OnWCommaAAAAAKAPBlefAAAAAID6QwAAAAAAdIQAAAAAAOgIAQAAAADQEQIAAAAAoCMEAAAAAEBHCAAAAACAjhAAAAAAAB0hAAAAAAA6QgAAAAAAdIQA...
<image>As shown in the diagram, AE=BE, BC=BE, ∠CDA=105°, AD and BC are opposite sides of the ▱ ABCD. Find the measure of ∠CAB.
25
6815
[ "25", "171.17", "491.69", "208.78" ]
A
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<image>As shown in the diagram, OA=OB, OA=OC, ∠ADC=70°, ∠CBA=70°. Find the sum of the measure of ∠OAD and the measure of ∠DCO.
150
5394
[ "150", "423.54", "170.63", "135.93" ]
A
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<image>As shown in the diagram, the length of arc SRT is 8, ∠TSR=70°, S is the center of ⊙S. Find the circumference of the circle S.
288/7
306
[ "288/7", "91.35", "363.62", "386.13" ]
A
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<image>As shown in the diagram, ∠ECD=25°, ∠FEA=∠DEC, ABCD is a rectangle. Find the measure of ∠FEA.
65
3508
[ "65", "464.61", "202.64", "143.39" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAAB/uElEQVR4nO3dZ1wU1/v//5nZXZpi773FaGyxt5imKXZNMcnHrmCJXSyoscaKBbsgYDcaNWqq0VR7SaJGY4+9F6wgZXdm/jfOz/nzRUWiyALn9bzhA9llmcWVPe9zrnMu1TRNBQAAAIAcNHdfAAAAAIDUQwAAAAAAJEIAAAAAACRCAAAAAAAkQgAAAAAAJEIAAAAAACRCAAAAAAAkQgAAAAAAJEIAAAAAACRCAAAAAAAkQgAAAAAAJEIAAAAA...
<image>As shown in the diagram, ∠EDA=46°, AB is parallel to ED, DC is perpendicular to BC. Find the measure of ∠CBA.
44
2903
[ "44", "7.34", "134.62", "330.63" ]
A
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<image>As shown in the diagram, ∠FCD=100°, CD∥AB. Find the measure of ∠AEC.
80
3614
[ "80", "189.9", "384.42", "398.17" ]
A
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<image>As shown in the diagram, AD=3*x+11, BD=5*x-8, BD=AD, BE=2*y-1, CE=4*y-7, CA∥ED. Find the value of y.
3
2562
[ "3", "202.97", "238.97", "286.0" ]
A
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<image>As shown in the diagram, ∠CAB=30°, the radius of ⊙O is 2, the center of circle O is O. Find the length of line BC.
2
4594
[ "2", "6.22", "76.86", "4.96" ]
A
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<image>As shown in the diagram, GH=x+9, GK=x+5, JH=5*x-2, FJHG is a rhombus. Find the length of line KH.
sqrt(78)
2339
[ "sqrt(78)", "316.75", "331.22", "201.43" ]
A
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<image>As shown in the diagram, ∠CAB=30°, O is the center of ⊙O, the diameter of circle O is AB. Find the measure of ∠ADC.
60
3395
[ "60", "279.37", "239.5", "481.62" ]
A
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<image>As shown in the diagram, ∠COB=70°, O is the center of circle O, AB is the diameter of ⊙O, DM⊥OM. Find the measure of ∠BAD.
35
6687
[ "35", "72.64", "227.24", "290.72" ]
A
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<image>As shown in the diagram, CB=20, EC=24, ∠CAE=37°, quadrilateral ACBD is a ▱, AE⊥CE. Find the area of quadrilateral ACBD.
480
121
[ "480", "462.61", "387.39", "337.86" ]
A
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<image>As shown in the diagram, AB=9, BC=6, D bisects segment CB, NA and ND are one pair of adjacent sides of the kite MAND. Find the perimeter of triangle DNB.
12
3479
[ "12", "214.82", "39.26", "229.12" ]
A
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<image>As shown in the diagram, ∠COA=60°, the center of circle O is O, the diameter of ⊙O is AB, D bisects ⌒OCB. Find the measure of ∠BAD.
30
6986
[ "30", "303.82", "300.11", "75.28" ]
A
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<image>As shown in the diagram, AD=90, ∠BAD=30°, ∠DAC=60°, AD⊥BD, CD is perpendicular to AD. Find the length of line BC.
120*sqrt(3)
5925
[ "120*sqrt(3)", "467.37", "245.4", "253.17" ]
A
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<image>As shown in the diagram, the perimeter of triangle ABC is 1, D is the midpoint of segment AB, E bisects segment AC, F bisects segment BC, X bisects segment DE, Y is the midpoint of segment DF, Z is the midpoint of segment EF. Find the perimeter of triangle XYZ.
1/4
5499
[ "1/4", "396.22", "467.25", "60.65" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAACG5UlEQVR4nO3dZ3xVVdr//7X3PicFElroIF06VkCqIOoISADBARtVAQm9RUf/cw/F320hFEkAUUHpKlJCG3RUpAaxjIp0UJSS0ARCes7e+/9gDec+k1ACJKetz/vBvODkEDZjkn19176utTTbtgUAAAAANei+vgAAAAAA3kMAAAAAABRCAAAAAAAUQgAAAAAAFEIAAAAAABRCAAAAAAAUQgAAAAAAFEIAAAAAABRCAAAAAAAUQgAAAAAAFEIA...
<image>As shown in the diagram, BA=y, BC=z, DA=x, DB=8, ∠BAC=45°, ∠BDA=60°, AC is perpendicular to BC, DA is perpendicular to BA. Find the value of y.
4*sqrt(3)
520
[ "4*sqrt(3)", "368.98", "25.96", "487.64" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAAEAAElEQVR4nOzdd1wU1/c38Dszu8vSkS5YsGAXFMWIXZNoNEWNJZpm78beEVCwx9hrYjeWGI2xRY2JvVdUsGJFkN7r7s7M88f5ug8/WyzALruf9x95EVyWYWHvnHPvOfdysiwzAAAAAAAwD7yhLwAAAAAAAIoPEgAAAAAAADOCBAAAAAAAwIwgAQAAAAAAMCNIAAAAAAAAzAgSAAAAAAAAM4IEAAAAAADAjCABAAAAAAAwI0gAAAAAAADMCBIA...
<image>As shown in the diagram, ∠BDC=40°, O is the center of ⊙O, the diameter of circle O is AC. Find the measure of ∠ACB.
50
6667
[ "50", "214.98", "97.84", "24.85" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAADNcklEQVR4nOzdd3wVVf7/8Zm5N5VUQIFgWUogAbGBroAivYv6VVoISUgvKIrYy+66ruvPFamBENIhiPSi9N7ERgsgTRLABiEJqaTcmfn9cb7MN4uUAKn3vp5/+JBw783ckJl73mc+53xkXdclAAAAALZBqesDAAAAAFB7CAAAAACADSEAAAAAADaEAAAAAADYEAIAAAAAYEMIAAAAAIANIQAAAAAANoQAAAAAANgQAgAAAABgQwgAAAAAgA0h...
<image>As shown in the diagram, GF=HG, HJ=JF, ∠FJH=72°, ∠HGF=128°, JF and JH are one pair of adjacent sides of the kite GFJH. Find the measure of ∠GFJ.
80
2797
[ "80", "122.7", "33.77", "111.36" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAADOzUlEQVR4nOzdd3xUVfo/8HPvnT6ZTHqAUELovaqIIE2RphQBpYn0JkVcdW27+l3L6qorLl06KL2ISpeiCNJ776QQSJsk02fuvb8/nuX+ZkMIARKSzP28/+AVksnMzUxgns85zzmHk2WZAQAAAACAOvAlfQEAAAAAAPDoIAAAAAAAAKgIAgAAAAAAgIogAAAAAAAAqAgCAAAAAACAiiAAAAAAAACoCAIAAAAAAICKIAAAAAAAAKgIAgAAAAAA...
<image>As shown in the diagram, ∠AOB=48°, the center of ⊙O is O, AE⊥BE, BE is perpendicular to OE, CE is perpendicular to AE. Find the measure of ∠CDA.
24
4321
[ "24", "65.04", "94.47", "184.88" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAAEAAElEQVR4nOzdd1xT1/8/8HNzkxD2BmU4UHGgVsWqiLMuLC7UjxNZglqr1qq1tba2WutHrXXWOpmOulfVuooTxT1wowiIKLIEMiDJvff3x/maXz52uCAB8nr+4aPVkBwguff9Pud93ocRBIEAAAAAAIBpEBl7AAAAAAAAYDhIAAAAAAAATAgSAAAAAAAAE4IEAAAAAADAhCABAAAAAAAwIUgAAAAAAABMCBIAAAAAAAATggQAAAAAAMCEIAEA...
<image>As shown in the diagram, ∠ABD=20°, the center of circle O is O, the diameter of ⊙O is DC. Find the measure of ∠CDA.
70
3054
[ "70", "108.22", "195.55", "297.44" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAABRnUlEQVR4nO3deZwcVaEv8KrqnpkQSEgCYQ0QwBAExRBlEX2sKiDwQJArAq4o4HIvKg9EQVG5qCzvKuKC9yEqiguLbArIIiIiCAgYHiibiGxCgEcCEzIz3VXvj/Po13e2TGamZ6o53+8f+fR0V/ecrkydc36nTp1Ki6JIAACAOGSTXQAAAGDiCAAAABARAQAAACIiAAAAQEQEAAAAiIgAAAAAEREAAAAgIgIAAABERAAAAICICAAAABARAQAA...
<image>As shown in the diagram, the area of quadrilateral CEBA is 72, the area of GIHF is 50, EC=12, GI=x, ACEB is similar to FGIH. Find the value of x.
10
1637
[ "10", "471.42", "486.9", "194.02" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAACbjUlEQVR4nOzdZXwUV/vw8Zmd3SQkuDstTnGXQHFKC7TFiyeQYAWKU6cCBYq7JAQtDsUp7m6lpbRI0WCBQEJ8d2fmeXGezD831mDZJPP7vuinTGZ3Z3dnZ851znWuI+u6LgEAAAAwB4urDwAAAABA0iEAAAAAAEyEAAAAAAAwEQIAAAAAwEQIAAAAAAATIQAAAAAATIQAAAAAADARAgAAAADARAgAAAAAABMhAAAAAABMhAAAAAAAMBECAAAA...
<image>As shown in the diagram, AX=6*x, BA=z, BX=36, CB=y, XC=x, △AXB is a right △, triangle CBA is a right triangle. Find the value of z.
36*sqrt(7)
2809
[ "36*sqrt(7)", "78.0", "200.12", "300.17" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAAC88ElEQVR4nOzdZ1wU1/s+/jM72+gIitTYe++9lxiN+SRqYokNBQv2rrEnGrtYULGAJZbEFktiiSVqNPbYFRsqCkiR3rbM7O/B/Xf+fEERYSky1/uBL0R2GWBH7uucc5/DmUwmBgAAAAAA8qAo6AsAAAAAAID8gwAAAAAAACAjCAAAAAAAADKCAAAAAAAAICMIAAAAAAAAMoIAAAAAAAAgIwgAAAAAAAAyggAAAAAAACAjCAAAAAAAADKCAAAA...
<image>As shown in the diagram, ∠CBA=25°, the center of circle O is O, the diameter of circle O is AB. Find the measure of ∠BDC.
65
3375
[ "65", "393.0", "18.39", "27.09" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAADZKElEQVR4nOzdd3xU153//3PvnRl1CUQRIIoQvYMoxnbAGFdwbIMNJsG9UEy1vSWbzS/rfHeT9e46ThzTmw3GJeDe7bg3bIo6Ek303lHXlHvv74/PMqtIQpaEpJnRvJ5/8BDDSFwNYu55n/P5nKPZtq0AAAAAhAc90BcAAAAAoPkQAAAAAIAwQgAAAAAAwggBAAAAAAgjBAAAAAAgjBAAAAAAgDBCAAAAAADCCAEAAAAACCMEAAAAACCMEAAA...
<image>As shown in the diagram, ∠AMP=60°, ∠CAB is the right angle of the isosceles right △ BCA, DEFG is a rectangle. Find the measure of ∠QNP.
75
2978
[ "75", "70.01", "487.79", "448.61" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAACR+ElEQVR4nOzdd5xU5fn///ucM21nG7ACoqiIiFGjWKIJij2aqNEoltgTox87CtKlijTpaKyxRE2MFZVg72KJJUbBAqjYAelsm3bK74/rt+c7mV2WZZndKffr+cc+ZmdnZ8/Mzuxe73Nf930bnucpAAAAAHowc30AAAAAANoPAQAAAADQCAEAAAAA0AgBAAAAANAIAQAAAADQCAEAAAAA0AgBAAAAANAIAQAAAADQCAEAAAAA0AgBAAAAANAI...
<image>As shown in the diagram, AB=4, ME⊥CE, MF⊥DF, NG is perpendicular to CG, NH⊥DH, quadrilateral ABCD is a square. Find the area of triangle ACD.
8
5367
[ "8", "201.88", "306.26", "224.84" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAAB3CklEQVR4nO3dd3wU1f7/8TMzu2kkBAgh9F5E6U3EAgjSg4BeveoVFRtX+CIgRVSK9GrBLiLgtSIIJFQpQmihKhB6EUFKqAmQujszvz/OJT8uISFANrvJeT3/4BF2J5sh7J75vE8bzbZtAQAAAEANurdPAAAAAEDeIQAAAAAACiEAAAAAAAohAAAAAAAKIQAAAAAACiEAAAAAAAohAAAAAAAKIQAAAAAACiEAAAAAAAohAAAAAAAKIQAAAAAA...
<image>As shown in the diagram, AB=3, AD=7, AE is the angle bisector of ∠DAB, AD and BC are opposite sides of the parallelogram ABCD. Find the length of line EC.
4
6389
[ "4", "232.41", "153.56", "188.62" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAACJh0lEQVR4nOzdd3wU1f7/8ZnZkt5IpYTee0eK0kSqggiilEtTVLgiqIDotYBeROwKKqJ0FAVEQUF6772EDkkIkIT0nmx2Zn5/nC/72wtWhOxu5vX8g0fYbMJJ2Nk573M+5xxZ13UJAAAAgDEorm4AAAAAgJJDAAAAAAAMhAAAAAAAGAgBAAAAADAQAgAAAABgIAQAAAAAwEAIAAAAAICBEAAAAAAAAyEAAAAAAAZCAAAAAAAMhAAAAAAAGAgB...
<image>As shown in the diagram, AB=3, the center of ⊙B is B. Find the circumference of the ⊙B.
6*pi
421
[ "6*pi", "55.44", "262.52", "333.02" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAADXSElEQVR4nOzdd1xUV9oH8HPvNHoXBERFFERRsXeNBY0ae0msmGg2JtEY03Y32fS+KZvEGNOMSizRWBI19hJ7jYoFe6FKlc4w5d77/vGs950FRMRpcH/fP/ygwsydYWbO85zzPOdwkiQxAAAAAABQBt7RFwAAAAAAAPaDBAAAAAAAQEGQAAAAAAAAKAgSAAAAAAAABUECAAAAAACgIEgAAAAAAAAUBAkAAAAAAICCIAEAAAAAAFAQJAAAAAAA...
<image>As shown in the diagram, ∠BOC=40°, the center of ⊙O is O, CA is parallel to BO. Find the measure of ∠ABO.
20
4426
[ "20", "415.96", "395.55", "243.72" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAAEAAElEQVR4nOzdd1xT1/8/8JNJEvZGVFBx4MBRJ+5RZ3GvVqsdakWt2mr142ytW1tbte7ZWls3jrpH3aPugQMBQUA2BAiQhIz7++P99f5SVt0E7uv5Bw+E3OQG4d7zOue8zxFxHMcAAAAAAEAYxCV9AgAAAAAA8O4gAAAAAAAACAgCAAAAAACAgCAAAAAAAAAICAIAAAAAAICAIAAAAAAAAAgIAgAAAAAAgIAgAAAAAAAACAgCAAAAAACAgCAA...
<image>As shown in the diagram, ∠BAC=55°, the center of circle O is O, the diameter of circle O is AB. Find the measure of ∠CDA.
35
4563
[ "35", "139.5", "450.64", "258.7" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAADOyElEQVR4nOzdZXxU1/Y38H1kZuJGcHeKQ3GKuzdYcSkBIkiRFqjd/5VCC8USCAkQoLi7tLgW1+DQ4iFYEhJiM3POeV6sm3lyEwiRSUbO7/uCT5iM7DlzMmetvdfem1MUhQEAAAAAgDrwlm4AAAAAAADkHyQAAAAAAAAqggQAAAAAAEBFkAAAAAAAAKgIEgAAAAAAABVBAgAAAAAAoCJIAAAAAAAAVAQJAAAAAACAiiABAAAAAABQESQAAAAA...
<image>As shown in the diagram, AD=2BD, AE=6, DE is parallel to BC. Find the length of line EC.
3
4967
[ "3", "107.08", "411.66", "295.54" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAADL1ElEQVR4nOzdeXicV3nw//M8M6NdsjZrs2TJ2nfNjGQ7TcqaBBJKSppS4IVQ+LG1kAsKlLZsZXsLL0tLL0rLTqFtStgClLC39E1YQizNrl2y9sXWYsmSrHW23x93Pa+JN9nWoxnNfD9/cAV5JD2WNec+9znnvo8WDocVAAAAgMSgR/sBAAAAAOwfEgAAAAAggZAAAAAAAAmEBAAAAABIICQAAAAAQAIhAQAAAAASCAkAAAAAkEBIAAAAAIAE...
<image>As shown in the diagram, ∠BIC=57°, DA is parallel to KB, GC∥LJ. Find the measure of ∠CIF.
123
554
[ "123", "145.61", "426.17", "171.51" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAACJ4klEQVR4nOzdZ3wUVfv/8ZnZ3VR67yAI0gREuiio9KZioxN6Db17K96KSO81hBBAEAQUCxaqClKk916ltwAhbXdn5v/g/Jz/3kkIAdLP5/2A12bZhEnY7J7vOdd1jmqapgIAAABADlpqXwAAAACAlEMAAAAAACRCAAAAAAAkQgAAAAAAJEIAAAAAACRCAAAAAAAkQgAAAAAAJEIAAAAAACRCAAAAAAAkQgAAAAAAJEIAAAAAACRCAAAAAAAk...
<image>As shown in the diagram, ∠EDC=35°, DE∥BC, DA is perpendicular to BA. Find the measure of ∠ABC.
55
2990
[ "55", "158.87", "303.83", "365.43" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAADEu0lEQVR4nOzdZ1wUZ/v//ZnZXUCqiiL2XtEYRcFOsySaRE0xxZJoqrmSmKhBBY29txRNotForGlGE9NEitgRe++9AjY67M7M/eD8y80PE2MBdtn9vB9cryvIyKgwc3zPdsi6rksAAAAAHINi7RsAAAAAUHwIAAAAAIADIQAAAAAADoQAAAAAADgQAgAAAADgQAgAAAAAgAMhAAAAAAAOhAAAAAAAOBACAAAAAOBACAAAAACAAyEAAAAAAA6E...
<image>As shown in the diagram, ∠ABC+∠CDE=∠BCA+∠DEB, AD=3, AE=2, CD=1. Find the length of line BE.
4
5795
[ "4", "186.5", "241.0", "223.86" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAADZAklEQVR4nOzdZ3xU1fo+/LWnpfdKElJI7yEJXar0LggKKoKIFelgL8ejqEdQUIqCysGC9CIepEmVJoT0kIT03nufsp8X95P9n18oBgjJTPb1feEHJ5PJzszOzH2tfa+1OJ7nGQAAAAAAiIOkqw8AAAAAAAA6DwIAAAAAAICIIAAAAAAAAIgIAgAAAAAAgIggAAAAAAAAiAgCAAAAAACAiCAAAAAAAACICAIAAAAAAICIIAAAAAAAAIgIAgAA...
<image>As shown in the diagram, ∠BDO=36°, O is the center of ⊙O, DB is the tangent to circle O. Find the measure of ∠CAB.
27
4846
[ "27", "319.16", "60.52", "219.07" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAAB3RElEQVR4nO3dd3wUxf/H8S13aYQSQpXeRaRKE1GaIr1JCWAvgIJIR/0iIEW6CCiiiILyFRJ6771It9CLgPTQAoHUu939/TFf8ouQhPS73Lyef/AId5vLEO5mP++Z2VnVsiwFAAAAgBw0VzcAAAAAQOYhAAAAAAASIQAAAAAAEiEAAAAAABIhAAAAAAASIQAAAAAAEiEAAAAAABIhAAAAAAASIQAAAAAAEiEAAAAAABIhAAAAAAASIQAAAAAA...
<image>As shown in the diagram, AB=4, CE=3, AE is the angle bisector of ∠DAB, AD and BC are opposite sides of the parallelogram ABCD. Find the perimeter of ABCD.
22
6409
[ "22", "181.42", "288.12", "129.37" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAACaQElEQVR4nOzdZ3wV1dr38TUze2enU01Euoj0Js12FBWBICogKkiRDgqBkEASwHJuhSR0pCZI74KFox6P3ooCgiBKEiAiIFJtRAyQXvbMPC/WzX44CAgYssv8vi/8SBLCUrL3rP9a17qWYpqmAAAAAGANqrsHAAAAAKDsEAAAAAAACyEAAAAAABZCAAAAAAAshAAAAAAAWAgBAAAAALAQAgAAAABgIQQAAAAAwEIIAAAAAICFEAAAAAAACyEA...
<image>As shown in the diagram, AB=y, AD=x, BD=32, BD=BC, ∠ACB=54°, BA is perpendicular to CA. Find the value of x.
8*sqrt(10-2*sqrt(5))
2297
[ "8*sqrt(10-2*sqrt(5))", "316.82", "486.69", "336.27" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAACdMklEQVR4nOzdZ3wU57n38Xt2dtUFCNF7791gusH03otAHRw7J7HjJCduSc6JneLESZw4sWM7dowqiF4sqgEDpjfTezdNgBAg1Hdn53lxP5qzpgihujv7+77wR1qtViOjnbn+d7lG0XVdAAAAAPAOlso+AAAAAAAVhwAAAAAAeBECAAAAAOBFCAAAAACAFyEAAAAAAF6EAAAAAAB4EQIAAAAA4EUIAAAAAIAXIQAAAAAAXoQAAAAAAHgRAgAA...
<image>As shown in the diagram, AB=2, AE=4, BC=1, DE=2, ∠ACB=90°, ∠CDE=90°. Find the value of sin(BA).
1/2
4209
[ "1/2", "469.2", "87.61", "304.14" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAAB1SUlEQVR4nO3dd3wU1f7/8TNbQgihQ5CmIIiXXhSxATaKUqSKSkmjVxEpCoqAFClKC0ggjSICIkWDCMhVkN5UQESK9CadJKTszPz+OF/mtzeBGGqSOa/nHzw2u7ObSdjsnPc5n3OOZpqmAAAAAKAGR2afAAAAAIAHhwAAAAAAKIQAAAAAACiEAAAAAAAohAAAAAAAKIQAAAAAACiEAAAAAAAohAAAAAAAKIQAAAAAACiEAAAAAAAohAAAAAAA...
<image>As shown in the diagram, AB=y, BC=18, CA=x, ∠BCA=60°, CA⊥BA. Find the value of y.
9*sqrt(3)
2126
[ "9*sqrt(3)", "479.92", "113.95", "119.66" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAAEAAElEQVR4nOzdZ1wU1/s28DNbYClLR7qgIgiCvWtMsWvsmpiYWFGx1ySa2E3U2KKosWHBnlhi7CXGHkvsBQQRUSlSpPfdmXle3H/34WeLBdhd5vq+yIcgZdid3bmvM+c+hxNFkQEAAAAAgDTI9H0AAAAAAABQdhAAAAAAAAAkBAEAAAAAAEBCEAAAAAAAACQEAQAAAAAAQEIQAAAAAAAAJAQBAAAAAABAQhAAAAAAAAAkBAEAAAAAAEBCEAAA...
<image>As shown in the diagram, ∠ABC=50°, O is the center of ⊙O, the diameter of ⊙O is CD. Find the measure of ∠DCA.
40
6213
[ "40", "237.89", "309.15", "123.22" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAADC80lEQVR4nOzdZ3xURfv/8TlnN72QkBBCJ4QSuvQiSC8CIgooRaqA3t4oIkgv0ouIBcFO6CjciCA1dGlSQ+8lQCAE0nuyu+f8H8yP/UdECAiknM/7gS8JSTjZPdm9vjPXzCi6rgsAAAAAxqBm9wUAAAAAeH4IAAAAAICBEAAAAAAAAyEAAAAAAAZCAAAAAAAMhAAAAAAAGAgBAAAAADAQAgAAAABgIAQAAAAAwEAIAAAAAICBEAAAAAAAAyEA...
<image>As shown in the diagram, the length of arc OAB is equal to the length of ⌒OBC, ∠BOA=72°, O is the center of ⊙O. Find the measure of ∠OAC.
18
4389
[ "18", "432.12", "403.44", "355.87" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAADNS0lEQVR4nOzdZ1xU1/bw8XPOzFBEmmLs2BEb2AuW2GI0UWPsmtgblsTkxpjEXqPGkuQmWADBLirGWBM1JnYBFVGxodh7RUDaMGeeF/vvPNxEjQUY4Py+L/LBmYFsZWafvdZeZ23ZbDZLAAAAALRBsfYAAAAAAGQfAgAAAABAQwgAAAAAAA0hAAAAAAA0hAAAAAAA0BACAAAAAEBDCAAAAAAADSEAAAAAADSEAAAAAADQEAIAAAAAQEMIAAAA...
<image>As shown in the diagram, AB=3, BC=5, BF bisects ∠ABC, AD and BC are opposite sides of the ▱ ABCD. Find the ratio of the length of line AF to the length of line FC.
3/5
5685
[ "3/5", "480.49", "38.26", "323.91" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAABZsUlEQVR4nO3dd5xU1eH473tnZnfpTezGFuy9Y9doLBhrTD4mGjFoNCFobCi9F3s3xoqxRGMUExUVYxJ7xyiWKFGIihpEAemwU35/nJ/z3SywFGF32fM8f/AaZmdnZ5d1PO97zzk3LZVKCQAAEIdMQ78AAACg/ggAAACIiAAAAICICAAAAIiIAAAAgIgIAAAAiIgAAACAiAgAAACIiAAAAICICAAAAIiIAAAAgIgIAAAAiIgAAACAiAgAAACI...
<image>As shown in the diagram, BA=18, BC=x, ∠BAC=45°, AC⊥BC. Find the value of x.
9*sqrt(2)
367
[ "9*sqrt(2)", "212.11", "50.49", "450.71" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAAEAAElEQVR4nOzdd3yN5/8/8Ose52TvRBKCRMTee+9ZW5S2qFGjlNJSasXWorqMGq1qS7VG7K2KIPaWkAiC7L2Tc859378/3h/nl69VI8lZr+cfHkFOcotzX/f7/b7e13VxiqIwAAAAAACwDLyhLwAAAAAAAEoOEgAAAAAAAAuCBAAAAAAAwIIgAQAAAAAAsCBIAAAAAAAALAgSAAAAAAAAC4IEAAAAAADAgiABAAAAAACwIEgAAAAAAAAsCBIA...
<image>As shown in the diagram, ∠AOC=100°, O is the center of circle O, MO is parallel to BC. Find the measure of ∠AMO.
50
4195
[ "50", "415.72", "100.93", "148.43" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAABVbUlEQVR4nO3deXxdZZ348XOXpHuByt5NBFQERCgtiL6gIigkKYJNmuKCgjJal8EFUZZxY9GBwcroAG0FR1kqwrjQNiyiCA1gS8uAiMoOtqW0lEJbuiS5y++P59frnaRJ0zRtluf9/qtNbsKNpveezznn+zypYrGYAAAAcUj39BMAAAB2HgEAAAAREQAAABARAQAAABERAAAAEBEBAAAAEREAAAAQEQEAAAAREQAAABARAQAAABERAAAAEBEB...
<image>As shown in the diagram, DB=12, ∠DBC=18°, CD is perpendicular to BD. Find the perimeter of triangle BCD.
6*(sqrt(10)+3*sqrt(2)+2*sqrt(sqrt(5)+5))/sqrt(sqrt(5)+5)
1777
[ "6*(sqrt(10)+3*sqrt(2)+2*sqrt(sqrt(5)+5))/sqrt(sqrt(5)+5)", "115.09", "116.73", "8.85" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAAEAAElEQVR4nOzddXxcx9U38LnL0ootZmayyMxsx2zLdtI8wSZNU0raMHOapu3TppCUAm1iyxg7ZmYWM7PFTEv33veP82Rf1aA4Bu2u9vf9Ix9H1q5H2rn3njNzZoYTRZEBAAAAAIB1kJi6AQAAAAAAMHqQAAAAAAAAWBEkAAAAAAAAVgQJAAAAAACAFUECAAAAAABgRZAAAAAAAABYESQAAAAAAABWBAkAAAAAAIAVQQIAAAAAAGBFkAAAAAAA...
<image>As shown in the diagram, ∠CAB=50°, the center of ⊙O is O. Find the measure of ∠COB.
100
4612
[ "100", "71.56", "228.94", "351.34" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAADU20lEQVR4nOzdd1wUV/c/8Dvb6EUQURRFDCr2rigWFBWkiC3GbtqTPEmMBWvsPfaW+iSxtySaiIDYsaEGKzbsXUGK9La7M/P743yd3wYQEenzef/hizK7Ozu7i+fce+65nCiKDAAAAAAA5EFR1icAAAAAAAClBwkAAAAAAICMIAEAAAAAAJARJAAAAAAAADKCBAAAAAAAQEaQAAAAAAAAyAgSAAAAAAAAGUECAAAAAAAgI0gAAAAAAABkBAkA...
<image>As shown in the diagram, VW=3, XV=2*a-2, ZV=(5*a+1)/4, ∠ZYV=53°, quadrilateral XWZY is a rhombus. Find the measure of ∠VZY.
37
823
[ "37", "284.19", "289.57", "330.84" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAAEAAElEQVR4nOzdd3xT9fc4/tfNzd5J003LKhuRPQqobBGUvYeiyBRBtrQVStl7FESEtzJlCAjKUJkyBEGWbEppoZSOtGnT7OTm/v44P+43ny4KdPc8/+Ah9Sa5Kcm957xer/M6FMuyBCGEEEIIIVQx8Er6BBBCCCGEEELFBxMAhBBCCCGEKhBMABBCCCGEEKpAMAFACCGEEEKoAsEEACGEEEIIoQqEX9IngBBCCBUO9gXuJ9QLRfFann8t4Evk...
<image>As shown in the diagram, ∠AZB=104°, ∠ZCB=94°, Z is the center of circle Z, AB is parallel to DC. Find the measure of arc ZAC.
162
1091
[ "162", "316.4", "141.11", "356.19" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAAEAAElEQVR4nOzdd1wU1/o/8DMzu8vSm/Qiauy9K/bYRUUTE01iV5qk3+TmmsRUTb+JMfbeolGxAPbeu6KoKBYsiKhIXxbY3Zn5/fF83R/XNI3Clvm8/8jLIOhx2zyfc55zhpNlmQEAAAAAgDLwlh4AAAAAAABUHQQAAAAAAAAFQQAAAAAAAFAQBAAAAAAAAAVBAAAAAAAAUBAEAAAAAAAABUEAAAAAAABQEAQAAAAAAAAFQQAAAAAAAFAQBAAA...
<image>As shown in the diagram, ∠COB=120°, the center of circle O is O. Find the measure of ∠CAB.
60
3514
[ "60", "193.64", "250.95", "123.9" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAAC2tElEQVR4nOzdd3yUVd7//6vNpJCE3jsiRQGRGjoKGHpvCbgrKroWurqye++99/29d1el2xBFsUEgEHoHg4A0BekgvfcWSvrMdV2/Pz6b+WVpBkgyM5nX8w8eZDKZnEwyc533OZ9zjmrbtgIAAAAgMGjebgAAAACAvEMAAAAAAAIIAQAAAAAIIAQAAAAAIIAQAAAAAIAAQgAAAAAAAggBAAAAAAggBAAAAAAggBAAAAAAgABCAAAAAAACCAEA...
<image>As shown in the diagram, AB=9, AD=3, DE=3, DE is parallel to BC. Find the length of line BC.
9
5773
[ "9", "91.24", "399.79", "450.18" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAADrp0lEQVR4nOzdZ1xU5/Y+/HvvaTD0DtI7KGBXsHc9lpgY/6ZpiqZp1BRN7yfJiUlMjsaoiUaTGNM0Rk2MMXaxIBZUBCnSe69DnbKfF+vnfuZgiQWYgX19X/BBhJkNMzDruvda9+YEQWAAAAAAACANvKkPAAAAAAAAOg8CAAAAAACAhCAAAAAAAABICAIAAAAAAICEIAAAAAAAAEgIAgAAAAAAgIQgAAAAAAAASAgCAAAAAACAhCAAAAAAAABI...
<image>As shown in the diagram, AB=AD, ∠DOC=120°, O is the center of ⊙O, DB is the diameter of ⊙O. Find the measure of ∠BGA.
105
6911
[ "105", "281.25", "407.13", "484.87" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAABzWUlEQVR4nO3deXxV5aHv/2ettQNk2BuCrRX9FYcAgYSE4HSPLzsda3tbZmIiAbRW7bntrQFiJiUk2SE7A21Pr73eSgaSndt5Oq3VemoHgQw7YFtrh1NtbfX0SrIz4UxFsvda6/n98ZR9KGOAJHtYn/cffeHOTlz4avZ6vs/zfZ6lSSkFAAAAAGfQo30BAAAAAKYPAQAAAABwEAIAAAAA4CAEAAAAAMBBCAAAAACAgxAAAAAAAAchAAAAAAAO...
<image>As shown in the diagram, GF=x, HF=32, ∠FHG=29°, GF⊥HF. Find the value of x.
32*tan(29*pi/180)
1506
[ "32*tan(29*pi/180)", "412.06", "198.39", "86.43" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAAD1WUlEQVR4nOzddVxU2f8/8HvvBCkKKCq2roW59rrGGqzdTZciKg0Gdq2BlIWFStm1ayuu3d3diooiHRP33t8f5+v98TFYVGCGua/nHz5wGIbDxLnn/T7xpnmepwAAAAAAQBwYTTcAAAAAAACKDwIAAAAAAAARQQAAAAAAACAiCAAAAAAAAEQEAQAAAAAAgIggAAAAAAAAEBEEAAAAAAAAIoIAAAAAAABARBAAAAAAAACICAIAAAAAAAARQQAA...
<image>As shown in the diagram, ∠DCF=30°, ∠FEA=45°, AE∥DC, AD⊥FD, FA is perpendicular to BA. Find the measure of ∠FAD.
15
3730
[ "15", "157.01", "349.54", "129.33" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAACPjElEQVR4nOzdZ3wUR57/8erumVEmCIkkcpCJJmNEEAJJSCQb25jFGLANmIztTf/13sa7vdvbvdtwu16TbWywccAGY0xSQESRM4gcRBRBIJSlme7+P6hDxxKF0oymP+8HvKTRaFSMRtP1rfpVlWKapgAAAABgDaq7GwAAAACg6hAAAAAAAAshAAAAAAAWQgAAAAAALIQAAAAAAFgIAQAAAACwEAIAAAAAYCEEAAAAAMBCCAAAAACAhRAAAAAA...
<image>As shown in the diagram, AD=5, DB=3, DE=4, DE is parallel to BC. Find the length of line BC.
32/5
5877
[ "32/5", "25.17", "204.85", "320.19" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAADBMUlEQVR4nOzdd1wU1/c38Cm7S+9VRFEBFUXFBgpYEmM39hZ7NNEkGluMJcZoTOwaW4qJvReiMcbeYhfEgooi2LAgvdctM/P8cX7uw9cWC7Dszuf9R14GWPbu7ADn3HvOvawkSQwAAAAAAMgDZ+gBAAAAAABA2UECAAAAAAAgI0gAAAAAAABkBAkAAAAAAICMIAEAAAAAAJARJAAAAAAAADKCBAAAAAAAQEaQAAAAAAAAyAgSAAAAAAAAGUEC...
<image>As shown in the diagram, AB=AD, BT=5, CB=CD, TC=8. Find the length of line CD.
sqrt(89)
867
[ "sqrt(89)", "408.35", "36.76", "339.79" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAACg1ElEQVR4nOzdZXxU1/r28bVH4krwNDRYcChEgASKlbZoKRYoFKeFyjlV2lM9dXfFCUWC0wJFihUnCe5uwSEhEJ/Zez8v1p95crAiSSYz+/d90Q9NJpM1yUxmXWvf91qKrusCAAAAgDGYnD0AAAAAAMWHAAAAAAAYCAEAAAAAMBACAAAAAGAgBAAAAADAQAgAAAAAgIEQAAAAAAADIQAAAAAABkIAAAAAAAyEAAAAAAAYCAEAAAAAMBACAAAA...
<image>As shown in the diagram, AE/AB=1/4, M is the midpoint of segment AC, BE is parallel to CP, EA is parallel to CP. Find the ratio of the length of line BC to the length of line CD.
2
4927
[ "2", "369.65", "159.21", "234.04" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAAD06klEQVR4nOzdd1wUV/s28DMzu0vvoKKCimLvJVGxJLYYS9CoUWOhCfZYEhNjYmJiS2KJEo2KSNFo7CVRI7bYC7bYu4IoIr2XbfP+cf+cdx9sqMCyzPX94/n4EMoAw859nXOfczhRFBkAAAAAAMgDb+wLAAAAAACA0oMAAAAAAAAgIwgAAAAAAAAyggAAAAAAACAjCAAAAAAAADKCAAAAAAAAICMIAAAAAAAAMoIAAAAAAAAgIwgAAAAAAAAy...
<image>As shown in the diagram, ∠OAB=35°, the center of circle O is O, PA is the tangent to ⊙O, PB is the tangent to circle O. Find the measure of ∠APB.
70
3559
[ "70", "188.78", "216.63", "8.11" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAAB0HUlEQVR4nO3dZ2BU1dq38V1mUigBEoJ0kM6LIAjSEUQ9ovSmgAhJIIFQQ68KhISEbmihhYRuOcpjo0nniGKhN0FFagKhhhSSmT37/bAe58lBRMTAJLOu3yeYhLAIk73Xf+11r1s1TVMBAAAAIAfN1QMAAAAA8OQQAAAAAACJEAAAAAAAiRAAAAAAAIkQAAAAAACJEAAAAAAAiRAAAAAAAIkQAAAAAACJEAAAAAAAiRAAAAAAAIkQAAAAAACJ...
<image>As shown in the diagram, AD=21, CD=7, BD⊥CD, CB is perpendicular to AB. Find the length of line BD.
7*sqrt(3)
1300
[ "7*sqrt(3)", "360.14", "482.65", "279.24" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAAEAAElEQVR4nOzdd1wU1/c38Ds7u0vvHbEgKqhgr2ADu4ldY0fB3ls0thhLLKixi71gjV1jV0AsqKjYRVBRQKQovcPuzDx/3K/z8DNqLMAu7Of9R14GF7zszu6cc++55zKCIBAAAAAAANAMElUPAAAAAAAASg4SAAAAAAAADYIEAAAAAABAgyABAAAAAADQIEgAAAAAAAA0CBIAAAAAAAANggQAAAAAAECDIAEAAAAAANAgSAAAAAAAADQIEgAA...
<image>As shown in the diagram, AB=16, OC=6, the center of ⊙O is O, OC⊥AC. Find the radius of ⊙O.
10
5171
[ "10", "417.08", "262.19", "119.55" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAAEAAElEQVR4nOzdd1xUV/o/8HPvnaGJBaVYEWNi7xVF116SrJv8NJaIdCkqiIAFk2w2uxsFjYCCGgtlhqImxjSxb3oxiILdKKhoEqMRBZUBBrj3/v541vtlbbEA0z7vP3zBzDAcYbjzPOc85zmcLMsMAAAAAAAsA2/oAQAAAAAAQMNBAgAAAAAAYEGQAAAAAAAAWBAkAAAAAAAAFgQJAAAAAACABUECAAAAAABgQZAAAAAAAABYECQAAAAAAAAW...
<image>As shown in the diagram, ∠BDA=32°, ∠CAS=125°, ∠CBA=62°. Find the measure of ∠BAC.
55
766
[ "55", "3.3", "499.59", "463.14" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAAC9Q0lEQVR4nOzddVyV5//H8fs+5xASKiAGKnb3rBlTZyuggGC3zphuzprdrZv6nTo7QEQxEEzs7pmzuwsDpDlx//64vp4fX7c5A6n79fxjD4dHvTjc576v9xWfS1YURQIAAACgDprUbgAAAACAlEMAAAAAAFSEAAAAAACoCAEAAAAAUBECAAAAAKAiBAAAAABARQgAAAAAgIoQAAAAAAAVIQAAAAAAKkIAAAAAAFSEAAAAAACoCAEAAAAAUBEC...
<image>As shown in the diagram, the perimeter of triangle CDE is 5, EO perpendicular bisects AC, AD and BC are opposite sides of the parallelogram ABCD. Find the perimeter of quadrilateral ABCD.
10
5425
[ "10", "484.5", "154.09", "89.01" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAAEAAElEQVR4nOzddVxU2fs48BsTNEhJiNgtdosidqyua7sqIiAoiCi2ri2KAQagooKKja6xrg2iWNiJhSiN0h0z997fH8/X++ODsajA1PP+wxcMM8MdnDnnPM95zjkkx3EEQgghhBBCSDVQsr4AhBBCCCGEUPXBAAAhhBBCCCEVggEAQgghhBBCKgQDAIQQQgghhFQIBgAIIYQQQgipEAwAEEIIIYQQUiEYACCEEEIIIaRCMABACCGEEEJIhWAA...
<image>As shown in the diagram, AC=AB, ∠AOC=60°, O is the center of ⊙O. Find the measure of ∠BCA.
30
6043
[ "30", "256.9", "349.57", "412.51" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAAEAAElEQVR4nOzdeVyO2f8/8HPdS/tC0WJrEUnIkiIhSXtkNzPGztjGlmUY+5ixLxkMZuzLzFgraZFQoSwVEVKRpH3fu7fr98f5un/3J8uESnW/nn/Mo8l13fdVbue83+ec9zkMy7IEAAAAAADkA+drPwAAAAAAANQfJAAAAAAAAHIECQAAAAAAgBxBAgAAAAAAIEeQAAAAAAAAyBEkAAAAAAAAcgQJAAAAAACAHEECAAAAAAAgR5AAAAAAAADI...
<image>As shown in the diagram, ∠CAB=110°, the center of circle D is D, the center of the circumscribed circle of quadrilateral ABCD is O. Find the measure of ∠BDC.
140
3221
[ "140", "338.06", "226.95", "352.59" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAADbhUlEQVR4nOzdZ1wUV/s38NmZLfSmdEGxIgoWVEREKWJJ1EQTTTfVdFPVxG4sscYkakzXxDvJbaLGRKMR6QgCiiIqCAIC0ntv2+Z5cd3Ms39QREV3YX/fF35kd2Z2FnZnruuc65wj4nmeAQAAAAAA/cBq+wQAAAAAAODBQQIAAAAAAKBHkAAAAAAAAOgRJAAAAAAAAHoECQAAAAAAgB5BAgAAAAAAoEeQAAAAAAAA6BEkAAAAAAAAegQJAAAA...
<image>As shown in the diagram, ∠CAB=20°, the center of circle O is O, the diameter of circle O is AB. Find the measure of ∠COB.
40
6745
[ "40", "443.76", "276.92", "390.45" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAADizElEQVR4nOzdd1wU1/c38Dszu/SmFGliBbEX7Nh7ib13sSKKNYklvWtM7JRYsHeNscVeotgVBSsqItJBpNfdmXn+uI/z2y8gogK7MJ/3H75wmV0H3J25595zzmVEUSQAAAAAACAPrLZPAAAAAAAAyg4CAAAAAAAAGUEAAAAAAAAgIwgAAAAAAABkBAEAAAAAAICMIAAAAAAAAJARBAAAAAAAADKCAAAAAAAAQEYQAAAAAAAAyAgCAAAAAAAA...
<image>As shown in the diagram, CA=15, CB=x, ∠GBA=30°, C is the center of circle C, the tangent to circle C is BA. Find the value of x.
30
175
[ "30", "413.58", "337.78", "241.18" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAAC/e0lEQVR4nOzdd1wU1/o/8DOzu5QFpXdEQMHeu2gSW1QUb0xyUyyxazQxiZooIqKCiko0iak2LImaeJObYqwxdo0gRY0tFhSkKb2zZWZ+fzxf98cFNUYpuzuf9x95GViW2WV29/mcec45nCRJDAAAAAAA5IFv6AMAAAAAAID6gwAAAAAAACAjCAAAAAAAADKCAAAAAAAAICMIAAAAAAAAMoIAAAAAAAAgIwgAAAAAAAAyggAAAAAAACAjCAAA...
<image>As shown in the diagram, AI=18, FH=37, GB=9, GB is perpendicular to HB, IA⊥FA. Find the sum of the area of triangle IHF and the area of △FHG.
999/2
279
[ "999/2", "369.22", "92.21", "48.4" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAACX3ElEQVR4nOzdZ3wV1dr38bVmdjoEQuhdqohIUbqUQ1GKgHQIJMBBRUFRuoDnvu9zHpGOiL1DCqFXaUoRUEBAEBEBpZcAoQVIz56Z58U65ORQIiXJLvP7vuCTTHaSITvZs/5rrmstaVmWAAAAAGAPmqtPAAAAAEDeIQAAAAAANkIAAAAAAGyEAAAAAADYCAEAAAAAsBECAAAAAGAjBAAAAADARggAAAAAgI0QAAAAAAAbIQAAAAAANkIAAAAA...
<image>As shown in the diagram, AC/AD=1/2, BC is parallel to DE. Find the ratio of the length of line AB to the length of line AE.
1/2
5623
[ "1/2", "79.08", "410.21", "457.96" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAAD8rklEQVR4nOzdd1wVZ/o28GdmTqF3REDEglLEroi912hi7wpYEuNqNBpNNmWT7CbZ3ZhobNiiIoK9xRi7xth7QaRYAGnSeztlZt4/np/zsiYxKAfOgbm+f+zHuAgDnDNzX/fTGFEUCQAAAAAAyANr7AsAAAAAAIDagwAAAAAAACAjCAAAAAAAADKCAAAAAAAAICMIAAAAAAAAMoIAAAAAAAAgIwgAAAAAAAAyggAAAAAAACAjCAAAAAAAADKC...
<image>As shown in the diagram, BC=BA, ∠BCA=25°, the center of circle O is O, AD is the diameter of circle O. Find the measure of ∠DAC.
40
6090
[ "40", "229.13", "46.23", "368.15" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAAB2ZUlEQVR4nO3dd3xUVf7/8XPvnUmDhICQ0KSEIkgHkY6IdBDpkBBw1bVQFCnqurvf/bnf3a8N6aIoiiIldJDemwaQjlRBqkgLECCkztx7f3+cL/lmKTFAkinn9fyDRzKZSe5Mwp3zPudzPlezbVsAAAAAUIPu6QMAAAAAkH8IAAAAAIBCCAAAAACAQggAAAAAgEIIAAAAAIBCCAAAAACAQggAAAAAgEIIAAAAAIBCCAAAAACAQggAAAAAgEII...
<image>As shown in the diagram, BO=6, CD=2, DO=3, △ABO is similar to △CDO.. Find the length of line AB.
4
5364
[ "4", "221.74", "59.82", "137.69" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAAEAAElEQVR4nOzdd1zVV54//nM+n3vpYKEoNuy9996xoYJ0S2IsgKCZ3Z3vziaTX2ZmM7vzyE5mZmNEjC3RxBilW7CLYu9dgzHYsaAgIP3e+/mc3x/vlXWNBeXC597L6/lXvMLlBOF8zvt93u9zuBCCAQAAAABA3SBpPQAAAAAAAKg9CAAAAAAAAOoQBAAAAAAAAHUIAgAAAAAAgDoEAQAAAAAAQB2CAAAAAAAAoA5BAAAAAAAAUIcgAAAAAAAA...
<image>As shown in the diagram, ∠GKM=62°, ∠HBF=38°, NO∥MH. Find the measure of ∠KCN.
62
1559
[ "62", "18.56", "210.38", "391.04" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAADMhUlEQVR4nOzdd1xUV/7/8XOn0LsgqKCI2MXeG/YKohhjkk1ioskmm2I2W5Lv9mw22e9udrOpa7JpJqbHhmJBUaOAvWNFBVFpUqUPTLm/P87X+bFoDDaY4b6ef+SBOINHc+fe8z7lcxRVVQUAAAAAbdC1dAMAAAAANB8CAAAAAKAhBAAAAABAQwgAAAAAgIYQAAAAAAANIQAAAAAAGkIAAAAAADSEAAAAAABoCAEAAAAA0BACAAAAAKAhBAAA...
<image>As shown in the diagram, AC=8, BC=15, D is the center of circle D, AB is the diameter of ⊙D. Find the circumference of the ⊙D.
17*pi
2460
[ "17*pi", "222.09", "230.29", "147.35" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAAEAAElEQVR4nOzdd3wUdf4/8M/MbEnvgVQSSgKB9EBoYgMFBBRQbAhSVKoF1POOO707PfX46lmQrtjAQ+kIKkpRFBBIBQKBhEBIQkjvZbO7M/P74/1lfvmGYoBstszr+YePGJLNZ5PdmffrUzlZlhkAAAAAAKgDb+0GAAAAAABA50EAAAAAAABQEQQAAAAAAAAVQQAAAAAAAFARBAAAAAAAABVBAAAAAAAAUBEEAAAAAAAAFUEAAAAAAABQEQQA...
<image>As shown in the diagram, AP=5, CP is the angle bisector of ∠OCD, O is the center of ⊙O, CM is perpendicular to BM. Find the length of line BP.
5
6270
[ "5", "154.4", "205.53", "309.72" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAAEAAElEQVR4nOzdZ1wUZ/s+/GtmtgFLFSkW7L1g7yU2bFETK7Yk9t5T7/SYxDu5Y8GSaGLU2MHeY41dbMTewIYCSt1d2rK7M/O8OH/uw1+NUQS2Hd8X+RgEvNgZds7jqpwsywwAAAAAAFwDb+sGAAAAAABA8UEAAAAAAABwIQgAAAAAAAAuBAEAAAAAAMCFIAAAAAAAALgQBAAAAAAAABeCAAAAAAAA4EIQAAAAAAAAXAgCAAAAAACAC0EAAAAA...
<image>As shown in the diagram, ∠ABC=130°, O is the center of circle O. Find the measure of ∠COA.
100
3923
[ "100", "242.43", "448.39", "241.67" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAACPt0lEQVR4nOzdd3yV5f3/8Xuck50TQNxbwkiQhCUijqptbSuGWZARSIAgsgk7EFCZgVarkJxMglJZoq3V1tFayEJBpiCCqK0ScpLgArJz7vH74/pyfikoBMi+X88/fMSck5M7Iee+r/d1f67PJZumKQEAAACwBqWxDwAAAABAwyEAAAAAABZCAAAAAAAshAAAAAAAWAgBAAAAALAQAgAAAABgIQQAAAAAwEIIAAAAAICFEAAAAAAACyEAAAAA...
<image>As shown in the diagram, ∠CAE=50°, ∠CEF=40°, AC∥EF. Find the measure of ∠AEC.
90
3766
[ "90", "401.82", "275.58", "456.15" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAAEAAElEQVR4nOzdZ3wUVdsG8DMzW7LphRQSaiAQQi+hd6QJqBQpAiICCoiICEgRUBRBQFAExQJI77333ntLgBRKeu9ty8z74X4ybwRESpLdzVz/D/4g7m4mYct9nXOfczhJkhgAAAAAACgDb+4LAAAAAACA4oMAAAAAAACgIAgAAAAAAAAKggAAAAAAAKAgCAAAAAAAAAqCAAAAAAAAoCAIAAAAAAAACoIAAAAAAACgIAgAAAAAAAAKggAAAAAA...
<image>As shown in the diagram, ∠BOA=38°, O is the center of circle O. Find the measure of ∠BCA.
19
6738
[ "19", "253.52", "316.9", "434.88" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAAEAAElEQVR4nOzdZ3wc1b0//jMzW7TSqvfeq2UVq7obsDGmGnzpLSSXAElIJ4TQkhDaTSEklBBI7p8Qem9uYFywrWbJlmxJlrTqvVplpa0z83/wvd6f4oaLrC3zeT/gJQutdFarnTmfc77nHE6WZQYAAAAAAMrAO7sBAAAAAAAwfxAAAAAAAAAUBAEAAAAAAEBBEAAAAAAAABQEAQAAAAAAQEEQAAAAAAAAFAQBAAAAAABAQRAAAAAAAAAUBAEA...
<image>As shown in the diagram, ∠EAB=35°, ∠OCD=80°, the center of circle O is O. Find the measure of ∠DOB.
150
6611
[ "150", "306.97", "63.85", "274.7" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAACXpklEQVR4nOzdd1yUZ77///u+Z4aOgAIWRMGGFAvYY4kaS2yxJGrUGBtNzW72nN3snu1nc3Zzvkn2t9mTqAjYe2yxRJPYY69YwIqKgoqIgtJhyv374zrOYbHEgswM9+v5Rx5mGIYbZu6Zz/u6P9d1yaqqSgAAAAC0QbH1AQAAAACoOQQAAAAAQEMIAAAAAICGEAAAAAAADSEAAAAAABpCAAAAAAA0hAAAAAAAaAgBAAAAANAQAgAAAACgIQQA...
<image>As shown in the diagram, AB=EB, DB=CB, EB=DB, ∠EAB=60°, the center of ⊙B is B, AE∥BC. Find the measure of ∠CDE.
150
3299
[ "150", "65.99", "69.19", "225.5" ]
A
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<image>As shown in the diagram, PT=4, RP=4, ∠RPT=60°. Find the length of line TR.
4
1188
[ "4", "317.93", "172.13", "171.65" ]
A
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<image>As shown in the diagram, ∠CAB=45°, ∠EDF=30°, ∠BCA is the right angle of the right △ BCA, FE and ED are the legs of the right △ FED. Find the sum of the measure of ∠ARD and the measure of ∠ESB.
210
5265
[ "210", "419.79", "434.95", "81.67" ]
A
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<image>As shown in the diagram, ∠DAB=60°, BA and CD are opposite sides of the parallelogram ABCD. Find the measure of ∠BCD.
60
6814
[ "60", "368.83", "217.21", "461.49" ]
A
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<image>As shown in the diagram, ∠ACB=48°, BA⊥CA. Find the measure of ∠CBA.
42
3292
[ "42", "299.12", "172.41", "457.48" ]
A
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<image>As shown in the diagram, ∠BAE=58°, ∠CBE=26°, ∠EBA=47°, AB is parallel to EC. Find the measure of ∠AEB.
75
2205
[ "75", "1.54", "202.69", "150.22" ]
A
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<image>As shown in the diagram, AB=32, AD=DC, BC=2*x-3, EF=12, EH=HG, FG=x-5, ∠BCD=∠FGH, ∠DAB=∠HEF. Find the value of x.
31/2
84
[ "31/2", "464.33", "315.21", "282.02" ]
A
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<image>As shown in the diagram, ∠ACE=109°, ∠DAE=24°, ∠EBD=95°, ∠EDA=33°. Find the measure of ∠AED.
123
669
[ "123", "236.8", "363.67", "88.93" ]
A
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<image>As shown in the diagram, ∠BOD=140°, the center of circle O is O, the diameter of circle O is AB. Find the measure of ∠DCA.
20
6963
[ "20", "258.02", "383.94", "71.5" ]
A
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<image>As shown in the diagram, BC=1, ∠BAD=15°, ∠CBD=60°, ∠DCB=90°. Find the length of line AD.
2
5476
[ "2", "441.93", "484.38", "128.06" ]
A
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<image>As shown in the diagram, CD=2, ∠ABC=60°, ∠BCA=90°, triangle AEB is an equilateral triangle, CD is the median of △ CAB. Find the length of line EF.
2
5466
[ "2", "344.98", "5.72", "481.08" ]
A