images listlengths 1 1 | problem stringlengths 13 714 | answer stringlengths 1 169 | id stringlengths 1 4 | choices listlengths 4 4 | ground_truth stringclasses 4
values |
|---|---|---|---|---|---|
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAHgAAABxCAAAAAA7ADjGAAAJ+0lEQVR4nOVaXWgb2RU+MilVwkKmzXozUBYPcZdMKayn+9BMyINnS8CTp1UCbQXFG6ctjUOXWvtQVvtS231xwEuF81AntOAsi5Gbgq3QBzv0wQ4lSA44kqEgLc1GcstW2ibtKLTpyDjL6cMdzcz9G0mplzzke5Hm/sx3z73nnHvOvRNDeD7oe068+0i8m/zv8yG+/M+emu8b8d2p3tof2Cfe3RtTfz/US4f9kviD93vtgfuCTQD4SU899kfi... | <image>As shown in the figure, in the inscribed pentagon ABCDE of circle O, angle CAD = 35.0, angle AED = 115.0, then the degree of angle B is () | 100.0 | 49 | [
"50^\\circ",
"75^\\circ",
"80^\\circ",
"100^\\circ"
] | D |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAJQAAABaCAAAAAB7tSDMAAAAqklEQVR4nO3asQrCMBSF4TMIhagIahBXyezii/j+T+NQKRZMo1g9V/i/JYWG9l86pFwJAIAnysldEF52B1RkKUs7d0Z8G3fA/+gkaeWueBT16wMAAMC3rN0BVVd3wNj9nLPgwAMAAAAAAADM5uAOQEXpl+UPXxlqdmIkpeYoxfR/43NzxzvaTyqN+2m4On7YMuhHqqZmTvLLEyn7WYqkrbpwUzAXdwAAwO0G4s0DSp7rlU8AAAAASUVORK5C... | <image>As shown in the figure, in triangle ABC, angle C = 90.0, AD is the bisector of angle BAC, DE perpendicular AB at E, if DE = 8.0, DB = 10.0, then BC is equal to () | 18.0 | 50 | [
"14cm",
"16cm",
"18cm",
"20cm"
] | C |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAH0AAABkCAAAAACOMmCqAAAP0ElEQVR4nL1aebhcRZU/p6ru0re735JN8gLkEfIeIPliICFgVhJAwj5G2XQmzPBFwTiA8jHoIKAiAqLDoBCUGEcRDMoiQREDDFsQMIRAIAEmBEIIWQjkrd13rapz5o+Xl+W9dF4TGn9/dd+lfvecOnWWOoUMtQGhJh9IAHTnhQXj4QAvaIWJqhE5ANtkGzlGevWkJQ5IDgAAtWLnbkdeuVi6Mh19R5OCKKjqrVqxYxH46+/++7j0uecFMrj8... | <image>As shown in the figure, the straight lines AB and CD intersect at point O, EO perpendicular AB, and the foot of perpendicular is point O, angle BOD = 50.0, then angle COE = () | 140.0 | 51 | [
"30^\\circ",
"140^\\circ",
"50^\\circ",
"60^\\circ"
] | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAMUAAABdCAAAAAAwZv0CAAAJfklEQVR4nL1cX2xUWR3+bimlNUhDFJYuyLA+AC5GprxwjWYHMLsOxqxTE9PyspSHbbsx4Y+LBhKDURNnExB0HyzKJqP7QJuYtPuylUQj4OIWu9HBGLfsWqZjow6bdKcWVqblTs/nw70zcztz/5x77m2/tJm5c3+/c853/nznd86cOxqxGshrMRW3pfNnAei/Xe9j16SSeGAY31fzW/Pt83nyxLMfwbuyV4fFG5s/oeYoRAfwja9dgeZptios... | <image>As shown in the figure, the points B, E, C, and F are on the same straight line, triangle ABC congruent triangle DEF, angle B = 45.0, angle F = 65.0, then the degree of angle COE is () | 70.0 | 52 | [
"40^\\circ",
"60^\\circ",
"70^\\circ",
"100^\\circ"
] | C |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAANAAAABuCAAAAABzD8KtAAAXHklEQVR4nM1ceWAV5bX/zcxdk9zc7GSBkEAIloAgWxBEUEEQXNiKiC1SN6yIVp+40mo3q6221T4tfdqCoPhQBJRFC2JZFCqCghQIsoUkZIWE3OTuM3P6x8y9d+7MNzeXpe95/kjmnm87v2853znfd2Y4GSYkgzdLSkBhq1r6QgpH6oCVKRBvJpQsWfHrIRMBQOZk7sJbNtJfVhcLHe5Wi3/29EtZrRlRTPhDgcEAAEvibOdL+Yc2Ydxlae+f... | <image>As shown in the figure, put the two vertices of a right triangle plate with 45.0 angles on the opposite edges of the ruler. If angle 1 = 27.5, then angle 2 is equal to () | 17.5 | 53 | [
"32.5^\\circ",
"22.5^\\circ",
"20.5^\\circ",
"17.5^\\circ"
] | D |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAALQAAABrCAAAAAD7zvcUAAAFl0lEQVR4nO2bwW/cRBTGP+88dtTdiEaRkhBIKoiQFmmlgVpCcAEk6JEDiCtS/yVunDkhOHDiisSxUqUcFqVSRRVAPQQUGpIoXWp3JubgXa/tHdszXjs2lX+HZGM72c/Pn997O34BOjpeREZNC7DDAQBBctK0EBt6AKBA7zctxIYeABxKNm1aiA09AMDEG4iGhdgQisbEp3GzQmyg2XfJWaM6TIjyxSzS/wOD7Lp8/tKJNrpodd4TxNTB7DVF... | <image>As shown in the figure, the straight line a parallel b, the point B is on the straight line b, and AB perpendicular BC, angle 1 = 55.0, then the degree of angle 2 is () | 35.0 | 54 | [
"25^\\circ",
"35^\\circ",
"45^\\circ",
"55^\\circ"
] | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAIEAAACBCAAAAADCy4aMAAAGHklEQVR4nMXbX1BUVRwH8O/ZPyChgroirUAtK27AEOvfXOWfGP4fe7GyrCn7Mz2VMz0000xNTTPN2EPTg03TQzXp9FI+NDWaAgICC4ZkyD9REFdAF4RdQJDdu+yf04PQS2N7zz0/vL8ZZni4v3s/e849555z7rmMgy5uO1ZV20WTGKFg6ugOv7NUNMtEcm3OAODUzOF708K5NAIAQLj3BZaaKpxmILk4A4B71qe15NIIAHAEQsv5DR0FDOaJ... | <image>As shown in the figure, the straight line a parallel b, the straight line c intersects a and b, angle 1 = 55.0, then angle 2 = () | 55.0 | 55 | [
"55^\\circ",
"35^\\circ",
"125^\\circ",
"65^\\circ"
] | A |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAKEAAABLCAAAAAA95biOAAAMVklEQVR4nM2aeVRTdxbHvy+EsIVV2SFsgiK7LOICstQNxFbr0uLWzSl1pq3tTO302MV6js60tZ2letrpZm1Hq1K3tmItIohBMCDIatjDDgaQsIYQ8uaPJPCSvJBFq3PPUd67v/v7/T7v/rb77gshg3FCEkZW1N7aeK/UxUyjiJA90J7uQ3o7y3itu5PV1eT/B6Gkvb22Shi7Oqt3vzoOyTSyzQmebfD9cikGV9bY2CjoDNsWSWB+Treruo2x... | <image>Place a ruler and a triangular plate as shown in the figure, angle 1 = 40.0, then the degree of angle 2 is () | 130.0 | 56 | [
"130^\\circ",
"140^\\circ",
"120^\\circ",
"125^\\circ"
] | A |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAHEAAABcCAAAAAB8JwXkAAAGR0lEQVR4nM1aUWxTZRT+XG6JE21A2HDQubgHWJeIYB2hLKNxDMiQkgguGHRuCjYxMWIIZMYXGh9YfJg8iEVMZkosBhElKUYk7UxLskF0ZBBYJ9Gx4CVbKITsNrFN2sXjQ2+3trv3v/9/WxLPS5tzzn+/e/773++cnlOQGQlIUtPUB6aWUgXEJVYbymT8TXUmlgIwgZjybPIDja8vMocoiS/58cH3APBitTnEx0jAOWEFkNq884A5rKwI7eoX... | <image>As shown in the figure, the straight lines AB and CD intersect at point O, and the radial OM bisects angle AOC, ON perpendicular OM. If angle AOC = 70.0, then the degree of angle CON is () | 55.0 | 57 | [
"65^\\circ",
"55^\\circ",
"45^\\circ",
"35^\\circ"
] | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAGUAAAB/CAAAAADTWlPuAAAK/0lEQVR4nO1aaVRVRxL+uI9FEDAoYIIaeYK7ElBAIhoiahQlRsE1weMSjSdOVHCccY6Mjp7o0cgEEiJRM0QUEiYcFQ0RTYjGBeOC0UTRBBeCoigoAwoCwnuPmh9v4S23+94LZ+bMj6k/r7uqur9bXd39qqsbpIwKAR9tssJGJEAJNfnsJLo6qEFRIwDKUHwCsgCPKUOVokCJ4Ydxg4jo5iOlI2ZHCr7Ic84niq0AoHDE/tW3fSAK/dLjv4Hi... | <image>As shown in the figure, the diameter CD of circle O crosses the midpoint G of chord EF, angle DCF = 20.0, then angle EOD is equal to () | 40.0 | 58 | [
"10^\\circ",
"20^\\circ",
"40^\\circ",
"80^\\circ"
] | C |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAL4AAABrCAAAAADs7GfdAAAIkklEQVR4nNWbf2wb5RnHv2dabaq09Z9suSFnDmmqHRioUWCN1mwOapDctdKCxpSWdZqRQEHKNGWlME+tSMeiNRNtl0r5I5A/mqrdyB+VgrSuuFIrkpFuLgEZSiAppNTIRstwtSZLtSba9Z79cT777uyz7733zjEfxbkffv283/e55973fe4HiJvJWX4bjCi0BwDOEZxbyPG/B6svn4j2nKNJzPrgEEFb+X2gwakNhxAA+WoYmwDH8jVTJ7d8... | <image>As shown in the figure, AB is parallel to CD, if angle B = 20.0, then angle C is () | 20.0 | 59 | [
"40^\\circ",
"20^\\circ",
"60^\\circ",
"70^\\circ"
] | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAN4AAABrCAAAAAA9C2OtAAAE0klEQVR4nO2cK1QbQRSGZ3oqcmqIxBHTc1LF4hIHjqji2qoWRxTgiAIUVAVUQCUocIAKDqoSR1BEVIDoIY6tYlWnIkvuAvuYx51HOHwCEnZel3vnn93Zu0sZGQ/kxvkOeRSOQcfFe9nEWfLKvfdm3jjzZt448972AGKgw18Ymu6ieYwyMjJSDVeDE8U4d83DiU0ngxPNd256jzKG4zs3zUPEUfMYUnw6aB7esuCitNChaTiTL808O9eCop3S... | <image>As shown in the figure, AB parallel CD, angle CED = 90.0, angle AEC = 35.0, then the size of angle D is () | 55.0 | 60 | [
"65^\\circ",
"55^\\circ",
"45^\\circ",
"35^\\circ"
] | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAGMAAABnCAAAAAAxwaNfAAAGCElEQVR4nLVaXWgcVRT+7iZ1IGzxwWLXspI2NrCxkmxNQvJQTR9qGw3ShqplXbE+WEopUok/WGhLRERFqbYUrNiHbSlUH2SFmlS0gaQUKt3U/BDdSItWuoEtlpraVGbaOMeHmZ25O3tndv72I9mZvXO53z3nu+fcOTMLqiFSADBEEFxSwyMZpjHkI6gEA3BuVnDBKxZ/60ETIOIAsPhaCBS4sL4Bbw8kBL5SiejdZ++E4KoMgDyRwA4GHG+b... | <image>As shown in the figure, AB parallel CD, AD bisects angle BAC, and angle C = 80.0, then the degree of angle D is () | 50.0 | 61 | [
"50^\\circ",
"60^\\circ",
"70^\\circ",
"100^\\circ"
] | A |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAIgAAABiCAAAAACuDsRqAAAHYklEQVR4nM2bbXBU1RnH/8859+7NsiQxGKwgLWLLB63Viq0VOukAjsigU2VGbMcWUEHqmGBGbEuZaqdOAKltQe0ojp2BGnTSikxx6IAgHTK2SNHAMCDiBDGIYgKygWjC7t6X8/RDNsm+Zffu3nsXnk97754997fP+T8v5+wsMS4OE+V5TOGvWwYQdz4vAwjhpX10EYAwXn6t1s24wO1/U95np+Co4EE6Jm9mpQoO04JemZ4H7r4ThSUCCjqP... | <image>As shown in the figure, AB parallel CD, if angle 2 = 135.0, then the degree of angle 1 is () | 45.0 | 62 | [
"30^\\circ",
"45^\\circ",
"60^\\circ",
"75^\\circ"
] | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAIUAAABNCAAAAACtCvg5AAAF0ElEQVR4nMVaW2wUVRj+Zh1ogCYlpgUfNmkgQIsltgKm29ikManlElirRZomJqLWGDU+tSomsjZGHohBeDCGggkGWxMS0EKoKSFiLWxauVhIarDuKuBi7NKYaBahzNnO58PMzt5mu7uzM8ufbWbmXHq+833n/89lBiRJdgEAOviATCIoAej2nym91zj/zCIJD8BcgARABFpKseDobx8XGQQNFABw86cNACobAsUFASkJxVn3YwYw5+2cJEn9... | <image>As shown in the figure, AB parallel CD, point E is on BC, and CD = CE, angle D = 74.0, then the degree of angle B is () | 32.0 | 63 | [
"74^\\circ",
"32^\\circ",
"22^\\circ",
"16^\\circ"
] | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAKIAAABtCAAAAAAHJ+WmAAAEqklEQVR4nO2a72/bRBjHv7OuCmsI7bKWVqWlk7chhjRgndA2sQAtVSWE+CGGxKu+4FUl/gVeReIP4O2UF/CGF5VgAgHqJKBJ10wjQDuSap20WlUJVqPgzRFLm6jUQ7xwy+wsts/xnW8gf96kvjx3/dT2+Tk/vQNpPOxIogW8iRRZECmyIFJkQaTIgkiRBf8BRSJaIJszP997xilCuOJ48tLMEHY/7XWMeAgutDwIdJ3tcfxeuCJRZIkUcDLu... | <image>As shown in the figure, AB parallel CD, point E is on the extended line of CA. If angle BAE = 40.0, then the size of angle ACD is () | 140.0 | 64 | [
"150^\\circ",
"140^\\circ",
"130^\\circ",
"120^\\circ"
] | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAIgAAACJCAAAAADSjS8rAAAEV0lEQVR4nO2bX0hTURzHfycNB77chyihF5+CMIoeiv4hzKKQMFjhg4pDrCCsrFi+pAW1YRRlYToydARRi2RcxGRI1sj+IPgw6A9CveyhYI+DEO9AuD1cN7dzz707996zcwbe71C3c+7u+fg933N2z9mGVKgMbRINkJMLgssFweWC4HJBcLkguFwQXC4ILhcElwuCywXBVTEg1dxbRAAAoFvFIP7rGqSS2hXVNSrCCiomIxsYJJ+OkGAQTQjj... | <image>As shown in the figure, use the benchmark BE to measure the height of the tree CD. If the length of the benchmark BE is 2.0, AB = 3.0, AC = 9.0, and the points A, E, and D are on a straight line, then the tree CD is () | 6.0 | 65 | [
"6米",
"7.5米",
"8米",
"8.5米"
] | A |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAI0AAAB+CAAAAAA8M83OAAAXDklEQVR4nO18aZhdVZnut9Yez1RjKiGpBEICJBBECJ0QCENkEEjzIAo0gtzGHgQREa4XtJWrXOG52s1gX2wBtYWm9bHBbpwgLeKQAMIFkaDInHmo1Fxn3tOa3vujBqhz6tQ5kPRz/eH7q/be66z97m9a3/q+vYuB/ojA/38TmIY/sWkMm4iImhkPU4nrEJFmnAhaOxo2J1LaZZQYxzaMEZE2juA2RSbFS74nmd183tpjtMImShMRjFIeN/bE... | <image>After filling some oil in a cylindrical oil tank with a diameter of 200.0, the cross section is shown in the figure. If the width of the oil surface AB = 160.0, the maximum depth of oil is () | 40.0 | 66 | [
"40cm",
"60cm",
"80cm",
"100cm"
] | A |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAH4AAABfCAAAAAALuCzHAAAGgklEQVR4nL1ab0xURxD/PbQiCda0QDgozQFNw0WNUdv6pyrHhyalkYCpJtKABfwT2tqkJvXINTE1TdpK/GQarbZaeFhiqYkm1RYxJe1xaEpsIiSVYpN6d0rTIkmp9UgFvHvTDyfHHezb3bc+mC+3uzM7vzdzs7uz855GsJ2ChZDVOt9+dBT4L8iKpswCPC6USYuSIgUAnclwwy+vVNX67kIK9DPGg1ozXfBIB5QqfHEABYcY43X+AmCpJq1H... | <image>As shown in the figure, angle 1 = angle 2, angle 3 = 30.0, then angle 4 is equal to () | 150.0 | 67 | [
"120^\\circ",
"130^\\circ",
"145^\\circ",
"150^\\circ"
] | D |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAI8AAABTCAAAAACD9AsbAAAFc0lEQVR4nM1a7XWjOhC9u2cbmBbUglrQlkBKICXwSiAlmBKgBFwCLgFK0JRw3w8JAcHxx8aWMycnB+sDXe6MRtJofhE/Sn6fLdXMKJYRf2/K9KhQAJIZiUIiot+rcsH0fko1ueAIVAUzB382laepcXnZwbFTBUxlIziuZHQGA0nSM5sUKPsaEsblxp47qdAByEqRE+uqerbcDZ7GltJln10q0BMgwXJXzPVwDmizacuTnqxhnBETB13NLz0W... | <image>As shown in the figure, AB parallel CD, angle B = 20.0, angle D = 60.0, then the degree of angle BED is () | 80.0 | 68 | [
"40^\\circ",
"80^\\circ",
"90^\\circ",
"l00^\\circ"
] | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAJEAAABlCAAAAABosF7wAAAGrklEQVR4nMVbTWxUVRQ+b6YVUcpAk1EJkRgR1LBComKLUltaqiEwDgUtrnRpYjH+bEiIGLcu0LgUKSQtgRYUmM7PG/qTIgG7MmpbkfCjqKAYBaVIZ+49n4uZdt78dObde1/Dt2pe7j3ve+ece/7u1ALNNvDTEp/CcpW1epD2qnOssL5q1phkgRPtXcstpR2zjGRNXG3DLDOSdk1Cqm3xlhEXPrDnJVRleMmIB8cLnvQFYkJVipeMUsHR/PfH... | <image>As shown in the figure, the straight line AB parallel CD, AE bisects angle CAB, angle ACD = 40.0, then the degree of angle AEC is () | 70.0 | 69 | [
"40^\\circ",
"70^\\circ",
"80^\\circ",
"140^\\circ"
] | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAFkAAABYCAAAAAC7PATWAAAJkElEQVR4nLWZe1wU1xXHf/fOrCuCoknXlpREw8d+fL9IUXwlQnzFGGM+qe3n05hiagwSBYnERVGDgCgvUUTxRaKo8RU1vqpNTKza6kcb89L6tqgRpYUmahZc9jFz+sfM7s7uzu6iiecPPjvn3vnOueeec+bcgREekfBHBX6EZBGAszGshSSJkAhEEojICYCIERhjxCADgEwACQYAYADISQT6zsoZv9fEwSwNAJPtDhlC5JBOClk+uOOuXXZC... | <image>Xuan Xuan and Kai Kai are in the same mathematics study group. In a math activity class, they each used a square piece of paper with a side length of 12.0 to make a pair of jigsaw puzzles, and cooperated to design the work shown in the picture. Help them calculate the sum of the area of the three figures circl... | 36.0 | 70 | [
"12cm",
"24cm",
"36cm",
"48cm"
] | C |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAG4AAABcCAAAAACqgt+BAAAFP0lEQVR4nNWZf2xTVRTHv7cTBkuNGDdX4sI0YCyi2MkwxY21wx+bARdMSGoixj80lMgfJohxf+gMf20mGjFhOMM/GDVWUCBxshp0LWSQOX7NhADqpEtY4jYlsnVE6Oj7+sdr1471/bh9r008//Sce2/7eefcc88771UQWjK0THMqb3FozrStfL+YuPVVPc/+VTxc7Z9fN6w8ZjePWpJsDrHvvnc15/MSbe8c/gjqBs+tHbPTOW0cvANA+Xcb... | <image>As shown in the figure, the straight line a parallel b, angle 2 = 35.0, angle 3 = 40.0, then the degree of angle 1 is () | 105.0 | 71 | [
"75^\\circ",
"105^\\circ",
"140^\\circ",
"145^\\circ"
] | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAALsAAABrCAAAAAAKxayZAAAVKklEQVR4nNVcd5gcxZX/Veru6Z6ZnQ1a7WqRhLJQwKCAjISQRfDZcIcDAo5gMhzG3AFnOAPG9oHDJ6J9BGPjzyDAJGPgDhMMmGQkIclCYZVAOXq10mrTxO6ucH+sZiXN7mrHm77Pv396p6r61a9fv3r1ql71EoOBgaYmsGAIABBI3gciaR/IKBKEA8ZI6LCPBPbF8xcFasBgANZ3IgeMOzSDMhwwFABpM57eYeBsRhujqTYpAADrA+oDxt1o... | <image>As shown in the figure, BD is the angular bisector of triangle ABC, AE perpendicular BD, and the foot of perpendicular is F. If angle ABC = 35.0, angle C = 50.0, then the degree of angle CDE is () | 45.0 | 72 | [
"35^\\circ",
"40^\\circ",
"45^\\circ",
"50^\\circ"
] | C |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAHkAAABYCAAAAAD0YQcGAAAFjElEQVR4nN2aXWgcVRTHz7SiIIVVWJoprgSTiIH1QdmAwUYn0gcjUk0h0DyIphBMJUUUuiFPJg8Ksb5EWDBYP2bfIi72wUgXfDAdU1m6fvRhNQ8mk5hESLpBErbqVjb792E+dnb23vna2Qj+XzZz5s785t5zP849NwKoUb+1M4xh6wgL3Js+BLLAqvPqi/3vH201mVVn6sztPLP7n5Dp2OfPP/59q9HgKCvKvFvhiEvGSvxCJTxOf0M12a1N... | <image>As shown in the figure, the straight line AD parallel BC, if angle 1 = 42.0, angle BAC = 78.0, then the degree of angle 2 is () | 60.0 | 73 | [
"42^\\circ",
"50^\\circ",
"60^\\circ",
"68^\\circ"
] | C |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAMoAAABjCAAAAAD/HcBSAAAQCUlEQVR4nM1ce1Bj13n/7r1CDySBHoiHkEAgYFlYWNgFFtgHXvZlr9OdNG3jifOY9I+4M2477mSmbaaZjieeiceZ1vYftd3xJO3EyR9u2qRNnHrrXdubzT5gEU/BAgtIQoAACb3R+3Hv6R88Fkn3SvdKbNa/WXa4557znfM75zvf+c53zgVD8LQQDhJUBPjFJYckj5dPoWBSVnjN1CfvhouAcB597WjhwgAA8DzKOP7xL0cPoWZN4MHWn76s... | <image>As shown in the figure, the perimeter of □ABCD is 16.0, AC and BD intersect at point O, and OE perpendicular AC and it intersects AD at point E, then the perimeter of triangle DCE is () | 8.0 | 74 | [
"10cm",
"8cm",
"6cm",
"4cm"
] | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAHcAAABqCAAAAACjGpETAAAKpUlEQVR4nMVb7bXkKA69M2cTUApsCEwIdAjuEOgQqBD8QnCF4ArBDsEOAUKQQtD+AH/j6veme2c4/apcGLiSkIQQ9B+Kf6X8+VtGmdM/jisA5h/yj+MSgB9C/zguBI9k/gVcGuH+BX5Fni3MvzC/3+hjNPRV4F/GfRr7ZWYB/OcXIIUgSXrIh1kn+LMz/bf4lfxHkNd3QnpRggAiyGb1f8FdBicIBHAGSJ5AAH1Fqf/4O/75IlUhyKdZ/Xu4... | <image>As shown in the figure, triangle ABC is the inscribed triangle of circle O. If angle ABC = 70.0, then the degree of angle AOC is equal to () | 140.0 | 75 | [
"140^\\circ",
"130^\\circ",
"120^\\circ",
"110^\\circ"
] | A |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAJ0AAABhCAAAAADpHfxoAAADlklEQVR4nO2bu24UMRSGPzu7Qkg0iI4GWiQkaFNEYiNq3mh1ZKXgSXgJiqBoazreIh1C4raxKXZnMoN2x8ce73iK/MVmE9nHv8/l95lLjGPGsLUJDOKBXT4e2OVj3uwWUy8ooBexqX3nrDWiHj0xOwkiQb/m1L4z4Lx69NTsPDPOO5M2fGJ2wYJcAaIqjakVJUiKQyb2nQvW2jWILvkm1zvxa9Aq3vQnmet8xlDlnFUfFpW6AKXk1WB3XxIx... | <image>As shown in the figure, AB parallel CD, radial AE intersects CD at point F, if angle 1 = 115.0, then the degree of angle 2 is () | 65.0 | 76 | [
"55^\\circ",
"65^\\circ",
"75^\\circ",
"85^\\circ"
] | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAALoAAACZCAAAAAC9XX+1AAAW2klEQVR4nNWdaXBc13Xn/+cub+kNOwECBEhQXCWSIiVKpMRYYiTZijyKR0nsRLGdKjspuZKKXZV8mcr3SVJTNZP5MFNTU8mkVNmUxEoyFVmyLUWOTWuhSUmkKIqbuIrgBhI7Gt393rvv3jMfAFAUARANoBsjnw9kFd7re344fe65yzn3ghj1kthHmh7/l38qPLb9wc6kqebtq5q3OCWjjX4ikj879uXfbfjeVcpma69B1L7JSWksRZ6qvL9q... | <image>As shown in the figure, a // b, put the right-angled vertex of a triangular plate on the straight line a, angle 1 = 42.0, then the degree of angle 2 is () | 48.0 | 77 | [
"46^\\circ",
"48^\\circ",
"56^\\circ",
"72^\\circ"
] | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAKkAAABnCAAAAABeXD03AAALzUlEQVR4nM2beXRTVR7Hf29J2qRJ27RFYYBRahmQQUBBBjuyadkcQaqouDCgDHhkBNEBBFlUTgWPcgA9InB00BHFAQ+Lg8giyuACKCIy7HuB0iVL0+zv5d17f/NHuqZJyEseab9/Je/e5H3e7y6/3/3d+ziEVqkfb+hgaHqFbxmQa6lqmjM97FLrI/UDgOfjrBwu7HqrI0V3ELx7byoLB219pFyuE13BP/Qzhhe0OlLQ3WBbli8VhHdTEFsC... | <image>As shown in the figure, a parallel b, point B is on the straight line b, and AB perpendicular BC, angle 1 = 36.0, then angle 2 = () | 54.0 | 78 | [
"54^\\circ",
"56^\\circ",
"44^\\circ",
"46^\\circ"
] | A |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAGEAAABlCAAAAAB4/NJpAAAHM0lEQVR4nK2aeWwUVRzHv293KZSjtNQWoRWWWs5irKCiwSqKBwgRpBSIFhAbjCcRDYpGA8YQY2IwAQtEBLlKaMstKCAaBBGoQhFptxc9oIdAz2233e7uzPOPstudmTfz5q39/fX2/X4zn33HvN8xQyh6VFrr7UTZY+lZALK+lFQ9PUy4djzNZp7QmFMuCpD2D52q7jMgVG/1iBKKTryr6TMg3CajBAHy9ykjNZ3qWQuSqgTRRTr/zw5tp/5N... | <image>As shown in the figure, if angle 1 = angle 3, angle 2 = 60.0, then the degree of angle 4 is () | 120.0 | 79 | [
"60^\\circ",
"100^\\circ",
"120^\\circ",
"130^\\circ"
] | C |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAI8AAABGCAAAAADQ75gzAAAE20lEQVR4nO2abWxTVRjHn3ajXde9XOZ0m6zrarcx0M1FY6AmxLcgBv1ifAGaKLIsTjFGMX4hwiBTwBcYMemcJEtx8rKXGBODCEzCYDILbpIggSh7gVI3tpbR6xxbt/b28UO3tPfutvee67nCB59Pt/97zsnvPM957nPvOdUg3FGmvd0AAvufJ7GR8lBdbgEITwmkZKIBuKMVC+jhgPdgtpl9KitWIvPP9w0Gijiw4NvJsgsbOcU83m+0mTR5... | <image>As shown in the figure, AB parallel CD, AE bisects angle CAB and CD at point E, if angle C = 70.0, then the degree of angle AED is () | 125.0 | 80 | [
"110^\\circ",
"125^\\circ",
"135^\\circ",
"140^\\circ"
] | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAALAAAABeCAAAAACmksFwAAAJMElEQVR4nNWbcUwb1x3Hf9dMoVqz3qR5wutcOYDbmiFV1tJtKHiFCOg8BVNvZUFqyICJJZXYVKLZCdWiOtKoWlEqqEYkDNVKNk+jmqsQoBvUkMIKUjaiUa20jlY780YmeWPSiBwpZjL+7Y/z2Xfnd3fvnolovv/k7t3v936f/N6Pd/fenTmEe0v37TWAUe0RcDPHcRzXzOC5R8BT7ihi2M7guWclUQGjDTYGvz0CXmiC0XI8yeC5R8CxU9yp... | <image>As shown in the figure, the perimeter of parallelogram ABCD is 32.0, AC, BD intersect at point O, and OE perpendicular AC and it intersects AD at point E, then the perimeter of triangle DCE is () | 16.0 | 81 | [
"8cm",
"24cm",
"10cm",
"16cm"
] | D |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAD8AAABGCAAAAABeGRMKAAADJklEQVR4nO3YW0gUURgH8P/szu663vbiehdveN0o8UKiIFmglZeo6CmJ6KGgKIqgKApJei6CqF6iqDeh6MGgkrQyMpSshLy7a4rpettdbS/uZeb0sM6oe8lZ6UFov6c5Z77fnDMMZzjfoQj8BTNrNhkdxGgTETpWTGlUSnWE30TKx9sM+pEhJkIqCxMjLpKlXAY37A7HMpOcpU2O3sh/HNBZEjOzVcoI+dpuh9VinBgfkGbklCt8/YIlDQDg... | <image>As shown in the figure, a cylinder with a bottom circumference of 24.0 and a height of 5.0, the shortest route that an ant passes along the surface from point A to point B is () | 13.0 | 82 | [
"12m",
"15m",
"13m",
"14m"
] | C |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAKMAAAB6CAAAAAD2Nry7AAALiklEQVR4nO2c+XMUZRrHn7d7rszkmFyTCTmGHORgcgcSw40GVHRXhVoQjCuwq+VRu1VrbZW/7H/gVu1VUq6UioAikVUBgVWjgoGQBHInJIEckHPMnUzOmel+94cENj3Tx9s9DbtW8f1p0s87b3/m7fd93ud93reDMPzfi/pfAxDo58Co8evbC4xGpxKIiPxjrGUztUglEmH59aynLtw03X9EvxjdTeNWWjUSYfnDODQw71YNRER+MDJDYTEP... | <image>As shown in the figure, in triangle ABC, angle BAC = 90.0, AD perpendicular BC at point D, AE bisects angle DAC, angle B = 50.0, so the degree of angle DAE is () | 25.0 | 83 | [
"45^\\circ",
"20^\\circ",
"30^\\circ",
"25^\\circ"
] | D |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAGcAAACTCAAAAAC2KVgqAAANGklEQVR4nL1bd3zURRb/bstuOokJkBiaUnKAoXOcgBJKEimaA+5UQERB7gN4gAjRg6DcoYgUaSKHcEhRwAsIRClCQATpoYWQSkhIgZC6ySbZzba5P37Z7Oyv7azkc++fzO+92flOeW/mvTcTBcH/hdTy4lxzaOsWwVHKiw9Gn20RGIDIkn10gXwFVnIznptWXcsMxw3O1phgAMZ9Fh7fvif28tT3TR9tMANIvEP3bMSKsumT7gLA0a9Ycaz3... | <image>As shown in the figure, the line l parallel m parallel n, the vertices B and C of the triangle ABC are on the line n and line m, the angle between BC and the line n is 25.0, and angle ACB = 60.0, then the degree of angle a is () | 35.0 | 84 | [
"25^\\circ",
"30^\\circ",
"35^\\circ",
"45^\\circ"
] | C |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAIcAAACDCAAAAACCHVfAAAAIJElEQVR4nO1bPYzbVBz/BzF4Ai+IbPWAhEFCmAl3Og9INVOzXbZLp15h6HXqdcplOjoFBnRlyjHdVUIkHdBdp0unZEsQQ8LknIQUIyE5TA5i+DPEX89+z+/DaSkSP+l07/nj5ef/5/usIbwWeOPfJhDhfx4kXhceb26hjcViPY6Kmg1mXaWNWiV/WQ/HP/tjw9A+jS78NYa57+gfO86r4zEcvhg7n1p1u3BjNX0xdHdc6xXwmH43MHfKvvry... | <image>As shown in the figure, it is known that in circle O, the central angle angle AOB = 100.0, then the angle of circumference angle ACB is equal to (). | 130.0 | 85 | [
"130^\\circ",
"120^\\circ",
"110^\\circ",
"100^\\circ"
] | A |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAIQAAACICAAAAAAD7RwAAAALfElEQVR4nM1cW2wU1xn+x2o2jbrNqsoiBrGJuWzK0qZlIlqxVZyuqSKxD4gSkca5GMUoyKuKSI4a1PoBKS9U2l6ipioQo0SKaY2yDQ5GSlotKq2N4ihLibo80BiUde2ypAI5FxITsWM28/XhzOzO5czMOet10094Z86Zc/nmP//55z83FFD7AeXkck0ifccScCDl5oBU+vaTABHtuyv5xZJQiA5p/5HKshTNMTv/vWXRL5rEr35GX5fKsAQk... | <image>As shown in the figure, triangle ABC is inscribed in circle O with radius 1.0, if angle BAC = 60.0, then the length of BC is () | \sqrt{3} | 86 | [
"2",
"2\\sqrt{3}",
"\\sqrt{3}",
"2\\sqrt{2}"
] | C |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAJUAAACXCAAAAAA5AUaYAAAUlUlEQVR4nO2ceXQUVb7Hv9VbFiAECAkkLAmBdGIgLAMMgiDCgKggBMMmMBIIW1hGx9FRx3dmPL5RHMaNRfYtIwoDLoMKKAhhB0USA2YBspKd7J2ll+r6vT+qutNdXVXdnYR5c955vxPoqrt+7r2/+7u37r1VDOE/UFT/2wCS8v9UnktbqAgAyrc1dTCKg2i8C04MAAZA7Yd+zIPg4cW7uiIbifnL3L7qjqexiXdUNigu2y9Y1/Ewdmmbtpdf... | <image>As shown in the figure, the circle O is the circumscribed circle of triangle ABC, and the bisector of angle BAC and angle ABC intersects at point I. Extend AI and it intersects circle O at point D. Connect BD and DC. If the radius of circle O is 8.0, angle BAC = 120.0, then the length of DI is () | 8\sqrt{3} | 87 | [
"4\\sqrt{3}+2",
"4\\sqrt{3}+3",
"8\\sqrt{3}+1",
"8\\sqrt{3}"
] | D |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAHEAAAB3CAAAAAARTPARAAAIpElEQVR4nO2aX2wjRxnAvytlG+hDTeGEKyFldQiygoduKyFcXSF70iH5LUYg4VY6YhC6hvahPnjAiIeEl7NOJ2EiIaJDSG6Rgg8q4tCXHBJgByE5kUjtPjkgiu0iZAOBdR/a9W6u+njYfzO73+6O7Sgv5dMp55mdmd/O9803f76dCwjnLA+cN/D/REKOXjtnonljXuC0xFvvXzxf4s8vzW/3qVoYnHxO+sB5Eu//5Bsgf/A8ib+8+bB8f17g... | <image>As shown in the figure, circle O is the circumscribed circle of triangle ABC. Connect OB and OC, if the radius of circle O is 2.0, angle BAC = 60.0, then the length of BC is () | 2\sqrt{3} | 88 | [
"\\sqrt{3}",
"2\\sqrt{3}",
"4",
"4\\sqrt{3}"
] | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAG0AAABwCAAAAAAx26HPAAAKfElEQVR4nK1abWhb1xl+lQ+igrKbLddU2eRo1Oqs1FkxqKEe8WYlcVf/MK7XenN/GObAsDNciBp7wyMeKswDFVLmgsVcvA6XhS2pDc5Y1irgtDJzqRtt3A4clC1OpUzZolSFKZM33TrKffbjfurqfkiynx/SPee+73nO1z3v+55zCLWjh4iIggAECDVp7qDa8fseDog1E5GDHDVp1sP2YLP1wevHD9WhWQ/be0Ga/fLu03VoUh3jFiUirg69... | <image>As shown in the figure, AB and CD are the two diameters of circle O, chord DE parallel AB, arc DE is the arc of 50.0, then angle BOC is () | 115.0 | 89 | [
"115^\\circ",
"100^\\circ",
"80^\\circ",
"50^\\circ"
] | A |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAHIAAAB1CAAAAAC3s+oZAAAIN0lEQVR4nO1aTYwjRxV+ScAxCxIOUbQtcdjWILSdC9PJqWEVpleshAEhZm/ew2gbCXYdDokjDpgD8uQAwyoHZyUkJ1y8CE28LNKYXJg9INlzQJ45DJ45eZBQunOyIy3q2cOq3T0bPQ794+76c7UdjYSUT5qR+9XPV+/1q3pVr+sZhPPGs+fO+DmlHA7/dd6U/lu5myxLeeeLl86Z8oOV/B0sR/nxo9cKXzpXyqd//BmoF86V8sHvvqw+zd1q... | <image>As shown in the figure, points A, B, and C are on circle O, angle ABO = 22.0, angle ACO = 42.0, then angle BOC is equal to () | 128.0 | 90 | [
"128^\\circ",
"108^\\circ",
"86^\\circ",
"64^\\circ"
] | A |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAGYAAABsCAAAAAC9L5jYAAAKoElEQVR4nL1aXWxcxRX+7tpgh7h1KrbKUl9kijdiQxJnU4cW1VYNxRVGzYNRTbcGo7rlx6oMwphItSo3UZGRTIuUACkxTRGOBLJpXEwFCk5Jgh1M5coIm8SOTeOAyRrYsDwYduPd4GW+Pty7d+//rmOL87A7c+bMfHPmzJy5c2Yk4psgzzeCgvzcRb+YmPl0CDj7MQG5DJdVyhsqinKsK+U2aPPH3xj6tOrqshuKcE0pgI/mEB87Gx6Rb66p... | <image>As shown in the figure, A, B, C are three points on circle O, angle ACB = 25.0, then the degree of angle BAO is () | 65.0 | 91 | [
"50^\\circ",
"55^\\circ",
"60^\\circ",
"65^\\circ"
] | D |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAGoAAABYCAAAAAA4+D3tAAAI7UlEQVR4nNVabWxT1xl+bpKO0qaKtDrDCDOvwjRmZsNTqDBKgs1iplRLIUzRPqRUbTUaOlEEG0jLj2zZ1lTkB90yLakoTFomYEMlXaYSVGd44CxmzRSQYSNNGEZJFyplgw6jsDXJde6zH9cf916fe+0Q/uyRE/uej/c573ve8/WeKxFiUNI/L0Rv3bh6F6N3ANt6lnvW2WuK8tfSQjKj0lW+GAmN+NbbtmKFGwBG7ySHpsejW4OBTXlq60Xl... | <image>As shown in the figure, it is known that in circle O, angle AOB = 50.0, then the degree of the angle of circumference angle ACB is () | 25.0 | 92 | [
"50^\\circ",
"25^\\circ",
"100^\\circ",
"30^\\circ"
] | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAIQAAABRCAAAAAA23FHnAAAHG0lEQVR4nO2aXWwbVRbHjxu2U1bWFiEXpjBso26Ks0SIKalEIszGQqF1tSGZVSMVVoGWpSQSPNQoFfghMDwYkYdUzUpNlVVX2iCKlH5IhhUgRwViquyKKgIXNeFjMe2EgGI1LwEHeeIs+9+H6xl7xmN7ZuIoWmn/keJz75w7/vmcc++M59oD2nht2mgAov9DFOQEosuzyeO5bXljId7u/BR4cmftKZxArOZEoqHW/g2F+PDXRES7/rWhEBcf... | <image>As shown in the figure, AB is the diameter of circle O, C and D are two points on circle O, angle BAC = 30.0, arc AD = arc CD. Then angle DAC is equal to () | 30.0 | 93 | [
"70^\\circ",
"45^\\circ",
"30^\\circ",
"25^\\circ"
] | C |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAIoAAACKCAAAAABQ7I24AAAKEUlEQVR4nO2cf4gcZxnHv3vNkG0Es9AWpkW5MQF3RDDTYOsWqzekF7sWsVsRc0cxtxE01yIkiOgVKXeCcNUIq6BeAuKmhWRTlFziP3fxj9weGu4aOHfvr71Y0ptFdLdyshsk7ubmyuMfs79u5p2Z9333jkTok2XZeeed9z7zPO/zzPvjmUQID4oM3G+ArnyIwhIxlK3jkcjPb84+ACjl+GeInvjK4O6ggPjFOnCGiJrDGwLXCIiIVs4feBXA... | <image>As shown in the figure, AB is the diameter of circle O, C and D are two points on the circle, angle D = 34.0, then the degree of angle BOC is () | 112.0 | 94 | [
"102^\\circ",
"112^\\circ",
"122^\\circ",
"132^\\circ"
] | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAHMAAABwCAAAAAAIvBCUAAAL9ElEQVR4nM1abWxb1Rl+bhsvTLjzNjnqRTW4tA5xyVANbUcGAacirJmWtekIM9KClEpdwhakZiKMIGVLhzopE63ophZFCtpSrZqiNSPd1oEDgd6MAEYpuIh0TtZkNXJQXVKNpDZa4uvedz/uvfb9OPfaDv2xR218zns+nnPe83Hf857DEQqCOO0PgKXz05cFYG4egMdHX7rPU7nNaS6UL6CviiuCU4f5N944e7n21s071tFGL4j7OI705Fxi... | <image>As shown in the figure, points A, B, and C are all on circle O, when angle OBC = 40.0, the degree of angle A is () | 50.0 | 95 | [
"50^\\circ",
"55^\\circ",
"60^\\circ",
"65^\\circ"
] | A |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAH4AAABnCAAAAADjkakHAAANK0lEQVR4nNVbf3RV1ZX+zslDHQ2kOomJNZFKIgkNMwOxCgouRKjgKFgKFeuABAulbaaLVOkICwnjVMu0TYV2rNBC2yCouARE/AEU1FCZBlCKaxEJgQBqYiGJ7RBDIT/u3d/8ce9977776yWQ/tG9VnLvO2ef/e19zj777HPeeYroMYm2/tB2sP6T3wMNnwDIzUe/W/NuKOlPZbORyn6NFwm0QCc+x0n1Ah4Qjca3dlWfGp036OZ0lXc9wI8/... | <image>As shown in the figure, the diameter AB of circle O is perpendicular to the chord CD, the foot of perpendicular is the point E, angle CAO = 22.5, OC = 6.0, then the length of CD is () | 6\sqrt{2} | 96 | [
"6\\sqrt{2}",
"3\\sqrt{2}",
"6",
"12"
] | A |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAG4AAABsCAAAAACu+NgsAAAJz0lEQVR4nNWaf2wT5xnHv4fp+CMuUVdHmGFmWrzGYKjcZRWeipZQMhZtIQkrUqop24KWJZUyjWhEKtOY6B9IBS3S0ERYUCot01JhmlRsUzoZKSvpFqZMqeSipU0osLgjrN5ChyOnJU3u7rs/7ny+s8/26zj7Y48EOd/74/O+z/vznueRiGLlWvxv1+8j9gEA3xZUBIKb9wiXlURwlPQHZXT06lTI7d/tkrZsBzDzL8Sn373356f37d9vyZi7... | <image>As shown in the figure, in circle O, chord BC and radius OA intersect at point D. Connect AB and OC. If angle A = 60.0, angle ADC = 90.0, then the degree of angle C is () | 30.0 | 97 | [
"25^\\circ",
"27.5^\\circ",
"30^\\circ",
"35^\\circ"
] | C |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAG8AAAB3CAAAAAAoK0FKAAAMT0lEQVR4nK1bbWxb1Rl+r9NSRk1vNdzW3dx5oka4uB+G7Ec2AklHp1ojjKCVtWEZC1pZNgU0ViI1SOnHtGpLNyPKiERRmQi0QCKFFUSAFoJwOjN1C5srmtYBXDXFAQIuNMGpZF/fnGc/7vX1/TjX8W3z/PE97z33POe85z3nPec9xwLICY5lTo5OEP13mmjxOqIVK9ctvdmSCYJ9AYKZT8sMIsN3o0ODsfN1K1Z+/0pacgMR0YkpITs8+knc... | <image>As shown in the figure, points A, B, and P are three points on circle O, if angle AOB = 40.0, then the degree of angle APB is () | 20.0 | 98 | [
"80^\\circ",
"140^\\circ",
"20^\\circ",
"50^\\circ"
] | C |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAG4AAAB6CAAAAAB7dzmqAAAK3ElEQVR4nMVaf2yU5R3/vG8rr4zD0+0IZzxWsYc9UjoP24RD0F5HHSyrQjcXMNYEk2qXgMEMDCTijmQSIdHZbdbUgPOIGHEw200crQV7jddYBu6qVK+ENm0tLJB2G/XqvLcc73d/vO9774977733Pa7bp0nveZ9fn++v53mf93kehpADxMgpvm905PS3mOoHAL8Tjsq7PauLcrXXgMlBJ5ONdfVELgY85RUuclQBwKfTuBz//KtPS2qCazx6... | <image>As shown in the figure, AB is the chord of circle O, OC perpendicular AB and it intersects circle O at point C. Connect OA, OB, BC, if angle ABC = 25.0, then the size of angle AOB is () | 100.0 | 99 | [
"80^\\circ",
"90^\\circ",
"100^\\circ",
"120^\\circ"
] | C |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAGcAAABzCAAAAACgbUOoAAAKq0lEQVR4nNVab2xbVxU/L4W9D3NnIV5WT30jG/GooVJnEaZmrJVTKR+iaeqClOJKyyCdpgRUYJ4atEzqZIEKM6IfgrSWdNVYkDph1m4eowhXyqiLOogUVHcoWzrmLpmcri6ewJs77aV1748P9/257/n9sT2BxFGb53fvue93zrn3nnvPuVcCtU6QTm2It8EvUFc7zNL1xzpDaQcHRLT/C9H/Oo5EdDj+focwbdltpX5vd+h/gPPzJ+hLHcK0... | <image>As shown in the figure, given the angle of circumference angle A = 50.0, then the size of angle OBC is () | 40.0 | 100 | [
"50^\\circ",
"40^\\circ",
"130^\\circ",
"80^\\circ"
] | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAJ0AAACSCAAAAAB6G5ffAAAL4ElEQVR4nO1cUWwcRxn+XbXq1hXNSSXkKkq9CRLeikI3iIcLkfAmavCmomTDi90Hkgs89AIoPQQPbkt1DhJySiQuCOi1itAZpOKUh56dh54tIZ1dNbLzkN4FidqoCncWtHeVGq1fkt0Qo5+H3b3b25nZmd3bQiT6xXK8s3Oz3/wzO9/8M//cEMIdjLv+1wRC8Qm7+Lg7oXI2Osuw2fKu0qOQSauDlzok8lb8s/jLnT/NvH+UfndteWmroaTH... | <image>As shown in the figure, AB is the diameter of circle O, CD is the chord of circle O, angle ADC = 26.0, then the degree of angle CAB is () | 64.0 | 101 | [
"26^\\circ",
"74^\\circ",
"64^\\circ",
"54^\\circ"
] | C |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAGQAAAB9CAAAAABxUJnbAAAMmUlEQVR4nLVae3AV1Rn/nRPcOPRixjZpol4MkYu5VjokKPVFSQIoOFiIQn3QKEGYhodTImaGdLQXnCkjHSlCK4+OoYR2qlQiVEVJlEeiZKpgCWqAIAmGJkIInQImIllzz9c/zu7e3buvrJZvMrln9zy+5/keZw8jDBSIuNaqzcwf8CwA4P5DdBxMG0tqOQZOWjAkzGjErh/BvEZ+eyTC+L9+1CkEY2XASDgAECe0f3lHRugyIQEAYmB4fgly... | <image>As shown in the figure, in circle O, AB is the diameter, CD is the chord, AB perpendicular CD, the foot of perpendicular is the point E. Connect CO and AD, if angle BOC = 30.0, then the degree of angle BAD is () | 15.0 | 102 | [
"30^\\circ",
"25^\\circ",
"20^\\circ",
"15^\\circ"
] | D |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAIoAAAB+CAAAAADe79a3AAAJJUlEQVR4nO2cUWgbyRnH/zbbi+I8RJBLUVtaL85RiyuUjWmpDG21pMmd+mQZDux7aCwX2jhHwXYJtd17sA1tHZ8NTqAXNaVU8cHFOVrOyUvtu4dGhgY7BcfKQxsdh6t1S07KNYfUB2flZsvXh11JljS7O7vS5gzt38byjj6tf/vN7My3M9+4hXBQ1PppA1T0fxSWvEbRzra0tLSceXIAUITfDmwSfbPrk08fBf8pBoHx5xMHAOX+0Tbg0JkP... | <image>As shown in the figure, AB is the diameter of circle O, points C and D are two points on the circle, and angle AOC = 126.0, then angle CDB = () | 27.0 | 103 | [
"54^\\circ",
"64^\\circ",
"27^\\circ",
"37^\\circ"
] | C |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAIgAAAB4CAAAAAAMQ+WXAAAOlElEQVR4nM1bfXRV1ZX/nfNQYQwGCCGhBoNJSILxI+JHYpEEEQUrjIy6ygyDCJJKbTpjVFrAtmG5YJXQ1SVaseKgJG2dBVZgzahUZg01IXwFtYYZoCFNAqFhTHjSNBBILvDO+c0f97737vu+7/FYM7+1IO+eu+85v7v3Pl/77CuIiNAy6EpL4GhP41dtOHMUQNFoFGY8kFkYIgotgwpiQ0QhEgx+Vr+7/s4R936jQN5QDOj/Oif++NXnZw9P... | <image>As shown in the figure, AB is the diameter of circle O, points C and D are on circle O, and point C is the midpoint of arc BD, passing point C to draw the perpendicular line EF of AD and it intersects straight line AD at point E, if the radius of circle O is 2.5, the length of AC is 4.0, then the length of CE is... | \frac{12}{5} | 104 | [
"3",
"\\frac{20}{3}",
"\\frac{12}{5}",
"\\frac{16}{5}"
] | C |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAG0AAABtCAAAAACOk7CKAAAJSklEQVR4nLVaf2gb5xl+zmnJWL2qay9YJWrUzGqrzIaZOgFDvDnZ1M2j9sio1wzqDo+lM8ywqcMK/iPgdfgPr81oUxxmNxlLSVIycOeCvc0guVGYC6YaZAMn9piUOlVClKlQZfKYRq7fsz/uTneS7k4nS3kw1t133/c+7/t+v7/vlQgnUDJ+KeHO39ZvxYHUDQC+Vty/3/fk083leR0gObOZcOP9aPxW92Ot+5rxuB/A9evcTKTSy74Dz4Ra... | <image>As shown in the figure, the points A, B, and C are on circle O, and it is known that angle ABC = 130.0, then angle AOC = () | 100.0 | 105 | [
"100^\\circ",
"110^\\circ",
"120^\\circ",
"130^\\circ"
] | A |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAHwAAAB5CAAAAADeuBrRAAALoUlEQVR4nNVbfUyd1Rn/vYC+VVE03qZv02sYLW4YukiE2ruU9qIh601WI0Y2lkgnzbrhgtlI5rU1wTEni7S62GSYuWBSmmHGIlv/WBNphuGjdEWhq0thNBEuWEhGhS6Xck3vVfr+9sd7P97vjwuZ2RPCfd/nec75nXOec55zznPOKxBZEh8bAoCs0wPIyTqlMBiMkGHhKwEHUAQc3/fiVwJ+7lEA2P3RVwL+1ycAYOc6rC6sLymFF4VjAMBs... | <image>As shown in the figure, it is known that the radius of circle O is 5.0, the central angles of chords AB and CD are angle AOB, angle COD, and angle AOB is complementary to angle COD, chord CD = 8.0, then the length of chord AB is () | 6.0 | 106 | [
"6",
"8",
"5\\sqrt{2}",
"5\\sqrt{3}"
] | A |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAK8AAABkCAAAAADV1j/eAAAMBklEQVR4nNVca5AU1Rk9t4GsNBWNwspAbUR5DFXBRFRmo27QAIPEoEkVvYggYAxDAUlMFaORH0msAGOM+ZFU1MxWfLAkhF0IDytqcHioyYLCLBAgxCgz65YIVZqdBYIQmFnte/Kje2Z63ndmm6Ryfszevn0f5373+7777BXE/xW0/zWBKjGwplzx7h05z5qcNKYR8r/QeKGgDxSgyD52bvzbWUzOS/L3f2HypLnucisGFb5pUKB309Zdnrtv... | <image>As shown in the figure, AB is the diameter of circle O, CD is the chord of circle O, and the extended lines of AB and CD intersect at point E. Given that AB = 2 DE, angle E = 16.0, then the degree of angle ABC is () | 24.0 | 107 | [
"32^\\circ",
"24^\\circ",
"16^\\circ",
"48^\\circ"
] | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAIwAAAB8CAAAAACeOQf7AAAJhUlEQVR4nO2cXYwbVxXH/xti4gRBBtGCVZXusJVY05dO+4LTCHlaEq1TIdbhJa5Qs14eaBoekk0QNQ8oWwm0WSKxSgXdRrR4g5B2I6F489Ld8FF7hSJnK23sfYCkCtQT+uGFptg8bO14LB0exh6PPXc+7ngMSHC0imfuHI9/c86Zc2fuPTdDhP8e2fGfBjDK/2GsZNAw754e+uxLb2bcKQ8Y5k60vv33+7427FKdBinKyDkiqsfvulMfrGUW... | <image>This question examines the theorem of angle of circumference, the key is to answer it based on the relationship between the central angle and the angle of circumference of the same chord. 4.0. As shown in the figure, AB is the diameter of circle O, C is the point on circle O (except A and B), angle AOD = 136.0, ... | 22.0 | 108 | [
"44^\\circ",
"22^\\circ",
"46^\\circ",
"36^\\circ"
] | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAHIAAABzCAAAAABh6gkEAAAL6ElEQVR4nNVabXBcVRl+d7uhCrE72t12nd6STrttVqOSbtXGJho+MhqYNkRICaWRj6FOBuMMiw0aNJM6YxgDFqaj0UltwagplKEEGCJECTQtjY3BaZghbVqyhNINdLthtLIxLLn3nscf5+7d+7l7d8sfn0n23nu+nnPe856P9z2HkAcGKsn/2NED+WSxgJscQ7zxJ4/gvdmbVznPYg3HlVuoq/gQwHzFhUtspcdx3f5w/LnPEJFny7JLbKQL... | <image>As shown in the figure, AB is the diameter of circle O, and points C and D are on circle O. If angle BOD = 130.0, then the degree of angle ACD is () | 25.0 | 109 | [
"50^\\circ",
"30^\\circ",
"25^\\circ",
"20^\\circ"
] | C |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAWIAAACTCAAAAACRjkyuAABeC0lEQVR4nM39eZwkyXUeCH52+O0ed0TelVn31VXoEwdBAA0QAG+QFEmRHO3srESJ0uqmdskZSkNK1HKkJUFS2llpZ4dDzoiSOBSHOgiAAkUcBIizgUYf6K6uO7PyjsyIjNPDbzez/SMis6q668gCsCBe/35dGeHm5mGfP3/23veemROhoAgkoKAAgrtFQYGA0MlHefuAglKEAASEqPF3hIpcUaIEBaCUkgrjQwe9EiUVIQQAFHn9xZRSSilC... | <image>Shaoxing is a famous bridge township. As shown in the figure, the distance CD from the top of the round arch bridge to the water surface is 8.0, and the arch radius OC is 5.0, so the width of the water surface AB is () | 8.0 | 110 | [
"4m",
"5m",
"6m",
"8m"
] | D |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAHsAAABSCAAAAABRD/RdAAAHkElEQVR4nL2af2xbVxXHvw/SZtK8PVAd1dMsuSBPGCViBktrqmVzQIV50lRCt5IOMuRJ6Q8poLZKoYlakVWd1FS0IoJm8paKmhGxVMlE/ijMkQpztpSZpeBUCXIAp3FIBe6SiQSvYDPnffnDfrGf8+z3/Oz0/JG8d+5993PO8Tv3nnttgTAqv97ytdwNhfIHEIywKQC4/UU8e95kEAsA+ISRhwQAeL4tstBwXb4zJDQovc4k6TcdSRodgDTK... | <image>As shown in the figure, it is known that angle α = 130.0, then angle β = () | 40.0 | 111 | [
"30^\\circ",
"40^\\circ",
"50^\\circ",
"65^\\circ"
] | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAIsAAABCCAAAAABClXpfAAAJiElEQVR4nL1ZXWxcxRX+Zu5er3djY+KEOiYpIXGooppCgCJRCgGCUyQa01RUfWhVkFo1feAJCfdHVV9KRQsIRFsEOKnU9qEvVWkbSFBTm4IqodK+VAIhIN4NP07wX7z+ubv3zp07M18f1r94/7yLel7u7sycM9+cOWfOzDmCiFW6HbGPzZGcudQPkXWQLs6487s2yb6BYgnZqowyidZFECKhD0SifbOsQWdxdjeKGU+1SVvsmuppGYxLRVvw... | <image>As shown in the figure, when the width of the water surface AB in the circular bridge hole is 8.0, the arc ACB is exactly a semicircle. When the water surface rises 1.0, the water surface width A′B′ in the bridge hole is () | 2\sqrt{15}米 | 112 | [
"\\sqrt{15}米",
"2\\sqrt{15}米",
"2\\sqrt{17}米",
"不能计算"
] | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAGMAAAB0CAAAAAC0g9NqAAAG3ElEQVR4nLWaX2wUVRTGvzvbHZZqQpUQ1ieWNuK+0aCYGkJbCMQND7LExLYaaCuN/HmxJBI1hlgwAQkPhSeCQduawLYYaElMWvtgIJHYmiy0iSYYUbYPWCJIayJ2Ozu7x4eZ2Z2ZnZl7Z/+cl7l3Zmd/e8/MfPPdc5cRqh5S9RE8xmXGdj75oJqMuYabRBc3hyvNGJnLN5ff2XEBWLevodKMy02LRvPq45MA8NK6MhkgW3Q927yktdJbztgP... | <image>In the right triangle ABC, angle CAB = 90.0, angle ABC = 72.0, AD is the angle bisector of angle CAB, and the intersection BC is at point D, and crossing point C is the high line CE on the AD side in triangle ACD, then the degree of angle ECD is () | 27.0 | 113 | [
"63^\\circ",
"45^\\circ",
"27^\\circ",
"18^\\circ"
] | C |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAEUAAABeCAAAAABQ94atAAAGF0lEQVR4nLWZbWxTVRjH//eOl0WZy2pKhlYGmwRcBCcyxSX9MJXCJiTwgei0BiRZtOqQYeHDPiyBCMpgvCzEaUYc0RrfMIEZTEYixCEhGTHTgjqg6IwpsgUa6JZ0jt7z90Pvbe/tfVk38Emze+85Pb/zvJznued0EnEXRLZpnxjcjiLdFcrExIHy7bm7QLm9CcjVP9YUAmictQDM0T/WFAlofeJ6rgx7iyJxb9F9OTLsKTu24eGcIXaU1sPS... | <image>As shown in the figure, AO is the height of the cone, the bottom radius of the cone OB = 0.7, the length of AB is 2.5, then the length of AO is () | 2.4 | 114 | [
"2.4",
"2.2",
"1.8",
"1.6"
] | A |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAH0AAACNCAAAAAC/eSrgAAAN00lEQVR4nLVcW2wcVxn+ZglrF0WkRqTZSBVrB1pPBGomfaATLlmnUhMDUthUCLsPKGtenAhBNgnC7gPbFkS3FcQpL92kD10XBZwiYQekOqkqZZ2g1K5A2RQJrSOXdQyItZG6TilkNxs0Hw9z2bnPrHf54njmnDnnfP/5z3/OnMs/BgNwEgDwFEkq2n/qASOkOPOFgkAE4PvX3tpc+1L0rc0ABftDZ0xLiPg/Ju4t7d+M+17/y08BCOYHgDXm... | <image>As shown in the figure, in circle O, chord AC and BD intersect at point E, arc AB = arc BC = arc CD, if angle BEC = 110.0, then angle BDC = () | 35.0 | 115 | [
"35^\\circ",
"45^\\circ",
"55^\\circ",
"70^\\circ"
] | A |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAEcAAABYCAAAAACCW7WNAAAIk0lEQVR4nK2Ye1QU1x3Hv3dmHywIBoioIGoV8JkKhsZ20zbEKsTH6qmtb82xPkgE6iuuJm167In1tLXqMSoGNBWjUtvaRlGipiBNbDFHTRWNpSYCiqjRQxOe7u6wM/PrHzOzO8susiz9nQP3zNx7P/f3/d3Xzg9EZAOAcuqVgYjIVkZlqOk1RwZRzf+BU2Ynstl7hSEQUSHQS2+IOAClNVSYVAsAACE044BaDEc2zinPLGQOnZsO1GJYiADN... | <image>As shown in the figure, in the sector OAB with a radius of 1.0 and a central angle of 90.0, OA and OB are the diameters respectively as a semicircle, and the area of the shaded part in the figure is () | \frac{1}{2}cm² | 116 | [
"\\picm²",
"\\frac{2}{3}\\picm²",
"\\frac{1}{2}cm²",
"\\frac{2}{3}cm²"
] | C |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAUsAAABfCAAAAABE7Lp7AAANcklEQVR4nO1dXWzb1hX+aHWwim5xtQ0Lu6GRvRerAbbQeVjodJjkAWvkAm3tAquTFIhlDIgdDE3sYmhtYHXSPcxGB9hJt0F2Hkq5fZD3YicFZqd9iOQBrZRuqJRuiBwMk9PuQQKGSXaGRupm6eyBlERJFElZlCwX/hKIvJeH916ee+455/6aIexDFcQAAAZ/8HNZSBHMPi/14Zvtf1FlJICWBhVlr2P5kX+FtWhql0uxsqQqI6hX3Z5F//2D... | <image>Use a sector paper sheet with a central angle of 120.0 and a radius of 6.0 to roll into a conical bottomless paper cap (as shown in the picture), then the bottom perimeter of the paper cap is () | 4\picm | 117 | [
"2\\picm",
"3\\picm",
"4\\picm",
"5\\picm"
] | C |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAGIAAABuCAAAAAD5DJmpAAAIWElEQVR4nM1aT2wcVxn/zbICI9rYEVA7qshuOdTbC55c0PZQ1gkc3Eu6e3JbijASIVzA7okKoaVBIo4F3UQcYlQEcU/hwhoquWokWie0yC6oWZdD7VrKxopUzTYqDnZEdp3xvB+H+T/zZvwmTiQ+Wd55f3/f733fe+97b0YjskjvKweuZWoAIJ+t+vlPP82KgJxyTYLo/Waqv5MVQssyUDx348A/SmcfJESvtPzR3RPLQwCoPQgIamdvnAXO... | <image>The picture shows a small paper cap with a conical chimney. The length of its generatrix l is 13.0 and its height h is 12.0. The area of paper required to make this paper cap is (the seams are ignored) () | 65\pi | 118 | [
"60\\pi",
"65\\pi",
"78\\pi",
"156\\pi"
] | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAALcAAABWCAAAAACoHVhkAAAIsElEQVR4nO1bfWwT5xn/cbJOVgFxbCmYzKPHFjrDKDkgW7I2Ii4fiiEhH0CAsQaSrYx2U9e0448WTVRrpYH2BxHrR7RVU5mqbaaMJYQCTgPlXHWS19FxXRkYcBSTZmC6FK6Crp4bXfbHneM73/edvbnSfkT2+77P87z34/Vzz/vc68dTJvC5BPG/JuAQ/+f930XJ8756SHN4Sqnfl7XcHa3hkl/vsX+ntYZLnTf/ARXRGi913uxy5rTWuMf+... | <image>Use a sector piece of paper with a central angle of 120.0 and a radius of 3.0 to roll into a cone-shaped bottomless paper cap (as shown in the picture), then the height of the paper is () | 2\sqrt{2}cm | 119 | [
"3cm",
"2\\sqrt{2}cm",
"3\\sqrt{2}cm",
"4\\sqrt{2}cm"
] | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAJsAAAA0CAAAAAC4QBVrAAAErUlEQVR4nM2ZP2zjVBzHf62ozmwWElKQkC43nSdqpprpjBBSKpCamyhiwGztRG+CzQvSiSknMbSIIT3ppFQsuZtSWFKxxJ3sTokYcDqlm72gZ3TDl8Gx4z/vOXbiHHyH9Pn98fv4vd/7vV/f2wL9b7X9XwMUqIDt4vjNYXAlZrv7cXL5BkE42hLa2/Fua9+W6ugjsHyHbqdERKTdkzRZLddOyGY9GdGz2866XJfWteNr8i41m+Frg38sf6Kp... | <image>As shown in the figure, the expanded figure of the lateral surface of a cone is a semicircle with a radius of 10.0, then the radius of its bottom is () | 5.0 | 120 | [
"3",
"4",
"5",
"6"
] | C |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAQ0AAACACAAAAAA0IGNmAAAQ5UlEQVR4nOVdfXQUVZb/VbcYloHBZMjYZLOGj/C1WTSCwRECZHYIAss34cNDZsgwAXfJsgg0yowI4kQmLirMOTDAZGbNnuFIFBwGcDFB1EBABF2DKxjQIEEMC4skgbASsev99o+q7q7qruqu6u7Ek97fyemqeh+33rt133333XerIhFxiiV3ru4q2awjxS03fjD46+N2ueFok5Z89xA77sxqedNurbiVjWEp/Qa8esBmpTvapCnfPd68fgLy... | <image>As shown in the figure, use a sector cardboard with a radius of 24.0 to make a conical hat (the seams are ignored). If the radius of the bottom surface of the conical hat is 10.0, then the area of this sector cardboard is () | 240\picm^{2} | 121 | [
"240\\picm^{2}",
"480\\picm^{2}",
"1200\\picm^{2}",
"2400\\picm^{2}"
] | A |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAG4AAABuCAAAAADjMHknAAAJMElEQVR4nLVaTWwcZxl+ZuSNDYKmUdV0I6ps0gMMl2bcA95UgmwkRJZKTdYHSCMBcS9NciG2WhW7qLt2BbJ7sY0QtRsOtkrBCKQ1RLLJCduVkJ0estsLNj+1m3JYB5FNE5B3M9v5Hg4zszv/O7NNXls73//zvT/f+73fNyMRMUnIqD/W/R85bj8AQFcHaHhrb68zNMTuJgO7v3zlyTIgYgsGAOPTxRkufZuig56MDydKKslckUKQ1B82HE+s... | <image>As shown in the figure, the length of the generatrix of the cone is 5.0, and the length of the height line is 4.0, then the bottom area of the cone is () | 9\picm^{2} | 122 | [
"3\\picm^{2}",
"9\\picm^{2}",
"16\\picm^{2}",
"25\\picm^{2}"
] | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAJgAAACDCAAAAABUuI2lAAAH0klEQVR4nO2cT2wcVx3Hv6+JlAuwHBKxkSyc2K7YQBBGXCo1xTZ1apd4glGBvbRqkKxYqAe3opvmEHl88AGBURCKUDZR1YKA2qLiT2zoLrshBjniTw9upUa21F3LVTi48qEObukYzHw5zJ+d2ZndfTPzCgjNV/buvJn3fvPx7/feb9688a4gVKp6vFeRpfsU2bF1WpkltWAXNFUOg1AZymLvaWXmVHqsLo5ryoypBCueR06ZMYVg174j+oQy... | <image>The production process of paper umbrellas in our country is very ingenious. As shown in the figure, whether the umbrella is opened or closed, the handle AP always bisects the angle angle BAC formed by the two ribs in the same plane, and AE = AF, DE = DF, so as to ensure that the umbrella ring can slide along the... | 2400\picm^{2} | 123 | [
"48cm^{2}",
"70\\picm^{2}",
"2400\\picm^{2}",
"2500\\picm^{2}"
] | C |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAG0AAACKCAAAAACF0puwAAAIL0lEQVR4nL2aXYgb1xmG3926ZoLNWrQQq03bVdISq067VkJpprTgcUsb1VAitxjv9sLdJRfr3LTaq8gJdJ2LsjYYdn2R2L6S65u1oUXrEtAWCtqFGG2hoCUXllxKpU1LtKVNRpTCjFPStxfSSDOj+TlnRvKHzc6cHz3zffOenznnTBCP0SYfJ2xstA3P1IkxRVKb+p1H6nh8MxdyX17zyuAYzMgVyWx5OGMcNF0rkzTU2uOgNbUqSbKtNsdP... | <image>As shown in the figure, a sector with a central angle of 120.0 and a radius of 6.0 encloses the side of a cone (the joints are ignored), then the height of the cone is () | 4\sqrt{2} | 124 | [
"6",
"8",
"3\\sqrt{3}",
"4\\sqrt{2}"
] | D |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAFUAAABbCAAAAAAnlJb2AAAGHUlEQVR4nK1ZbYhUVRh+zrnzsTO7qauOSixBGKlFIoYmipSkmIUkbfbl+ickI+iHQQgZ2Y+gT7EQKQlL7BsxwZJCiEDUhJDNyo8wVqXMj8V1l9mduXNnzvv0497dnb2zd+7MnXm4zJ17znufe85z3vc959wLRoSQ7CNJY8g1vkqNiFAooh0AtIb5w1cZmRXQgOP9vSJNY7WAhPfP+GgaYC1DyXfdHFY/orMKgP29zWbVQHHbBQAiTEL8dREg... | <image>As shown in the figure, in Rttriangle ABC, angle ACB = 90.0, AC = 4.0, BC = 3.0, rotate triangle ABC around the line where AC is located to obtain a rotating body, then the lateral area of the rotating body is () | 15\pi | 125 | [
"12\\pi",
"15\\pi",
"30\\pi",
"60\\pi"
] | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAI8AAABuCAAAAAA7EB9oAAAJI0lEQVR4nO2bf0xV5xnHv7zlejWsckvixR8VvMZ4nWECropZixdLE1xtxrUjA6IZDruSdYaVGuOGXYW4Y7ZQtTNWukydZrXC2lWoq4VEnLftOlgTxcWuYFrhVlwHZhPSkfV6snf749xzz6/3nPOec67d/vCBcN/zvud9zofned7f52ZQ/F8J+V8D6OTO8CTqx13WzKBYOZhOFElmj/vdVcygIG5DKHH80MSq1TOCQVzB2MWPK7YXJvM3oset... | <image>As shown in the figure, cut a circle and a sector piece of paper on the paper so that it can form a cone model. If the radius of the circle is 1.0 and the central angle of the sector is equal to 90.0, then the radius of the sector is () | 4.0 | 126 | [
"2",
"4",
"6",
"8"
] | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAMUAAABMCAAAAAD47Cw8AAAJYElEQVR4nNVbf2gjWR3/xhNXZLmc7ujNejn7x8UzexWMdmGzXJacUDUHHahcsNzd/hGh0D+CuHANVq0bxIoVqvSPIh33j41YcMHqIqxucYqbZXtuz3pkwe7l2J1KuAg3Z44zd90/In37Pv4xk2SSzLyZSbtL/UAyee9933vfz/v5fd+XCYEOPd49FiKERBIfeliqDAxc/0qISEji/4BFaJj+4CVz+Fn893T2+/c9ZA4/i6UT35ZWPGRCh312... | <image>As shown in a sector iron sheet OAB, it is known that OA = 30.0, angle AOB = 120.0, the worker master combines OA and OB to form a conical chimney cap (the joints are ignored), then the radius of the bottom circle of the chimney cap is () | 10.0 | 127 | [
"5cm",
"12cm",
"10cm",
"15cm"
] | C |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAGYAAABwCAAAAADJO1o4AAAIY0lEQVR4nLVZfWgcxxV/q1Ns/5F2G3LFWyJHhruSs1XKGsm105xYlSq1UgS5QokwdonSBmTa0srFIXIxuTNRqAIqVqgKLnKJQlVwW7Wngh0cEOWuVqpzTXoKiX0XfG4OVMo5dumZuHiN9+b1j/242d2Z3R1FeXC7s/P1e7+ZN2/ezEkIolJLCjeBjuhVLYX+0rP2qcJI5uvaliviMICCoitnkrpoIxRgY8rPtPWO08JkJEET+E+q9JvGn6uy... | <image>As shown in the figure, it is known that the radius of the bottom surface of the cone is 6.0, and the length of the generatrix is 10.0, then the lateral area of the cone is () | 60\pi | 128 | [
"60\\pi",
"80\\pi",
"10\\pi",
"96\\pi"
] | A |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAGUAAABlCAAAAABxF3ITAAAH4UlEQVR4nLVafWyVVxl/zr30XjpKFxtgLXagd1qphaSwVTtSLEjpBGSpdIBbADFEzdyWFSbLZpfOmLBoQNMYtmhYZLg4G6ugoWN0rI6PBSJIyVbLdcJqHZuMzsLtut5737f3PT//uPf9/jjn3tVfCPc95zzP83vOec573uecUwbKAYykICtnRch4klU25RAg5dCRETXd1+K9b8+45b0F6Q0LpSlkWXSc7tUi5Z8un/HfzN+qtb71XyXp8YMO... | <image>Lulu cuts a circle and a sector piece of paper from the paper (as shown in the picture), and uses them to form a cone model. If the radius of the circle is 1.0. The central angle of the sector is equal to 120.0, then the radius of the sector is () | 3.0 | 129 | [
"\\sqrt{3}",
"\\sqrt{6}",
"3",
"6"
] | C |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAGQAAACHCAAAAADFWaOkAAALjklEQVR4nLVbe3BU1R3+zg0mVoJr7QYWmzbVLBKNjw21kipOUMOQGorYwQnTBs0gsLZ0Bqi2hpbqVGgHW8ZhKoEozoAKDpYU1IIklDqhowUBWarRgCSQcUGX1A4LS4fdZe/5+sd97N3du7s3r++P3XPP6zu/xznnd87dBUcIkjMhgG2SJEaOhDPbuBsBUioYIQjEe6ejAgDEiJEA704ZjcULfcDIqYtsAUSAHEl1AR0Brq0KcETV1Xfhdsyf... | <image>As shown in the figure, there is a sector with a central angle of 120.0 and a radius of 6.0. If OA and OB are overlapped to form a cone side, the diameter of the bottom of the cone is () | 4.0 | 130 | [
"2cm",
"4cm",
"3cm",
"5cm"
] | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAHkAAAB4CAAAAADzzQIwAAAJhUlEQVR4nMVbf2xT1xX+nu0sYkubohnF2lJCG1hBYSNaUMlEKjotrEiV13Trlknr2qBlTSdWFaaYBQGKuyIRNjrCxtQEqEo10JgGC6WVoHUmBeGOIGAwkSisOFu60C00mWSaqCTxy/32x7OdZ/v9uO8Z0iM53B/n3u+ee8+599xzHwqRB0UeLHfd1pMPML6ZR9u8kDcH3YsMJY/Z3v/g2jxa5yHzIB4Ium+dD3Lnc8qyTwV5/6885fkYhs9t... | <image>As shown in the picture, the length of the generatrix of the cone-shaped tent roof is AB = 10.0, the bottom radius is BO = 5.0, and the lateral area of the cone-shaped tent roof (excluding the seams) is () | 50\pim^{2} | 131 | [
"15\\pim^{2}",
"30\\pim^{2}",
"50\\pim^{2}",
"75\\pim^{2}"
] | C |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAGkAAAB1CAAAAABo/ZAGAAALmklEQVR4nLVaf2xb1RU+Tuq6rOmibUY8hpEFMbKnlJE2nWqJbAk0E0YKmdE6pRNFhFGaSdUgU6s1k8qCWCbMxkYmNVNG/mgQ7RRomJkaJmekiysFLSVsHmpDQLiLi4fmKoDcugjHdu+3P96v+967z34J4lOi93zeu/c755577zv33EtYJ5h6M+KijtLjtQvU0Trhki8Z19sMxzbeiNol1muTjFJwPwAcfPkLtElWc+yT3xIR3Xqbk5c/n0kx... | <image>As shown in the figure, in circle O, the length of chord AB is 10.0, and the angle of circumference angle ACB = 45.0, then the diameter of the circle AD is () | 10\sqrt{2} | 132 | [
"5\\sqrt{2}",
"10\\sqrt{2}",
"15\\sqrt{2}",
"20\\sqrt{2}"
] | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAMQAAABmCAAAAACxGWFSAAAMrUlEQVR4nN1cf3AU1R3/bO5iosaGqRc49OghBAwelUh0iIJNGUG0RprSjOAQh9jipDSdIRYYQ4mAU1TUoHEaNTSo5xg1DHFCJYzYRhswEWywQXuIyiGHAQ3G1tCgxNu9/fSPvR97u3tJ7sjdxX5mwu1+39u3n8973/f7LaAGqwBgUb/WPKohEBqsOfXy8eIrX9aaRzNStAbxk9twxdxkUIkd5tAlBQA48fF88fEtHcniExNUJSEAAN76eNwF... | <image>As shown in the figure, in triangle ABC. angle C = 90.0, point D is a moving point on BC (point D does not coincide with point C). The circle with CD as the diameter intersects AD at point P. If AC = 6.0. The minimum length of the line segment BP is 2.0. Then the length of AB is () | 2\sqrt{13} | 133 | [
"8",
"2\\sqrt{10}",
"4\\sqrt{3}",
"2\\sqrt{13}"
] | D |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAASgAAACHCAAAAACAUZtKAAAcl0lEQVR4nO1deXxU1b3/njvLzTIhYciEhEwSMgGSkhBCKDWCSABlEQRU+rTVumFdgApVXl2er+Ir7cOtFaWo1ZbyRK2iiBaoQUAQUBYhEAhkQhISMiEhk20yS2a797w/7uxLmCQzk/T1fT98mHvPPfec3/ne3/md31lDKEIBJQAAHkxI0fsLShHhHPqNEMUiAMrKeZCICgPCMOD5yObRT4T+/WyrCCJNFAAG4IHQ9DyaCJ2o5zLHRKVaMAwi... | <image>As shown in the figure, in order to measure the height AB of a pavilion (the distance from the top A to the horizontal ground BD), Xiaoming placed a step DE (DE = BC = 0.6) that is the same height as the pavilion step BC beside the pavilion, find A, B, C Three points are collinear), place a mirror horizontally a... | 10.2 | 134 | [
"9米",
"9.6米",
"10米",
"10.2米"
] | D |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAIMAAABqCAAAAAC6vb3wAAAM6klEQVR4nM1bXYwlx1X+vqrqnvHs7G7WkD/HgDzrCIORbIlonQdnRhgJZR8cJUiBKAaxiwghYEdxcgeywbHXli12vSYhksWPEJmxhEgkHhBEMnnCmjERIrwsEkGg5A5R5EQkthcneOenu6o+Hqq7b/f9mzu7O8DRndvV1VWnvjrn1Dmn6vZAs9EyAKzO2PiAhFkb9jYkrB0KBoMZ6avLQO9rs7Y+EM2KYQt4BV+981AwuBnbbZ4tP//y5sah... | <image>As shown in the figure, in order to estimate the width of the Jing River, a target point P is selected on the opposite bank of the Jing River, and points Q and S are taken near the bank, so that the points P, Q, and S are in a straight line, and the straight line PS is perpendicular to the river. Choose an appro... | 120.0 | 135 | [
"40m",
"120m",
"60m",
"180m"
] | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAJ0AAABQCAAAAAAmOyhgAAAIi0lEQVR4nM2af2ydVRnHP8/bdvdaHaMd0JaZzbniLtPABExWEtkmQzbYnfxQcYtol4BkGoEt3NmEsHXBuB+YTQhqOtQO/nAbJAZQNvV2tkSzzhhhEMw6ubdDEu0dbO0adL3b+p7HP973/n7f29tfufebvj/Oc35973PO85znnLdo5aADwhpRNWmJRaUgLjHVPdIMAqgjLKOuckFEVTUSzZZVjO72sguF5vnZQtFy0cmD7H0w/a6CCkBF6E4h... | <image>As shown in the picture, Xiaoying designed a flashlight to measure the height of an ancient city wall. Place a horizontal plane mirror at point P. The light starts from point A and is reflected by the plane mirror and hits the top C of the ancient city wall CD. It is known that AB perpendicular BD, CD perpendic... | 8.0 | 136 | [
"6米",
"8米",
"10米",
"12米"
] | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAHoAAACECAAAAAB6qmBRAAAMjklEQVR4nN1bf2wcxRV+G4cGgeFS6SxfmkNnyxfZrYO4YBBGBM4Up7kgNxgSFFoFkQjXoUQqqZqIVHVqWgXhqK1w1BgCjoQjKKQQ4oi6zVmE4AhHcpSEC63DJcqlvupsxc6BZLAhjnc9X//Y3bv9MbO3G6dU7SfZNzvzZr59M/vezryZJcwacaoDMERSnbd6NHtqTFcmGDDU7LHaHLoW6JUI537qsdKsqUF05PXXJ0n6NKJdfmPUEtGZO2Nx... | <image>As shown in the figure, in circle O, point M is the midpoint of arc AB. Connect MO and extend it to intersect circle O at point N, connect BN, if angle AOB = 140.0, then the degree of angle N is () | 35.0 | 137 | [
"70^\\circ",
"40^\\circ",
"35^\\circ",
"20^\\circ"
] | C |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAGIAAAByCAAAAACNGFtJAAAJzklEQVR4nLVafXBU1RX/3fs2uyTZfBDYkISQQIAEmtpAMBAC1YaCZUACItDCMLZWrTpOwQ502hlaKtqCg6J26DClTsHaFGzVkSqxCKMWavgsFoFATSKQYEKSjSEfkI/dvff0j/fefmR3376XhjO7896977z7O+fcc+49994HMkm9L5jlHEwcsYgAAN7v9cTkjEKxIRgAwt538+8cBACwusaKoSKYhOhbt/7LCQB0s90BiGf+1HV7EgDVbFbJ... | <image>As shown in the figure, in order to measure the degree of tree AB, a certain mathematics learning interest group measured the length of the tree's shadow BC in the sun as 9.0. At the same moment, they also measured the shadow length of Xiaoliang in the sun as 1.5. Knowing that Xiaoliang's height is 1.8, then the... | 10.8 | 138 | [
"10.8m",
"9m",
"7.5m",
"0.3m"
] | A |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAK0AAABkCAAAAADRI+/jAAANOUlEQVR4nNWba3Ab1RXH/xtHiZ1mMAE8sTPUsgsppp0BmXSKSCCy6VBcOqQyLZhXEydhmjCFRiahOJ1BgbTFaYfIgQ8NtBQ7lBKnQ+WBKYEPHZTHBLsDZJUZSpwa/EhLJF4SlMESFtl/P+zr7mpXdmqLqgci773n3LO/PTp79+69V2BJyWYAAMIu6jkoKXn4cf8n5D1fdVGXGG3uhbsW9r53Q72LusRoP3/vmsy+BSuWu6hLjPa1wcULFi10... | <image>As shown in the picture, it is an ancient masher in the countryside. It is known that the height of the support column AB is 0.3, the length of the pedal DE is 1.0, and the distance from the support point A to the foot D is 0.6. When foot D touches the ground, the head point E rises () | 0.5 | 139 | [
"0.5米",
"0.6米",
"0.3米",
"0.9米"
] | A |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAJwAAABuCAAAAAD3iSWDAAAHfElEQVR4nM1bW2wUVRj+zuylUIn4UKQJCyhoLNQQJCRoMGBStBCIIYGEmwQwQolgbEgwELkUiEaiGDQ0QPRheUDAaEqilG60SSsXW2mCGLA10kKzawRphGqr3Z2d+X2Y2fvczszZ1i/ZnZ0z//nn2/9yrjMgoVgFANtEaZMgFJ/taaTEt/VEQrQJJkc35yPwcg9jQrQJJvfbn6WE7imCtAkm17wEbO+FDWK8KppcZCtjP0RLxXgVfjFqdMTu... | <image>As shown in the figure, the light source P is directly above the crossbar AB, the shadow of AB under the light is CD, AB parallel CD, AB = 2.0, CD = 5.0, the distance between point P and CD is 3.0, then the distance between AB and CD is (). | \frac{9}{5} | 140 | [
"\\frac{6}{5}",
"\\frac{7}{6}",
"\\frac{9}{5}",
"\\frac{15}{2}"
] | C |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAMcAAABcCAAAAAD/z/6aAAAP7UlEQVR4nNWceXxVRZbHv1XvvveSkIUHCSYmAbIAiaDGtoEoClGQIcLMSIsjjmLjzODHFqYbl3ZpbZHGGRHcWrQb2/l83NoWu+1GaRAakU2WCNjNJgTCTgJhy062l1s1f9x73xISJAiRdz6f5N5b2z2/OnVOnTpV9wkNKKkFFmkBKAmmixAK5HciOe9Usq3cVqnS+ie0XrUTQABIBRYM5dS6CHx+GzldJ9H2nQ5mKhn2iINKtPwUtMOwdBh3... | <image>As shown in the figure, Xiaoqiang made a small hole imaging device in which the length of the paper tube is 15.0. He prepared a candle with a length of 20.0. To get an image with a height of 4.0, the distance between the candle and the paper tube should be () | 75.0 | 141 | [
"60cm",
"65cm",
"70cm",
"75cm"
] | D |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAALEAAABaCAAAAADSwehYAAAHm0lEQVR4nNWbf2wUZRrHv++77ZbDXsi5u2lx21ALjWDr2QCmnrk1xJZEpU0NhauxGiQirba5K4dITIMlVFIj9dREtCiGI6gBxbujlYoCCq2cP1gvjbTApXgHYRHJ7hrvvDbs7O4898fOzM7+KJ2dnWW232Tn3Xl3+ryffd9nn/eZ952CiGgALh/RyVK4fJT1AhGJNH5HHxGdbDSbRos4AAaEPwXB14RpIA4AGFz35SWGobtAJuNoUIR46N5f... | <image>As shown in the figure, in a badminton game, Lin Dan, the athlete standing at M in the field, clicks the request from N to point B in the opponent. It is known that the net height OA = 1.52, OB = 4.0, OM = 5.0, then when Lin Dan takes off, the distance from the hitting point to the ground NM = () | 3.42 | 142 | [
"3.42m",
"1.9m",
"3m",
"3.24m"
] | A |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAMAAAABgCAAAAABuqyI1AAAMF0lEQVR4nM2bf5BcVZXHP+e+/pXO/EpiEglhKdCgVbuw4YdiCEFgIULAGDFbm6AYKBWxIhtYWBdRwXWtZYtV44+VXcJaCAwSCxTUBUrIiiQkyy8d1I0shNqYwAYzGsIk09P9ft2zf7zunvd6unt6JtMz852afn3vPe++833nnHvvO/e1KNMa/b890FUKTV59lYyKaHHROxMCqSlSrCWo9H5pz/xsqdiRCUIH8N3O/oVb58ZlpjWB3910H+99... | <image>While measuring the height of the building, Xiao Ming first measured the shadow length BA of the building on the ground as 15.0 (as shown in the figure), and then set up a benchmark with a height of 2.0 at A, and measured the shadow length AC of the benchmark as 3.0, then the height of the building is () | 10.0 | 143 | [
"10米",
"12米",
"15米",
"22.5米"
] | A |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAMsAAACJCAAAAACnAJOIAAAMxElEQVR4nNVcfWwUxxX/zfpUg2JqK7KAKE6pjRHn2C1GcQLIwJmSyGcBrUmgTkQ+bAECFRAl4WKSkEJEKFCXJk5AmEJqu5AU8mmVkFuToJgzFNM4xahH7BRzBoUKSKmCi9PY5e5e/9jPu1vbd7e7t+efdLdfs7PvN+/Nm9k3M8sIAEAn784RdhhGLDhxO1vkMIKpSFyqHdnWymEEWJABaMyZTVZLoh8cA9CDLIfVghgADgD2PIkHrBbEAHAA... | <image>As shown in the figure: the length of two vertical telephone poles AB is 6.0, the length of CD is 3.0, AD intersects BC at point E, then the length of the distance from E to the ground EF is () | 2.0 | 144 | [
"2",
"2.2",
"2.4",
"2.5"
] | A |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAGoAAABwCAAAAADTB7q2AAAJGUlEQVR4nL2aYWwc1RHHf7N3ramwGlVJoG1CCTbBaaHhELSAgmrTgnIRYKImVahwsa9YSWhoCXXaumqoU5UKV41UqGKHEEtxqC1BQqqkQDkTxUkQSEWKelaVlEJxbCRDi5SKEPsDjvdu+mF373b3dvfu7HP/lk+782bf/8282d1581aU6mDo8kQJDaNKTDOPlFSpEpU+9qV6gCgfVYlq9/UfCIDMO9X45K2La0spVYdq589YDvwfHNjbI1dZ... | <image>As shown in the figure, a square DEFG model should be cut on a piece of triangle ABC paper. Among them, G and F are on BC, D and E are on AB and AC respectively, AH perpendicular BC and it intersects DE at M, if BC = 12.0, AH = 8.0, then the edge length of the square DEFG is () | \frac{24}{5}cm | 145 | [
"\\frac{24}{5}cm",
"4cm",
"\\frac{24}{7}cm",
"5cm"
] | A |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAPAAAABICAAAAADtpydWAAAK+ElEQVR4nN1af1Bc1RX+zrKAqdjVFgKOzCQIdpkhGdYCNa1JwVEmyRhDTLFpa1KTBkEho1GI1pnY3fhjJDWOsQPIOnaM1lRGsElsathKdGmawigWSIkhSsLG0BkstEKgNdm3+07/eG+Xx+7bt29hEbMfw+6795577v3uefec+2OJESMY2t/ZaVy2bGOqtpjhq+nNHEK22P6C0bKejruHLAe1xSlGLLyl5/UcAEDXplXPa0pyTKAp5yIzi8zM... | <image>On 27.0 2009.0, 10.0, 2009, Shanghai team player Wu Di came to the fore in the National Games and defeated the top-seeded men's singles player Zeng Shaoxuan with a score of 2.0:0.0, and won the men's singles championship in tennis at the National Games. The picture below is a ball played by Wu Di in the final. I... | \frac{4}{3}米 | 146 | [
"\\frac{8}{5}米",
"\\frac{4}{3}米",
"1米",
"\\frac{8}{15}米"
] | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAHgAAABxCAAAAAA7ADjGAAAJqklEQVR4nNVbf2hcWRU+01WyapZhcUJn8e2O2lkzJXWZGhcqjSS1szRKjcENG3CzmJXY+WP+2NFGNkJglM2ygY1QMFkjQRqlQjCDUzCwqRsxYsHgLDvqpqZ1UzLudO0sKXTsVBh7X+7nH+/HvJ/3vcnMUjzQMO/d++53v3vOvefce08DoBbKpYNxv1UPtBKXveC/bkuBJx+L3hfg147+y3/lFgIXq8c62u8DMGZepM/4r9464J/MBT4F/3Ok... | <image>As shown in the figure, points A, B, and C are on circle O, angle ABO = 40.0, angle ACO = 30.0, then the degree of angle BOC is () | 140.0 | 147 | [
"60^\\circ",
"70^\\circ",
"120^\\circ",
"140^\\circ"
] | D |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAEwAAAB+CAAAAACrTqhRAAAMf0lEQVR4nKWZz3LjSHLGvwIEgoQocahWT/eM97Cx171v+LDWPoHfwfsEtiP65BfxcfwCPvkF3L774gjfrPF4e2darT8QSBBAoYCsnw+U1Bqpe1vUJCMoogr6kFmZ+WVWwaFnCk7SoEyXxzQzl0hKnoslJ0lZhz9WmG+vng8mSRoO3VwDEpK098vAsk62WmRxC/YLNENSnM3yxbWSX2zm1gE+XS21uRl5tje3EhOHyiP7hd7cytC7Rfiq3148... | <image>As shown in the figure, AB is a ladder leaning against the wall, the foot of the ladder is away from the wall 2.0, the point D on the ladder is away from the wall 1.8, the length of BD is 0.6, then the length of the ladder is () | 6.0 | 148 | [
"5.60米",
"6.00米",
"6.10米",
"6.20米"
] | B |
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