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": "iVBORw0KGgoAAAANSUhEUgAAALsAAAB5CAAAAABE2w8JAAALhUlEQVR4nNVcf2wUxxV+y4/QIlr/cxVXOHBL7cTkUjB1pTiqiy3hqk7iFEe4ckyocqg4/sNIOAYCKg4miisZxZUsxUhUptI5JcFSjWhVQ0DYqiEOdeIoSOm156hOYvVc9ZAj4eRMOeplvv4xu3v7e2fts/B9At/tzsybb9++eTM77+0Rcgz1REQtAIBllGN4+/hFNjd4iogol7gDREQTFdKKnZ8R5RZ3kohoamY10cQmotziLhERhp4iant3... | <image>As shown in the figure, in the quadrilateral ABCD, the angular bisector of angle DAB and the bisector of exterior angle of angle ABC intersect at point P, and angle angle D + angle C = 200.0, then angle P = () | 10.0 | 449 | [
"10^\\circ",
"20^\\circ",
"30^\\circ",
"40^\\circ"
] | A |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAJgAAACQCAAAAADR+v2QAAAKm0lEQVR4nO1cXWgb2RU+UX5QsrQRW0ImpRDVYTdaApvJQtspZWOna6iavij0wUpTI5VtbWcfEgcKVfZFWlpiWheULWWdZBcUlzpKW9ZKoeB0H+osbJFVqiiBggxNVvJDkZYapD640kiWvz7MjKSR5k8zV+0S+oFhfs5cfb7nzr3nfPdIu0CfTrj+1wT08H9ig8IpsexDJjT64ZCYeIUNjX44JPbTvUfZ8OiDM2J3RoY2Rh01vLH56r79rJj0... | <image>As shown in the figure, BP bisects angle ABC and it intersects CD at point F, DP bisects angle ADC and it intersects AB at point E, if angle A = 40.0, angle P = 38.0, then the degree of angle C is () | 36.0 | 450 | [
"36^\\circ",
"39^\\circ",
"38^\\circ",
"40^\\circ"
] | A |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAANIAAAAcCAAAAAAxEL5aAAAC3UlEQVR4nO2WPUwUQRTH/7u3O8h1eCGIJEIO+YjlFTQIqAHB0tiYICSGj4LExEJjpaWRQGGjBgs7rlGhxK9QGCkOcwQSOsHckSgGTzsNOzs7z2Lv9o6wu+iuxtyFfzI7s/N2fvve25mdUQiVJvV/O/D3dRhSOagY0tXwsPAIX4I/3rEqtL8VWOERvgR/vGOt6IlXMToMqRxUDKkpPCw8wpfgj3esWrFLCeUMACA8wpfgazzjPHV4xisDVXZI... | <image>As shown in the figure, extend the line segment AB to C with the length of 8.0, so that BC = 4.0, M and N are the midpoints of AB and BC respectively, then the length of MN is () | 6.0 | 451 | [
"2",
"4",
"6",
"4或6"
] | C |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAIYAAAB/CAAAAAAPj+WcAAAMqElEQVR4nM1bf2xbxR3/vIQSGAEPzVHdYQhtAzFqAZcgNR3Z7NAWItGVbFQKiDClIzSgDrWjZWRSpyKtCE8YrZuolNJpBImNQLNlbFDSNV0dKaytCjWIjLQ0oYa0kM5BhLqA+2zfZ3+8Z+f9sv3suO0+UuJ333t393nf7/d97+7dnUQUCkoAcPffAVR9VFlwcUuUFVvwtZVhip/MO3OhaFAiACRlL6Tgkg0XioYECQD2XgMA1314oWio2LMc... | <image>As shown in the figure, the four points A, B, C, and D are all on circle O, angle BOD = 110.0, then the degree of angle BCD is () | 125.0 | 452 | [
"70^\\circ",
"110^\\circ",
"125^\\circ",
"130^\\circ"
] | C |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAHAAAAB3CAAAAAD+jpsvAAALvUlEQVR4nNVbbWwcxRl+1ncoDkp1SZHDoaS5uFLiQ5XiBYnmCCV7qarEKTQ5aMAJpdQIqQ79EE4DxUXtUSq1pmrjhKqqA4U4CQiDqjppWsJHpVxskdqpKuxULXbqcA7i4xxUzqVRs072bp7+2N3z3e7s7p1TfvSRfLv7zsw+M+/M+87MO2uFqBX6r3bWXGYWdTWXMLb+G0Dt9Zwz4cHTKwEoHzuh3aQzoabyx4+P0GqSvr/13eVzJauJECAI... | <image>As shown in the figure, the quadrilateral ABCD is an inscribed quadrilateral of circle O, angle BCD = 110.0, then the degree of angle BOD is () | 140.0 | 453 | [
"70^\\circ",
"120",
"140^\\circ",
"160^\\circ"
] | C |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAL8AAACFCAAAAAAvYHYRAAAKPElEQVR4nO2cfVBU1xXAz7ObNqKOJlkV2yVRBKNAqGXSDLEfYostRtrB0XTVWKWTpEkFdcVo1gksfkBsRjFGY4fGtO520o42altl1UxBsZGOpMmQWkAqYEh21UXTlojgx244/WNhd+97975333vsV6e/AXb33nPvO+/uueedd969CAhxzYhoK6CT/+sfXUj9hcHf+OF/a/zjD7r+8WNDhsC7EJ2F+LkoBPVHGDqHOFKfZj/xpD5N/3hSP179... | <image>As shown in the figure, a cargo ship sails from point A to point D in the east direction at a speed of 24.0 nautical mile/hour. At point A, a certain island C is measured in the direction 60.0 east by north. The cargo ship arrived at point B after sailing for 30.0 minutes. At this time, it was measured that the ... | 6\sqrt{3}海里 | 454 | [
"12海里",
"6\\sqrt{3}海里",
"12\\sqrt{3}海里",
"24\\sqrt{3}海里"
] | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAM8AAAB+CAAAAACmfBpTAAAOV0lEQVR4nM1cfWxb1RU/r6XOBIZMwqEv4OKWGGJwurl1S00JTSmZcNfQBogU2KLhaqVhBNGgZiKwbJ20okZquwUpmTKlDCNlwixmKWtKHUhFCokISydHq7sESFW3CSNtIurUmea47jv74z3b7/vDdvL6gzr2veede3/369177rmXQNANSKgSO1WmQeeSzLKSE9B0FAr0LyX75jXo1JOPKJD99/oRi++t/jwNj+vGB5OfRO+IWDwBMPfmyr4P... | <image>As shown in the figure, PA, PB are tangent to circle O at points A, B, point C is a point on circle O, and angle P = 36.0, then angle ACB = () | 72.0 | 455 | [
"54^\\circ",
"72^\\circ",
"108^\\circ",
"144^\\circ"
] | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAJUAAAB0CAAAAACp0S+0AAAJO0lEQVR4nM2bX4gbxx3HfzYKqE7BKuFATUtvuRBu78nrJjS6XsFym5JNoPWm0CIHHKsPiWVTsBz6IBeKdNAiFxeUvEQphMov5vxk3T20utSluhqCzpSLzg+pzrQguSldFVzWfris0lX49mFX/3Znd0fSWtefwaeZ+Wnus7/57cxvfjN3CDRraZ2nguijgxmLnhUrvkqHZ2KegawvUV321QrNgGQge5fCtSiP4gwGrSdahmPwAMx0BG8sH234... | <image>As shown in the figure, PA and PB are tangent to circle O at A and B respectively, angle C = 55.0, then angle P is equal to () | 70.0 | 456 | [
"110^\\circ",
"70^\\circ",
"140^\\circ",
"55^\\circ"
] | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAHQAAABJCAAAAADJFV2IAAAGJ0lEQVR4nO2Zf2xUVRbHP+fND1kcbf+AiCGkWMtSlk2oErMQ3NBCsEPC0lnBwMYirkEQqwtaElQ0dFcTNUp2mxWEIGEJi8tuw7Zrsku7KO3+sYvZYCgGt+AvRoUIYkyRhg3z4x3/eO/N9LVv3sz0hzGm38nMfefc++73nvPOPffeN6iaSwEmXtFvDQbI35aeUL2vvA9AGXFYXe4QqUlutDQGkExUwctzNwHIyJMKEJeTqnvDN2uG9GgZwLQz... | <image>As shown in the figure, in a square grid with edge length 1.0. Connect grid points D, N and E, C, DN and EC intersect at point P, then tanangle CPN is () | 2.0 | 457 | [
"1",
"2",
"\\sqrt{3}",
"\\sqrt{5}"
] | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAIEAAABgCAAAAAAf006rAAAFsUlEQVR4nO1aXWwUVRT+zkAcTBrXB1fRlFRaHqqNUGpbSGi2KjWGGAgPNcHGRFAiovGHuCU8SOUB/CESMEFtEViNYjBAWq2kUcrPLgWKBWyaEk1oNyE2sVITbdIYBrL3+DAzu7Pbzu50fm598NtkZufO3jnfOd+5Z+fOXLA8CGZmjgBAPNMKiQwMROIcx3D6kBiyQYxkWXK+eajIspv2NBEFr4vOt5yRCMHMHAMsGjBLiwEAEADEhjm2IJlp... | <image>As shown in the figure, in Rttriangle ABC, angle C = 90.0, AB = 10.0, AC = 8.0, then sinB is equal to () | \frac{4}{5} | 458 | [
"\\frac{4}{5}",
"\\frac{3}{5}",
"\\frac{3}{4}",
"\\frac{4}{3}"
] | A |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAALMAAACICAAAAACJwoVBAAAJvklEQVR4nO1cTWwbxxl9UhYJ4x7M1jZKtwdtbNdiW6TeBkVC2621DVyYySU0eojcwJZ8cdmiSOj0YCVBQPlSNTAQykBTxpfKSqDSPdSUD4XcHkqqcCDLqEwbaCEFSUPqUIhFnJIoYJMG1/h6WFJc7h9nZ4dSAvhBInd2Z968nf12vt2Zb9hH+MKhf7MFcOCh5o2BaM3aib6+vr7wZ4JpOyBas/S7kSWiYwd7KVq4bTyoh4E3nn5dNK8BwjXf... | <image>As shown in the figure, the quadrilateral ABCD is the circumscribed quadrilateral of circle O, and AB = 10.0, CD = 12.0, then the perimeter of the quadrilateral ABCD is () | 44.0 | 459 | [
"44",
"42",
"46",
"47"
] | A |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAGYAAABkCAAAAABRfBq1AAAFQ0lEQVR4nN2aT2gjVRzHv91X3FiEzbpIB1p0FtREFA1eHPFPhmUXUg9ruqd40OrFtnpoexC3B5FVofWUKitdT7agtixIi5d2kXUTXGj2IKm40HRlyfQgaanarFiTZfP252EyySSZZN6kMxH225CZzry8z/u+93sz8968LkIndKgjlHsM0y2eVNPWd1JAAoA/BISlYFAS/W2XWAhkEsmETw71KoAKIL8OJHYyGZ8aVmW3MNrcvE8NqxZF1xLJ... | <image>It is known that for a horizontally placed cylindrical drainage pipe, the radius of the pipe section is 1.0, if the water surface is high 0.2. Then the width of the water surface of the drainage pipe section is () | 1.2 | 460 | [
"0.6m",
"0.8m",
"1.2m",
"1.6m"
] | C |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAHIAAAB4CAAAAAALLfnHAAAKzElEQVR4nNVbf2xdVR3/3CdKQU0BU/dMDI8ZWZ8h2e6WmF2Y7G3GhDch4xUT3qaENRpXhn+szVjSRX2DP0zBaJkxoRsyOmSmC4mvYLAlUWhXA60aeeUP6crgsUTZaxf3Cjb2lqLn4x/3973n/moXE7/JXu89557z+X6/53u+53y/50wh1kj6E4fSNcisHstg9qM9/0zZbg2QCgDgl7Mb/neQAIC3P9aetskaIfVT5b+vRzp7WCPk8d73/vVF... | <image>As shown in the figure, A, B, C are the three points on circle O, AB, AC are on the both sides of the center O, if angle ABO = 20.0, angle ACO = 30.0, then the degree of angle BOC is () | 100.0 | 461 | [
"100^\\circ",
"110^\\circ",
"125^\\circ",
"130^\\circ"
] | A |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAGcAAABbCAAAAABLksTzAAAJE0lEQVR4nNWZbXBU1RnHf2cNTarMpIzQYExHE6wTh1gDFhu17KYVR1roq1pptZpMqeiAwsimY8cYaKUjNtGJAw7tiN1ltKP1lY620ikO2WVaENpKByy0yW7sYAVBhVad3A1y//1w7967u9nN3k3zpU9mc889L8//eTvnPPcc5FKEuERap1Up2UE6hXBpIP46xMGrKEPySiZId59t026gMSCKxz1ijAkZkwyO0xBiuAme2w7kijs+JcIp2SJc... | <image>As shown in the figure, in the rectangular coordinate system xOy, point A is on the positive semi-axis of the y-axis, points B and C are on the positive semi-axis of x, and angle BAC = angle ACB = 30.0, AC = 4.0, point D is a moving point on the x-axis, the symmetrical points of point D with respect to the strai... | 2.0 | 462 | [
"2",
"3",
"4",
"5"
] | A |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAALwAAABcCAAAAADxZoD1AAAK3UlEQVR4nMVbf2wT5xl+Dzpot0yRNqd467EMcJZMXlWzMI2WSIna0GQiy7LWiD9GR6alsVAqFRFPiwQom5qKaAobSAlCTBNBUJU12TJp2eqsZkRrqiGlxaCGpQhnNoQOs1Srh9FmLu737I+7893Zd+f7YbJHcXzfj3vvuffee9/v/b7PHMgtptYFXMtwhlWuJSy/XAYazuCe/MEv+crAwxEck4f0OR74h3y44nBMnhM/ycyTVZ+ViisOd2YD... | <image>As shown in the figure, angle BAC = 110.0, if A and B are symmetrical with respect to the line MP, A and C are symmetrical with respect to the line NQ, then the size of angle PAQ is () | 40.0 | 463 | [
"70^\\circ",
"55^\\circ",
"40^\\circ",
"30^\\circ"
] | C |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAKUAAABfCAAAAACsSVh5AAAJ50lEQVR4nNVbf2wbVx3/uoEGqSfMD08YyOaqtRa3roRLGjWoLQlaoN4asrBaCn8YlkpZghRQIzUalqgUJCI1SBkK4JRUYVrYIhRoWFraFYelNNMyKSXVHDRP7li2emsruXRCXhLUa2Luwx93Z/vsd+/eOVk7Pkp05/e+797nfb/vfd/3vnfnAJnj8T8T0QPvSnBwhO4FNvEqzzbHge9vW7nfJPks11YDRAP7jn0kPYOITjoc31jrtpblsvzb... | <image>As shown in the figure, AB parallel CD, BE perpendicularly bisects AD, DC = BC, if angle A = 70.0, then angle C = () | 100.0 | 464 | [
"100^\\circ",
"110^\\circ",
"115^\\circ",
"120^\\circ"
] | A |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAH0AAABfCAAAAADgj5fEAAAGnklEQVR4nN2aUWgcRRjH/9NKFyESkEDu4cq18Qql50MlLVgbuxUqDdhqkagIAVMJFIlgH3ptwEJ9EBppwQiFVqtkgxWijaTQIhULhk0L1VTShwt5ue4F40MkYlsbcE/T/fuwe3e7e3t7u8lcCv4hl9252ft9883Mt9/MriCiaSK5MWLNGFoTteIu+ezo9KNqA5oOEc3zw227onZRHEVrewHr1QbAI9LPvsXtj4w+fEq0iUbQH4tQpyCICeMR... | <image>As shown in the figure, in triangle ABC, AB = 10.0, AC = 18.0, point M starts from point A and moves to point B at a speed of 2.0 per second, and point N starts from point C and moves to point A at a speed of 3.0 per second. One of the moving points reaches the endpoint, and the other moving point also stops. Wh... | 3.6 | 465 | [
"1.6秒",
"2秒",
"2.4秒",
"3.6秒"
] | D |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAALIAAABqCAAAAAA9jFT2AAAJjElEQVR4nNVcf2wT5xl+ztDSStGyqs5itFBDEhZW09Xjh8pEurANFEsNAXVBFDVoqcqPbam0VKQjUiN1U5gapKBWWpJFoypBZBojmRhrWjklpUyCLVpYw7YgQARsRrZGo6qyea2ci3PP/rizfee7s8/OxY4fOb773rvvvud777n3e+87XwQCADBU7EWewCEvZn+UWxrpQKHc+lg5AALMKRtLcAAgur3/AgABEHLMxwIcAIRg6BtFBcgLFwNw... | <image>As shown in the figure, in triangle ABC, angle ABC = 110.0, AM = AN, CN = CP, then angle MNP = () | 35.0 | 466 | [
"25^\\circ",
"30^^\\circ^",
"35^\\circ",
"45^\\circ"
] | C |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAKMAAABgCAAAAABUe51GAAAMTUlEQVR4nO1bfWxb1RU/L3xk8irM5hVXbcArCQ5SqxkyodAwSERaUhGWoKWoU7eGQFkz4W0pAZE/OpmiCqVbRKgWSiWCyL4qtppmG02Tdt2aKJRlRWrNCCKgDCcsqEZeF0xcZuclvr/9cd+n3/P7cNmGpp1++L37zr3nd++559xz7rtPAH3mqeS/DcAB/R/jp0NFY7SZx5c0zfMqC59tm4FALsdR6c/v3wARMWvOi0XiUppgRAKRa11zlOIP... | <image>As shown in the figure, it is known that the bisectors of the four inner corners of parallelogram ABCD intersect at points E, F, G, and H respectively. Connect AC. If EF = 2.0, FG = GC = 5.0, then the length of AC is () | 13.0 | 467 | [
"12",
"13",
"6\\sqrt{5}",
"8\\sqrt{3}"
] | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAIkAAABfCAAAAAD5KLsnAAAOhElEQVR4nL1afVgU17n/nd0k9tZtQh+lLBHL9YMogrCbB8OuM1SMEjbVIEQT7b14vWnjJ/ahXkxjYmz1xtwm0aY1BbVRG5PaGwxr1PoF0cfPmQgBZEEbMAjiVROMJKECDYLs6R8zs3PmY5dF4/39sTvn8/3Ned/znvecOaC3gSwAwKO30zQ4LJBQ5gMACoowsDe7xu8vHR1O1ZDQCJOZ9OYTACAg4TTv7XbcevPRceHRDtGRRpjM5KXYUeF2... | <image>As shown in the figure, parallelogram ABCD, points E and F are on AD and AB respectively, and connect EB, EC, FC, and FD in turn. The area of the shaded part in the figure is S~ 1 ~, S~ 2 ~, S~ 3 ~ , S~ 4 ~, S~ 1 ~ = 1.0, S~ 2 ~ = 2.0, S~ 3 ~ = 3.0, then the value of S~ 4 ~ is () | 7.0 | 468 | [
"4",
"5",
"6",
"7"
] | D |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAKAAAABcCAAAAADM9OGTAAAIgElEQVR4nM2bX2gc1xXGzwjjhzZEga6aDdp6FXldmQrKBofiEIHVYNp9MGvTKvihSr0BZQXeB8vIUD0I/GLaDXWKKF5XtSjVgwIhcnHbbNMRdRxBXDCIMg64MQEbLYgWYRW69rp4WKnz9eHOnzszd2burHZcf6DVzOzce397zpwz56xGCihSUMyNlRfz0Wd3Q/aKRD0Sp1tnb59JhEa8omU4GUBLs/tySdCIZVklEhD266/y/0wQyF7Pc81F... | <image>As shown in the figure, in parallelogram ABCD, the diagonal AC and BD intersect at point O, and points E and F are the midpoints of AB and AO respectively. Connect EF. If EF = 3.0, the length of BD is () | 12.0 | 469 | [
"6",
"9",
"12",
"15"
] | C |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAALkAAABVCAAAAAAwQBp5AAALpElEQVR4nNWbf1AU5xnHv3t40ZneRNNAxBE1KpZL7m5yCTFKDwJWHQ9D8Kww0JE0OkVNm2YwQzImUzomjWnMRFvpBIshrZCaCoMGTDA5JUYYuBED5nA4Ijaox6CJFtpgYFrkYJ/+sbt3t3d7dy97aKbf4cfu+777PJ979n2ffffdPZBqZQNA3LB6A6pUBmSMFRGRBqp1LNtJ9PNFIyD1NiYrN3ee6OBdcwBA/acfsxIRZW+dklAyukzaSkRU... | <image>As shown in the figure, parallelogram ABCD's diagonal AC, BD intersect at O, EF passes through point O, and intersects AD, BC at E, F respectively. It is known that the area of parallelogram ABCD is 20.0 ^2.0, then the area of the shaded part in the figure is () | 5cm^2^ | 470 | [
"12cm^2^",
"10cm^2^",
"8cm^2^",
"5cm^2^"
] | D |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAJYAAAB4CAAAAAA1JFTMAAAIe0lEQVR4nM1cXWwcVxk942QSCSwZgS1csoJQb+WUoHbzRKpUWtNGzT5U2wUi4KFSHRGMREB2ZCMFGtWO1AcjUnBQrKa0VVzVoIiYbkBWsZsU/FAgFVW2lcJDlLXsSEHdooqua4naM8scHmZmd9Yzd+bOX8mx5Zn7M3fOPfe7/3cM3kEoAsBFksT/m0obihe5gArJDtwxIPTlAvoBAFK0nlWUh/URAEyRFRT86UAnhodycrRuKe+QL+64C4SS... | <image>As shown in the figure, in parallelogram ABCD, the bisector of angle BCD intersects AD at point E, and it intersects the extended line of BA at point F, BF = 4 AF, BC = 12.0, then the length of AF is () | 3.0 | 471 | [
"6",
"5",
"4",
"3"
] | D |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAM8AAABsCAAAAADoYrnDAAAJ+0lEQVR4nO2cX4gb1xXGjxqnTjfQGBJTQUstrx8iUuIKE8qkbm3F2K2a/kGUQpcWx9pAw8YtZJtCUR+C1tCypX6QAyXb0rhyH8L6yapLidIELGhrVD+shR+MDCHRusaRSWPGtLVn3b2arw8z0vy7d+69I2m9hPxgl5nRnZnvmzPnzpk7w6RAHyo+dq8FjJmP/Gxuxu/nWCqVSqVS9bFvWAkNP3dfVWpWWTgDrB/ZkVDQiGj4+eUtpWbs2j46... | <image>As shown in the figure, in parallelogram ABCD, AB = 10.0, AD = 15.0, AC and BD intersect at point O. OE perpendicular BD and it intersects AD at E, then the perimeter of triangle ABE is () | 25.0 | 472 | [
"20cm",
"22cm",
"25cm",
"30cm"
] | C |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAMQAAABrCAAAAAANh3KMAAAI3ElEQVR4nO1cbWxbVxl+ru3rtJlKK9IiVxrYcdGSAuoCAmFaRp2pVb0xkIP2w3+yptrUZmFo635A/kxJQSidOilMgiUVAXeILJEmJS0SS6gQEahREiQvyx9cCVq7VJm7LZPzJ4uTe52XH/66vr4f51xfOwnqI6X1Pffce5/nvO95z3vO/RAIux+O7SZgBx6K2CmwU8QlQRCE7/7LxjMyQrCzY1861iH/8taNRhtPyQQ7LSEnvHA9dX/dxlOy... | <image>As shown in the figure, in the parallelogram ABCD, E and F are the midpoints of AD and BC respectively, P is the moving point on the edge DC, G and H are the midpoints of PE and PF respectively, it is known that DC = 10.0, then length of GH is () | 5.0 | 473 | [
"7cm",
"6cm",
"5cm",
"4cm"
] | C |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAJMAAABVCAAAAABoP4lgAAAJkklEQVR4nLWaf4xcVRXHzxv/aJSRIWGqW5wy0m5Zkg1hrTFZobJVCB20bjdKshhQB0JYZEmouDEl1v61hjXWsJq2LsHYNUIkaa0Ki1200g1uwoY/dkqyyQZt3aVLoA4Rxw4J896+dz7+8d78fm/mvWX8/jGZuXPuOd97zrn33XveNZBwwBAMkdmuvpAdNo5YWEFDxBCx9ocdwwZQVh2ak4sfXrtDRFREO01IVAxXdSROKsduelsQYpHH0h7E... | <image>As shown in the figure, in the parallelogram ABCD, the diagonals AC and BD intersect at the point O, and the point E is the midpoint of CD. Connect OE. If the perimeter of the parallelogram ABCD is 24.0 and BD = 8.0, then the perimeter of triangle DOE is () | 10.0 | 474 | [
"10",
"12",
"14",
"16"
] | A |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAIwAAABGCAAAAAA72CMwAAAGWklEQVR4nM2ZX2gcRRzHv1v1rXgPbuSkqdH0bIp5MJIHKw1exJZeIaSlBHwpEmhMkIgGe2IfgqEQMA8pFmxq0j4YoWC1kVqs9VJjqNCHSh4uhWqpXEwkVk+DNXpVjsvsfH3Y+7+zu7P5A34h2dvd38x85jfz3dk/4KrUDgBoXV1hV22CrclZACAILV1snyWvbNcLtrXfMAzjU+8YmynXMKvfAUnmYsydyJ0I1O/2T5hAUiMz/XXb9PtoANOt... | <image>As shown in the figure, in the parallelogram ABCD, point E is a point on AB. Connect DE and CE. If DE and CE are the angular bisectors of angle ADC and angle BCD, and AB = 4.0, then the perimeter of the parallelogram ABCD is () | 12.0 | 475 | [
"10",
"8\\sqrt{2}",
"5\\sqrt{5}",
"12"
] | D |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAGAAAABPCAAAAAAxCZ8HAAAMIElEQVR4nLVZSXMcR3b+Mmvt6q7egAYhgCQIUuKIlC1S29jWSEFNhMMRDk2EwyeHL/5r9tkHzzgcmtHQligK4iICBBeAm7DvS3ejl6quLbMyfeitADYJkGHnoZFbve+9773MfJkgEscWxz5+zisLPX7K0u83OrUTKPM2AHOlhVq7Rv5fAFZS10Z/ct5C9AkBvMX3rcvWvbei50QA9/gYcEU8fxt6jgGQAOCXRzWB4fdnZ3pd/1cAkjAAz8hp... | <image>As shown in the figure, make three parallel lines through a point in the triangle. If the perimeter of the triangle is 6.0, then the sum of the perimeters of the three shaded triangles in the figure is () | 6.0 | 476 | [
"6cm",
"8cm",
"9cm",
"10cm"
] | A |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAMgAAABVCAAAAAApy/TfAAAIkklEQVR4nO1bXWwcVxU+YzfJA1Ys0BomZMEiduulrugS98GVUR1Ki1aw2lh0wUgE6iDLfnBEV8RSLWGwhCqxCAcZyU2XGKlG5MFgQxRl29pqoKnkB0t+2FZy60ZZmy2rVq4MrdWNlM2d2fvxMDP7OzM7Pzvb8vNJq537M+eeb+65d+45944A+u9Ay0etQKPwfyIfN5gTcTSA1l5zcpcbgOoRERxIlZ5ypIwznBYEQRAeJQMiUGt8+rZ90fjp... | <image>As shown in the figure, in triangle ABC, the straight line DE parallel BC, angle ABC, angle ACB passing through the vertex A intersects DE at points E and D, respectively. If AC = 3.0, AB = 4.0, then the length of DE is () | 7.0 | 477 | [
"6",
"7",
"8",
"9"
] | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAKAAAABrCAAAAADVi9aGAAAJIklEQVR4nL1bbWhb1xl+rtLWfwRhzGk0olRLos1mHsSb/zg0w1lxF8McR+3KXLOs8UaWrOtYHBqYBwHnRyANW4gZTuYtg2ksUId4dTfSTWmTxaWDhbmgFFzMhrMoOB0eDquJDFV8r86zH/fq6kr3SLofR3tA9vl49Z5H5+M973vOvRqhGG8/2QmAmiJ1EUV6bOg/igCAKn7qCZ54artSfaoJ/qLz32oVKiaYe7hrUxSAupmtjiAB4Kc/xucB... | <image>As shown in the figure, in triangle ABC, angle B = angle C, D is on BC, angle BAD = 50.0, AE = AD, then the degree of angle EDC is () | 25.0 | 478 | [
"15^\\circ",
"25^\\circ",
"30^\\circ",
"50^\\circ"
] | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAKMAAAA9CAAAAADka4ZvAAAG3UlEQVR4nNVaW4wTVRj+hyxyySry0E2NxMpyq5KQglEnIJYXQo2GrfGyEkgYeXCf1I2LWoyUoJEmRlYfxAUCWx8WVx+EEEM3+LCbkNR9QcqDSR8WCqvoAglDwmXLmWnP58PMdqczZy5lgdUvaTtz/st8Pd+c/5zpKeFeo4uIiKjP1swttk3CQG55r0MTNQKQ5OvzFa3cTPqbi2zNUs1GBy8JAyXLex1mNMRRurPX10cfXU9fs7ZWeztMW/7n... | <image>As shown in the figure, in the quadrilateral ABCD, AD parallel BC, BF bisects angle ABC and it intersects AD at point F, CE bisects angle BCD, and it intersects AD at point E, AB = 8.0, CD = 6.0, EF = 2.0, then the length of AD is () | 12.0 | 479 | [
"8",
"10",
"12",
"14"
] | C |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAMIAAABKCAAAAADMadRYAAAIiklEQVR4nL1bXWgj1xU+1w5sYbdRQxV2SrSIXU0SB+dBXbewARUVvElNkVxBDSpkS/1gWykq1EusxQUTl2Ko2brUpSa1o5b6IQ8KXXC6MdSN3I2hWzC4oFC8mOLRIhABNyrERAmoVHO/PsxIM5JmpDszsj/WoL0695zz3d9zzowY6AwARrR7NXQWqjsxYOWAZ62MiF72rEUQVhQYeaMBAtGd+DUPKpyA9X8hgREhe/WVM1mi7YbIYhbGGWPM... | <image>As shown in the figure, in triangle ABC, AB = 10.0, AC = 6.0, the straight line DE parallel CB passing through point A, the bisectors of angle ABC and angle ACB intersect DE at E, D respectively, then the length of DE is () | 16.0 | 480 | [
"14",
"16",
"10",
"12"
] | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAFsAAACECAAAAADaNQi/AAAJM0lEQVR4nLVaXWhcxxX+ZtdkC1Yrlwq8oao3lgQViFKlSs1CjWWw3chU6xqcpnZqyKZWLbd5aWg2+CHBr0n94ocWtIpcyTQCpVaQ2jrU6UoggUOjutR9cFk/rFIZFeIiQ5SoBaU7d74+3L2792fuvXOpfGDh3jNnzn7zzdw5c2ZGEIllYX83hYFdKrlrHANMXCf1TQKvFLph1FqRmJPxrmOGdRJzssr9BUNTY99s8FAeRe9O+xZ2/41fTvWY... | <image>As shown in the figure, it is known that the length of one waist AB of the isosceles triangle ABC is 4.0 centimetres. Cross any point D on the bottom edge BC to draw two waist parallel lines, and they intersect the two waists at E and F respectively, then the perimeter of the quadrilateral AEDF is () | 8.0 | 481 | [
"4厘米",
"8厘米",
"12厘米",
"16厘米"
] | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAHgAAABxCAAAAAA7ADjGAAAHt0lEQVR4nMVaXWwUVRQ+U3mopMbwUKwRWUv4WaPCQIwM8aHEpLAYqUtCoA0J2YRI4cHQUDXlwVrxoZiYgj64BR8WtQGfWjR2eTABrNaWxHTxaanFxiKyQkwJgh3SHe/nw/zs7Oz83LmzwAk0s3fOnO+ec885c+65I4EikPppp+ijNVFwi63/CD8bCTjzzcqHAnzlaov4wxGA1TcPXGt8GMA9n9/+d7n44xCl40S07Ibw48IaX7kJjCxeKKzw... | <image>As shown in the figure, in the equilateral triangle ABC, BD bisects angle ABC and it intersects AC at point D, and cross D to draw DE perpendicular BC at point E, and CE = 1.5, then the length of AB is () | 6.0 | 482 | [
"3",
"4.5",
"6",
"7.5"
] | C |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAHcAAAB0CAAAAACaxvL4AAAH3UlEQVR4nL2bf2wURRTHv3OFbTQ1aGhjMdVGftgTjBQ1sSqmGtSeqdKiVYzQhNiDgqBIrKkaY2vUeEb88YdXitYEA0YFDL8k9kxRiJCoNVIMCiYgJf5qjRpKa9Ldtvv8Y2739nZn7/ZuZ/vSXrcz0/nsm3nz4828MkKAEh9pRV1jgyAnFCQWzDUnWG5SxsLHJo/bwRhbCyBEHcpLUyeP+ygRxQHoDx6jhrn23CmBcU3ZMfl25S6TxbUP10C5... | <image>A ship departs from point A on the sea level and travels 40.0 nautical miles to the west by south direction 40.0 to point B, and then travels 40.0 nautical miles from point B to the west by north 20.0 direction to point C, then the distance between A and C is ( ) | 40.0 | 483 | [
"30海里",
"40海里",
"50海里",
"60海里"
] | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAPAAAABhCAAAAADNBHOoAAAIwElEQVR4nO1cb2wb5R3+eUr/kAJBlEoBVY2brvSChHphpTi0VClqh8uYahAIF5Q2tFKxGJSUFS2Aprr7EJc/UrrCmqJCA5tCQCCnG39siqjNlshpwbj9sLmA2iQtxUYL9fIh2O2Z/fbhXtvv+e7sO997dx+yR63iu/Pd83ve97nH773nswNhZuFndhdgNf4v2Cpces0e3jp7aAH2zrOH164efvvcEnuIbRI80bDIHmKbBF96Y/1Yky3MNgne... | <image>As shown in the figure, there is the "herringbone" steel frame, where the inclined beam AB = AC, the top angle angle BAC = 120.0, the span BC = 10.0, AD is the pillar (ie the center line of the bottom BC), two support frames DE perpendicular AB, DF perpendicular AC, then DE + DF is equal to () | 5.0 | 484 | [
"10m",
"5m",
"2.5m",
"9.5m"
] | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAI4AAABMCAAAAACettBrAAAFsElEQVR4nO2af2wTZRjHvy901zFQGluSkUxXCkKHGgdZ6mRkdsrCREg6gkiYCEEh2eQfBhijELpkGOL8mZAVg+AiThoxY2h0hBnauE03YnFEQhfFrXMbLLol+wNM293y+se1Xbuy997rrocxPtmSu+vz3Pu553neu+fe5wjFv0lm3WuARPkfhyWp4ogvEULIy9dVhZmCE/qY2053Yp2P3rx/42gacY6OKbC8z4qFR02fpA/H/cdifsOr87MA... | <image>Translate triangle ABC to the right along CB to get triangle DEF. If the area of the quadrilateral ABED is equal to 32.0, the translation distance is equal to () | 4.0 | 485 | [
"4",
"6",
"8",
"16"
] | A |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAKgAAABUCAAAAAAzcCMKAAAIrUlEQVR4nM1abWwcRxl+ZhO1AgKW2jOc0guXtgcpvgCppaCLamFQjRXKQa+RA0JI7bVRCM21KMoHioQV+JEqhgbxJ3E/VAmnSkVBVv5wjlIwrYNcMLYl/4iTAj3aKpeCMaE596rkYt3Mw4/9uNu7vfPu3vrUR/btzsy7O8+878w778wO6Av7gfiNb/l71h80eAYxK+apXvzIp7w/6x8+iIrSQ/2vgN077gqeTmP40eiPb74EaNz4heDpNIag... | <image>As shown in the figure, in triangle ABC, angle ACB = 90.0, angle ABC = 60.0, BD bisects angle ABC, P point is the midpoint of BD, if BD = 6.0, the length of CP is () | 3.0 | 486 | [
"3",
"3.5",
"4",
"4.5"
] | A |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAKUAAABKCAAAAAD/UstRAAAKa0lEQVR4nNVaeXAUVRr/XvdMzyQkQzIhQ0ISDASMOeQICwHCcphaBJTaBFd3sVbR8sJiYwmLKMoi6q4HRkVWQcRbVlctOcpSxGNjjCxEkSBLVBKNBEMOc0ySySTTPdP97R/T3ZmZvDedZNhQ+1Wo+d73fb/3fu8+GoLwfyDchStaHnyo6X/HgiH42tEOO6DU1JTPi0qsaF22mBhhyIj3uHz5l4V2mzPa47C0xTvk6r2/3mfYoSPflnzyb18P... | <image>As shown in the figure, the height of the floor of a truck compartment from the ground is frac {3.0}{2.0}. In order to facilitate the loading, a wooden board is often used to form an inclined plane. If the angle between the inclined plane and the horizontal ground is not greater than 30.0, the length of this woo... | 3.0 | 487 | [
"3米",
"2.5米",
"2.6米",
"0.87米"
] | A |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAOMAAAB5CAAAAADuGMm1AAAM0klEQVR4nN1cf2xbxR3/viQao4QZhNMa8UagDWtG0eSmoDlrtojRUW/r2jACXkc3eSjgaQXRERBBams0VSOMTstGpCVQKSlkwxVF6RjdUlrALY6aLhXuRKqIOdFSUram7sDMXXHznu+zP55/Pfs92+/5nKR8pCTv3d27u8/d9+6+9/3eRQBxBUigd75BNHD9B/fxzdk8KjjnJwizG9wzQPDuG4mIiHMTmoLAuxJS69k3riT69Jt/Wsw5Z9Oo... | <image>As shown in the figure, in Rttriangle ABC, angle ACB = 90.0, AC = 6.0, BC = 8.0, AD is the bisector of angle BAC. If P and Q are the moving points on AD and AC respectively, then the minimum value of PC + PQ is () | \frac{24}{5} | 488 | [
"\\frac{12}{5}",
"4",
"\\frac{24}{5}",
"5"
] | C |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAJYAAAB4CAAAAAA1JFTMAAAK6ElEQVR4nM1cbWwUxxl+dwPCUKuOf0CPlvRiROVro8CRqGUBVWdXCpgmgXOEsI0IvrSqHP6Uc4HKNK0jIrVGhdht/xhQWpvE8YHanmkaQGokbKgsO1Kbo6oaQxyf+YrPRMrRQMQ5NrtPf+z33n7fOuoj5JudfWf3mfedeWfmnVkI/rCPiKh61z2fxZ3AgPxh//A75ZPP8++U+yxvD9ZnubnxTeVU1TtxJFA2CvzSuv7eZiIKrx8PkowKv7Qu... | <image>As shown in the figure, in the quadrilateral ABCD, angle BAD = 130.0, angle B = angle D = 90.0, points E and F are the moving points on the line segments BC and DC, respectively. When the perimeter of triangle AEF is the smallest, then the degree of angle EAF is () | 80.0 | 489 | [
"90^\\circ",
"80^\\circ",
"70^\\circ",
"60^\\circ"
] | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAANcAAAC7CAAAAADTIFRIAAAbwklEQVR4nN2deXxdVdX317ljxrYUKlAQH4q0AloKyFgqlIJAlUGoDGqVV0VfRQZFwBkFH0DxQdGHGbQyDy+VQUVGGWSQSVDmMrSFtmnT5OYOZ9jj9/3jJm1K09ubpEmb/j5Jk557zsn+nbX32mva+wTI6ug5FvTx2QhBan03YIjQJ69gBAuqG7XkNZLZBX2Nr40AG+v4ytR5HiIjqmPWKa8R11tX5dXTfCWmjBXReCPOjTxafcuLwGVaJC2S... | <image>As shown in the figure, the perimeter of triangle ABC is 16.0. Point D is the midpoint of the AB, BD = 2.0, passing point D is the vertical line l of AB, and E is any point on l, then the minimum perimeter of triangle AEC is () | 12.0 | 490 | [
"12",
"14",
"16",
"18"
] | A |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAHYAAAB4CAAAAAACxlm9AAAI+ElEQVR4nNWbX2gV2R3HvyeKQrXV7c6y1222Qc1D3GzLLWk1JdHJaqCxTSEPlquQVgWtLbuwCrn+gVi34EO6+pC2AQN52MmaUhcEC2shbnfp9SbW2Gy5LbqkS5OJ9EobSMDY2O2d29v59mFm7p25d24y/xT8EZIzc+bM55zf+Z1zfr9zJoIIIxz/0hYjIXyVqwlFBXaZOH/UsNhT8uZA5URQJVMAGN6yK1j5wK0VAGZRKwcrHUrJl36A7U8f... | <image>As shown in the figure, OA and OB are the perpendicular bisectors of the line segments MC and MD respectively, MD = 5.0, MC = 7.0, CD = 10.0, a small ant starts from point M and climbs to any point E on OA, and then climbs to any point F on OB , and then climbs back to point M, the shortest path the little ant c... | 10.0 | 491 | [
"12cm",
"10cm",
"7cm",
"5cm"
] | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAMkAAACACAAAAACE+hJ9AAAJ/klEQVR4nO2cX2xbVx3Hf0Edc8tDo1Ub4YVcZdpqXuBuQsPRtOYWRczjpa54qPMQ7EFVuUXaHLGJZBJy+sBclAeHF1IxkAEpSwUs7lsmEJgOoSxj7l2fsomCnYfKkZbJ6UO4rh304+HY1/f/+Zt0TP2ole+9vvmd+73n3PP7nd8510MInxE+d78vQBkPlHz6UKukdlOpOS6UKrk3o9IaJ0qV/PShUZXm+FCp5M2x+/nUKSx7a+e5zx9VZ44X... | <image>As shown in the figure, in triangle ABC, BF bisects angle ABC, crossing point A to draw AF perpendicular BF, the foot of perpendicular is F and extend BC to point G, D is the midpoint of AB. Connect DF and extend to intersect AC at point E. If AB = 12.0, BC = 20.0, then the length of the line segment EF is () | 4.0 | 492 | [
"2",
"3",
"4",
"5"
] | C |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAJcAAAB/CAAAAADH4w9KAAAM/UlEQVR4nO1ce7BdVXn/fWutvc/NpWAQI4+GAqECilCHh4ZXExJJFKMlqCWkkSoUHcrLOkOrdWyLdaqtaO1MaaekYGullJcUwyNBCVgEEkwUnCgzHV4hhQgGIiG55+y91vf9+se5edzbc87dO/eckD/6m2ROTmavtX/3e6+1vnWF2Cvh3mgCXfD/vOoh7ImXEAoBxVcfsmfkVTi/9mc1WO0hXhqkdWXT6rxrj/Cij389PEOsxpA9wiuLd84I... | <image>As shown in the figure, in triangle ABC, points D and E are the midpoints of AB and AC respectively. If DE = 1.5, the length of BC is () | 3.0 | 493 | [
"3",
"4",
"2",
"1"
] | A |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAJUAAAB6CAAAAACT207EAAAJpUlEQVR4nO2cb2wbZx3Hfy7tFALSqkXV3Fc70rIdSENHEJun0tZFGcvgBSfxIhk0xBsjC5tEPECahzQllSrSEGluECMtmXBBZOkYxJkmEbRKOBugNFO9S1+l458dIXQZZDqElN0FB315cX98Z9//59ZOqF+18t35bH/8e577Pd/n95yTAr0PtedGA7jq/5eq+mYCb+JQAlQ7T7K/R4sSoJrcdwf7mzjFTvVCd/J9k/kdN7aO3vLBJEjsYqXa... | <image>As shown in the figure, in triangle ABC, BD and CE are angular bisectors, AM perpendicular BD at point M, AN perpendicular CE at point N. The perimeter of triangle ABC is 30.0, BC = 12.0. Then the length of MN is () | 3.0 | 494 | [
"15",
"9",
"6",
"3"
] | D |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAIwAAABqCAAAAABLtuZ9AAAIvklEQVR4nM1bX0xb1xn/HYxGiFhJJiUYldRlZYMqU+pU2mSzrCTTSoy0Uk+qYFmlzkRqn6YudaKFaBJN8zASNYG+rCipJrMpxaIPBaKBTSYBIeNPX0getgJ1646M1ibSIBlZbODa3x7uvfb9a18bY/dLZN/zne/e87u/8zvfOfdcwwiFtcgfzySOiwqGgmdh65frSVfhwDAABM+N738TwAAAC9xrlhQLCyby5m+XqwEInVZYMOf//PB/NQD4... | <image>As shown in the figure, in triangle ABC, D and E are the midpoints of BC and AC respectively. BF bisects angle ABC and intersects DE at point F. If BC = 6.0, then the length of DF is () | 3.0 | 495 | [
"3",
"4",
"5",
"6"
] | A |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAMUAAABcCAAAAAD7Oi6nAAAF+ElEQVR4nO2bT2wbRRTGn0srVHoAiVayECjT9NDkALgVglZwMCiFUDi4QoJemjiXkubkAhKRQLJ7aiUiuQcgl0obkNIcQPGNQouweqhMiiLTA0qlCq19ABdR5HAI65Cgj8N6bSfef29m1kQln9omXvu9Nz/PzJvZ6b4Y6D7Qjv+6AVq0TbF1tNUo1kdisVjs2F88q61GsfPz3Dwa1qc8K0+K1UtEdO5txUbxtW720YPH7vCMdnq9cWEP0eq1... | <image>The students have all played the game of seesaw. The picture is a schematic diagram of a seesaw. The column OC is perpendicular to the ground, OA = OB. When one end of the seesaw A touches the ground, angle AOA′ = 50.0, then when the other end B of the seesaw touches the ground, angle COB′ is equal to () | 65.0 | 496 | [
"25^\\circ",
"50^\\circ",
"65^\\circ",
"130^\\circ"
] | C |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAHMAAACJCAAAAAA6IVhFAAAHZElEQVR4nO1bQWgbRxT9UXNQcqlo4mZNE6KkB28OJUpaqIIvajBUoYcql0aFCqmBuqovzaG07sm6FBeU4kMJIpBihWDkJGApJ/vmFGJkhyryTYE0WD60MsUgl+Kugiz/HnZXu6udmZ0Zx6KHPBJrd2Zn3vw/8//Mn9k9gNB3+PpP+YqTAy9u9Z1z54utvnPeu/N2vznX/0xIlpTmfPHd1frJPnNev/HPtiQnoBxmAGBoU66spJzrm4grJw7J... | <image>As shown in the figure, in triangle ABC, AB = AC, angle A = 40.0, DE bisects AC perpendicularly, then the degree of angle BCD is equal to () | 30.0 | 497 | [
"20^\\circ",
"30^\\circ",
"40^\\circ",
"50^\\circ"
] | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAJAAAABmCAAAAAAB5kdgAAALD0lEQVR4nLVbbXBU1Rl+TjbZsMnS4C4XsppMzAcIiTKtjIL4AfiBg7BIa4EBZYooOB3H6YAuaCk62tpSYqEjztTEjozFUStMqwI6skkRbVFAxUpjkOwGKuAQViIkAtk1uU9/3L27d+/e3XtvcvtMsrn3Pee859n3vOc9nxGEk6Boqa6lyJLqH3KjwFE6ELgNEFoJoBGY83GWkABCwVqdxGYTCAebjALNNbcNUaGTFhKIojpo2yaZcLTJ0LQc... | <image>As shown in the figure, PA and PB are two tangents of circle O with radius 1.0, points A and B are tangent points respectively, angle APB = 60.0, OP intersects chord AB at point C, and intersects circle O at point D. Then the area of the shaded part in the figure is () | \frac{1}{6}\pi | 498 | [
"\\frac{1}{3}\\pi",
"\\frac{1}{3}\\pi-\\frac{\\sqrt{3}}{4}",
"\\frac{1}{6}\\pi",
"\\frac{1}{6}\\pi-\\frac{\\sqrt{3}}{4}"
] | C |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAIUAAABxCAAAAADesj/vAAAKPklEQVR4nMVbe2xbVxn/7k208LCUP5aoHo0ItO7izawkYUAmmSVSg2YgKhmq6IYqLRNZLS0Tq7pKiyCAkCYlFZmUSYlIV8SC6FhF00hsofFa94HaQshE3I7SUJGmntJH0m7MlSth+/ieH3/ch++9vnbuw2HfH/Y9557H73yv853HJVSCxkjoyL2IsQ6X9UXyTknhIvgb9z1AJyIEd014Z0SuaTcAvHQE30t/crw4+J9XiYg2BdjjPpdNCC5Z... | <image>As shown in the figure, in triangle ABC, angle A = 90.0, AB = AC = 3.0, now rotate triangle ABC anticlockwise around point B by a certain angle, point C′ falls on the straight line where the height of side BC is located, then the area swept by BC during the rotation of edge BC is () | 3\pi | 499 | [
"\\pi",
"2\\pi",
"3\\pi",
"4\\pi"
] | C |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAGwAAABxCAAAAAAVRRlUAAAaHUlEQVR4nL2ae1RUV7buv81O1U5VKlR4VACbR/uiUVpUPLQ2TeuJGt9cPT4vnOiIik0Srg+40ko0eBKNxhcnGtsYzVBpE8LRiO0DW03oCG00aAseNVT7IlyqiVgMKtWUVbXZ7FXf/YOYSHwchyd91j+bXYPix5zrW3PNOdeSiM5BCVXPJgCU7rz++CPozg8S9PmdT9z1+AfBgNWxsf8Iwn1hxf2/5kN+8UeEEX+7PejZp/5nYBI25yCBfxeB... | <image>As shown in the figure, the sector OAB and the sector OCD whose central angles are all 90.0 are stacked together, OA = 3.0, OC = 1.0, respectively connect AC and BD, then the area of the shaded part in the figure is () | 2\pi | 500 | [
"\\frac{1}{2}\\pi",
"\\pi",
"2\\pi",
"4\\pi"
] | C |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAIkAAABgCAAAAAAMBA5fAAAITUlEQVR4nO2aTY8jRxnH/1Vd1e/dtns849kNmc2yKJFQ4Agn4IIiJITEgQvfiQ/BLQeEFAEnBBECReKEEikgBSXs++yOx/a43e/1yiFrexLvsiKa9uYw/5FsP+Vx+eenn6ququchFp+rjPNBE7Q+9qXKFwGKgK1tsiaB5PODgtUHewKxmklDeR2uG+gG0cHBRTLfFwisBj9w4W0atj5Z0lQa19Lnfu7q1QSd1W/eVRufbEgUw9wZEtgXfPLK... | <image>As shown in the figure, in order to green the environment, four sector open spaces with a radius of 1.0 are drawn at the four corners of the rectangular open space for greening, then the total green area is () | \pi | 501 | [
"\\frac{\\pi}{2}",
"\\pi",
"2\\pi",
"\\frac{\\pi}{4}"
] | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAIIAAABqCAAAAABVf9bOAAAH4ElEQVR4nM2bX4xUdxXHP+fctbeosQwWGfyDLJC0xkgbEmWXJrDbxMT0wSd8rUwfeBGQgG18qNE3aAzYkABtWjO7+tD6J2piuqCJULayi02TtlZTmghLYywDMXSBhmaAOceH37137uzO7J/ZnVlPNnPn3vnd3/n+vuf8zu/8zr0rzlKLLjWAJYQwICLyGgC+VLJ11Ee56G6yZL4gzsS6i19WepYKweiTUHpyrbB0higDF9zda0vmjkMXfWj9... | <image>The lateral surface of a staircase is shown in the figure. The measured length of AB is 3.0, and the slope ratio of the stair slope BC is 1.0:2.0, then the length of the slope BC of the staircase is () | 3\sqrt{5}米 | 502 | [
"3米",
"6米",
"3\\sqrt{3}米",
"3\\sqrt{5}米"
] | D |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAJoAAABzCAAAAABF30SBAAAJOElEQVR4nOVcf2wUxxX+3h5r/qhVpxWIqCElbQw2gShGdQupQUQKiANsDApJUKgaKgXagCmObBoSQBwCmiBMChKmJKSFKNA2MZQfvuPulJCAAoIoIB/FFAdMagJFceu2EFO1Ztl9/WNv93bv9ri93bmaqp+tW++bmbffvnkz8+bHmRh3K6T+JpAdwqltXQ/U7hGhqTBWE+IlhaEmQSlP+FciEFuJaBEAaM1Fa4r8ahNKbSEzNwPAU3/gJx/y... | <image>At a certain moment, there is a passenger ship at sea point P, and lighthouse A is measured in the direction 30.0 north by east of P, and is 50.0 nautical miles away. The passenger ship sails at the speed of 60.0 nautical mile/hour in the direction of 60.0 from north by west for $frac {2.0}{3.0}$hours to reach p... | \frac{4}{5} | 503 | [
"\\frac{4}{5}",
"\\frac{6}{5}",
"\\frac{\\sqrt{5}}{5}",
"\\frac{2\\sqrt{5}}{5}"
] | A |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAEQAAACPCAAAAABmVyIZAAAIJklEQVR4nO2af1AU5xnHv+9yZZP2hmvrWQ7EYhECGfzj/NEWaxxsxHqOCEZJJTOZKZmgJjEzMhUbZ0q6ptLGTGAgE0ASccaZpi0z1BETkwGjRmc0tSPp4QjBtiBMQHsU/wDhj1uBe/rH/rjdvd099pI/eQbu3p+f93me971332d3QRGSpOU4UUkHJSIcGCQhaIR0uXjCaToCAGbzbgFgzLy5HaSFMe4AA4CW5NpvxegVV1TDmo8TlWBfIj5x... | <image>As shown in the figure, it is known that there is a laser auxiliary signal within a certain range of the lighthouse M. A ship is sailing at a constant speed from south by north at a constant speed at sea. The ship measured at A and measured that the lighthouse M was in the direction 30.0 to the east by north, an... | (\sqrt{3}+1)小时 | 504 | [
"(\\sqrt{3}-1)小时",
"(\\sqrt{3}+1)小时",
"2小时",
"\\sqrt{3}小时"
] | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAI8AAACxCAAAAADYeLGSAAAQKUlEQVR4nM1cfVBV17X/rX2556JeIVERFYwoGEycROIUY62tEW1CXlM/En3tTOOLxE4waJM2aot5KFLtSBqTTBtBM2/yeJn0j5eqMXEchcb60TbR1xAh6Zj6hYICERTl44rcA3ev98c59wO4eM+5nKNdOtyz99lnn9/Ze+211t5rr00M24gJQGl7Pi9atgQAJFHEZ2LsgwPq8ysMPGOkTPQkAb391SnVABjybuIpdRCtBhjY4dqiACCO9D77... | <image>As shown in the figure, at 8.0 in the morning, a ship departs from point A and sails northward at a speed of 15.0 nautical miles/hour, and arrives at point B at 9.0 and 40.0 minutes. From point A, lighthouse C is measured in the direction 26.0 west by north. From point B, lighthouse C is measured in the 52.0 dir... | 25.0 | 505 | [
"36海里",
"25海里",
"20海里",
"21海里"
] | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAJAAAAB8CAAAAACjq2adAAAJl0lEQVR4nM2bv4/cxhXHPzMccrh3K+/dSTrbguBfQRA7hWEYCAIkRVykMeB/QAmQLlUQBHGRdCldpnJ6qYn/ghhI4cIq3KRKJRtBHNiSLdt3uruVeLdLznBeCpK7e9L9WpL2+gF3SxI7j999837OvFHCNAU4WuN7QTrspVkGrGUQVo0GUMJ4xKVHsHEA49SuHtBkAMbD+mG+cjSA3hkwxsAELNmq4YAScovxlZQ2DlaNB4Mxkduob9KVYqkw... | <image>At 9.0 in the morning, a ship departs from point A and sails in the direction due east at a speed of 40.0 nautical miles per hour, and arrives at point B at 9.0 and 30.0 minutes. As shown in the figure, the island M is measured from A and B. In the direction of 45.0 north by east and 15.0 north by east, then the... | 20\sqrt{2}海里 | 506 | [
"20海里",
"20\\sqrt{2}海里",
"15海里",
"20海里"
] | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAIIAAABXCAAAAADtm8K9AAALaklEQVR4nMVaeXRU5RX/vTdvlkxmMntICImYL4shiNSKINZ9Q3oQD+BhOwgioBIh0lZwQ1yoXbRYoSqLYSsq4tJWTlHcKxQBLbQoiCCrgCaZfSazvHnv3f7xJiQzyQyZ2iT3zMl97353Jne+d7/fd+/vG47Q28L3dgC9EoKcNvE9H0Jss6+XQ1Aa3hN7OYR9y8z5vRvC6XcvHiCkmoTOPbtLxG1jWjgu1dazs0CrOd1hU6/Owv5VfoSmpH3t... | <image>In order to measure the width of parallel river AB, angle ACB = 30.0, angle ADB = 60.0, CD = 60.0, then the width of the river AB is () | 30\sqrt{3}m | 507 | [
"30m",
"30\\sqrt{3}m",
"(30\\sqrt{3}+30)m",
"(30\\sqrt{3}-30)m"
] | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAALEAAAB/CAAAAACFoHzdAAALAElEQVR4nM1ca2wU1xX+rlkCdTaNVZYWJRvxSB+LCc4CBeMuDo7ghwmOIJIjsCkBKlFUgUTqUEgizA6p2kZtU6WVkZBQqrWogEomD6m1QbEjr3HBKG6NgxU7KuEhb1UMRi0C06o7zOmPmZ3XembvHc96/Wm1O4977n5z98x53TsLmkJIojqzccSxESaJTE4oRERd4TEionRZq3PDIkwRMAC4sYQA4JXwOueGU4YxAKA/OExAc/gFlzZTirEc... | <image>As shown in the figure, it is known that a fisherman on a fishing boat sees lighthouse M in the direction 60.0 east by north at point A. This fishing boat sails eastward at a speed of 28.0 nautical miles/hour, and arrives at point B in half an hour, and sees it at point B The lighthouse M is in the 15.0 directio... | 7\sqrt{2}海里 | 508 | [
"7\\sqrt{2}海里",
"14\\sqrt{2}海里",
"7海里",
"14海里"
] | A |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAHoAAABbCAAAAACZws6rAAAGs0lEQVR4nNVaT2wUVRz+XosKUUJ6WOwBWikq6wUWEpMBYrYkiBiTTcul4MEQD0I0xK0lEY00JEaIxKzRxNRCImqKxYMtIal6YgmkLtGEJR4sWK0UiLt4aIVitzO7O5+H2ZnubufP29mpiV+yO2/fvN/75nu/N7O/93sjiFpBAQCY+6SnZtMKNNRuYjDnu+75oCsX6oPawKlzT1Z1JQOBg0IIsfl+HdS/TcYAQNTsrw/693BWe8U/de5A/PZa... | <image>As shown in the figure, it is known thatfrac {OA}{DO}=frac {BO}{CO}=frac {1.0}{2.0}, the area of triangle AOB is 100.0 ^ 2, then the area of triangle DOC is () | 400.0 | 509 | [
"200cm²",
"300cm²",
"400cm²",
"500cm²"
] | C |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAI8AAABQCAAAAAAFYHm1AAAGc0lEQVR4nM2af0xVZRjHv+85TGqxmEujNpIfUsjSvKhN0xi0dGIG4sKkaRP+CCht4C7NnDTZsqkpoSX+3CKmLhxu3OmU60yj1E0WDVwspEAuE5osKxFbQ+57nv44914O3PPj/jqnvuPunvd9n/ecD+/zvO/7nHMPI1ioC3E2AwvBCgyvxsoMTSzlqZyRYmRiJc/B9N8MbSzkcY0smh5jZGQdD+3dgucMrazjOVTLkshwNlvG4xohcs5kRmZR... | <image>As shown in the figure, in triangle ABC, angle BAC = 90.0, AD perpendicular BC at D, if AB = 3.0, BC = 5.0, then the length of DC () | \frac{16}{5} | 510 | [
"\\frac{16}{5}",
"\\frac{4}{5}",
"\\frac{8}{5}",
"\\frac{22}{5}"
] | A |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAALQAAABVCAAAAADFvpHJAAAJLklEQVR4nL1af2xT1xX+Tsge0uYt/4RSBBuUtNAfY3MFFWNMg8EKGW2TrEUlLWELgxB3sCURE3RaxiqVP0CDiZaEJsMVzuYUR0kEjIbZY8Fkg26ISE41o8FEaBhlogJNmKTqnkNy9sd7z372e36+z/bjE8R+1+fc+73zzj333HMfMWyg8g8Apl1z2dFxAEV2hPlEVYT5B3PHnGKTnQEAe6SZxv/nBvYt2e4IIREQAHukCWe+AjA/9i9nGAng... | <image>As shown in the figure, in the parallelogram ABCD, AE:EB=1.0:2.0,S~triangle AEF~=3.0, then S~triangle FCD~ is () | 27.0 | 511 | [
"3",
"27",
"6",
"12"
] | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAKQAAABuCAAAAACMredPAAAK20lEQVR4nNVbXWwU1xX+7spNQ+LK0NZgtyiOCbBLkcLCS9dOIozUglETbEjin7ZKtk9IraqCiFr3oa7aSoBaQh76QKFSTCriNTwEGxVsNyo2v7tIFXZaqba1wSRAWYzadYCIJd74nj7M7OzMzv2ZnbVd9ZNs78yce+fs+e45955zr0EK7AEAtKtEFgSMoMAbl94vzzz/2PvlIKaSm2cEFM8om/x2ORYdv/Y74H+gY958KiXZx1cbAdTUJedd... | <image>As shown in the figure, in the parallelogram ABCD, AE = EB, AF = 2.0, then the value of FC is () | 4.0 | 512 | [
"5",
"4",
"3",
"2"
] | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAALkAAABrCAAAAAAOMHykAAAKv0lEQVR4nNVce3BU1R3+ztlFOj6GoQWTjmkzINFAlhqwk4YJshFQEdEaqyXq8BqjYEFBJRKrBAEtWnUKlYlQoGx8dGRqzXQ0FYvRPHBKcCRjG5tEJMGJdVRaqm7aMdm95+sf997du2E3e+/u3Y39ZnLn3rPn8Z3f+Z3f+Z1XBJEi2vImAVAy1fTpIvWC5xAqnfTpIuWS7/dPBpWbVBxCpKgtgQvnEIASwlU6DuBNLVkv8vzAaCpLSkUrYNdy... | <image>As shown in the figure, in Rttriangle ABC, angle BAC = 90.0, AD perpendicular BC at D, DE perpendicular AB at E, AD = 3.0, DE = 2.0, then the length of CD is () | \frac{3\sqrt{5}}{2} | 513 | [
"\\frac{21}{2}",
"\\frac{\\sqrt{15}}{2}",
"\\frac{9}{2}",
"\\frac{3\\sqrt{5}}{2}"
] | D |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAJIAAABtCAAAAABv1GeeAAAHZElEQVR4nL2bT4wTVRzHv29DInAhrBcPRt3dipsYe7JcqDERFg/urPGwJCJwIhATuW29QeKBg5ANiQlo11huC16oCSRu6HLgxmJMDBJjmClGORmpiYnUME3e18Ob6Uy705n3p+w3u9vO9s3009/3vd97896rIHS0PjWjVW6znj5nesaEXrE50+vGWtguxIQQ6ybnUEc1T6tYluYDknrvEkkrSvWD1y0CFFWJGaygZnKeDlJbTHkWSAIA1j20... | <image>As shown in the figure, the known point D is the midpoint of AB, AF parallel BC, CG:GA=3.0:1.0,BC=8.0, then AF is equal to () | 4.0 | 514 | [
"2",
"4",
"16",
"8"
] | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAJcAAABuCAAAAAAPad50AAAK80lEQVR4nMWcbWxb1RnHH6ebAeHNSLjCFYZCY4hRgN1RWM0algz6YmklLSxaO83S/KEk2jqpHammTjBt0yotqEXqWAOp8qEWtJAu6QITojeitJmWapEicWHt5LRrG7MWYRZU3DrS4hvv/Pfhvvuee6/t2O3/Q+7bc+/5+Zxzn/uctxBusDqJiIZtp6nByTIwj+udwxBJKj/fRI2Vj3xOl0Ag8skXEtRiv9hoLh6O+kdBPrk6QNu7BbtZo8Wc... | <image>As shown in the figure, it is known that the radius of circle O is 6.0, M is a point outside circle O, and OM = 12.0, the line passing M and circle O intersect at A and B, the symmetrical points of points A and B with respect to OM are C, D, AD and BC intersect at point P, then the length of OP is () | 3.0 | 515 | [
"4",
"3.5",
"3",
"2.5"
] | C |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAIgAAAA/CAAAAAAeHt9DAAAGiklEQVR4nLWZX2gURxzHfxtbBBtMHy71JEcP9dpcG2ljI9Q2AYNVekI4Y7GkDwqx1aRwpZEm0FBEX/KQB4WASVXy0BRSmmokSILetdH6EKhwhattJEiTeiFpmxLRw1h6Gc/99mH/387uzV7iF5LZmfnd7Gdnfr+Z2VkCABnFKkpERPWC1n1E9ctt/LoSItpXIknSC0tUhC5HfwG+f1nINi3dAr5au9GhGgCiKaC9fMlrd8gAi4D1sB4Ra1bZ... | <image>As shown in the figure, in parallelogram ABCD, E is the midpoint of CD, AE intersects BD at point O, S~triangle DCE~ = 12.0, then S~triangle AOD~ is equal to () | 24.0 | 516 | [
"24",
"36",
"48",
"60"
] | A |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAJwAAABrCAAAAACnRLQwAAAH20lEQVR4nM2bf0wb5xnHv++5LWtLRaTSkUlW2wRTaEEK0ayJiqShTVDQQjLWJEqlTWNIicoU2tBBRiikoYUUIkjHJkiXJRKlSqVGkLYRbURKfjRDaJlGZE9xFVLM5EmkEltWNS3aRInv6R/vnX1nzneH7bvzVxb2+97rez88z/u+fp/3fY8RJH2aswYAMaSPBPnD4ssMANKJLQrX+uhqJzk0JcO9XfyloxyakuBC3zz9SCYA0i1stwTO092E... | <image>As shown in the figure, in triangle ABC, angle ACB = 90.0, D is the point on AB, connect CD, angle ACD = angle B, if BC = 13.0, CD = 5.0, then BD = () | 12.0 | 517 | [
"8cm",
"9cm",
"10cm",
"12cm"
] | D |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAGwAAAB0CAAAAABFiIjnAAAHtElEQVR4nL1af2wUxxl9c+fUEnGEqhyxFZ2x6rjKAREcwghTjgJKJJzSKpUaqTUJJW5JWupUBZekSIlqR0UVUimllaO2IlWPijQgNT/+qA2oRLGRC0Z2Ck1c1hJNob2r6jRIEHxUdr27r3/s3t3u3uyvu3WffLc7M9/u23nfN7Mz31kQtYPCOJ67L+VpF4uACyaX+m0fu0jITPywZen/jexY+p8+FjWTlXyeL6y+b9ECk4niyc96hHd4RCjj... | <image>As shown in the figure, it is known that D and E are the points on AB and AC in triangle ABC, DE parallel BC and frac {AD}{AB}=frac {1.0}{3.0}, the perimeter of triangle ADE is 2.0, then the perimeter of triangle ABC is () | 6.0 | 518 | [
"4",
"6",
"8",
"18"
] | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAH4AAABWCAAAAAAst30PAAAGV0lEQVR4nMVaX2gcRRj/9qoU9eD8E+mp1wbTCFdT47URvGLlCgkabB4CnpS2echDS5XrQ4m1BAkNaNGCoQQ9oVTBK6YQpSU+pG0CKW1KWlNTOGxjr0KsKZeHk4g9vCgHmZufDzt7u3c7u5dcduMv5Gbnm2/nN9/MN9/M7C7BXfAEUevih1bFHnIVc55bwFcPP2up4Krti41dAHD0wv9hPejMXx8TEdU/b6WiwDVyhVjovZi9knvWK0R//FJX... | <image>As shown in the figure, in triangle ABC, D is a point on AC, if angle DBC = angle A, BC = 3.0, AC = 6.0, then the length of CD is () | \frac{3}{2} | 519 | [
"1",
"2",
"\\frac{3}{2}",
"\\frac{5}{2}"
] | C |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAHwAAACBCAAAAAAneYGlAAAJhElEQVR4nMWbf2gcxxXH38r9oxC1LvhEryBQbF3omaTtlRYiiECF2I1c3yUuyJiCad1WcUr0R+ViCRUM8h/9oTYudYsLOtsUQ+S/IqI0Pdln35m64NayXXAgok5hzzW9QJScC07PpZq7vfn2j/01uzd7O6fbkx5Itz9m97Pvzcyb92ZnNZCCQCMq7hxUKdqO9CiV0ohorxY1WwkOAtF0ZmfkcC3c7NCIcG7n15UqqC1R0Fwjovu0KxM5W7HO... | <image>As shown in the figure, DE parallel BC, BD, CE intersect at O, frac {EO}{OC}=frac {1.0}{3.0}, AE = N_3, then EB = () | 6.0 | 520 | [
"6",
"9",
"12",
"15"
] | A |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAHcAAAB+CAAAAAA7XdGeAAAHYUlEQVR4nO2bf2xTVRTHv/eVQUERa2QUROaQHyMm2xgROpR0I/7YIM5hogGCZEMjzBDYAgnbPzCJEU1wm8RfSGIRCGCiMBLdxj+sgGMsKttizCosWwAXYMaNKW5k67vHP15f19LX19e+22LMzrK+H/f0fd4999z7zj3vFhQPGS7AThrMagqvIUGstAEAkk7tv4KJb+voCeb2f+XbSeu+g7/SE8AlAEB7q+9wRhI6Zz2YAC4DALS2qce9A3tf... | <image>As shown in the figure, a beam of light reflects from point A (-3.0, 3.0), through point C on the y axis, and then passes through point B (-1.0, 0.0), then the length of the path of the light from point A to point B is () | 5.0 | 521 | [
"3",
"\\frac{7}{2}",
"5",
"6"
] | C |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAFwAAABqCAAAAAAUp2k0AAAGZ0lEQVR4nLVaXWwUVRT+ZiFIQpMaXdI1lr+2WLQKK2gCEaWaGkloSkF4gwSNlAdIQIGosQYf+tCkbaymRUw1AUVNaE15qKSV8pPYB0hNWqRBMSW7hhJpWk2b9aFld+7nw/zuzv/O8qU7e++5Z745e+65Z+6ZqUSExUBJ3GEkEpKZSB92HAxLLqFxeUXByal+TsYntW7hyCXlk0xteqxI7RaOHABAtL6PpxyHw5AT0slOaZWzQhhyCYkU2V/m... | <image>As shown in the figure, in triangle ABC, if DE parallel BC, frac {AD}{AB}=frac {1.0}{3.0}, DE = 4.0, then the length of BC is () | 12.0 | 522 | [
"8cm",
"10cm",
"12cm",
"11cm"
] | C |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAGwAAAB3CAAAAADDHPpJAAAIdElEQVR4nL1aa2wcVxX+ZtfGUgr1D6x4UbYNcSyyqSXXVUCpeHQdiIgLRnJVVONghAtBQkRBjilVASVuioH8oMoiVsS8pK2aSgFSxRKRuwYse02FUuWHq9JmU8ktFbaqtUpbRwTwzszejx+zs56duXcea9fHsmbm3rnnu98599zH2dGIhmVhZypag1jjWOYJIFpXNwH24zvvhLZNYE/d/WZUFzQIRqzcOrDztu0B0/Cz47graqtGzfjUT7U7... | <image>As shown in the figure, it is known that D, E, and F are points on the side BC, CA, and AB of isosceles triangle ABC respectively. If AB = AC, angle FDE = angle B, BD = 2.0, CD = 3.0, CE = 4.0, AE = 1.0, then the length of AF is () | 3.5 | 523 | [
"3.5",
"4",
"4.5",
"5"
] | A |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAALcAAABTCAAAAAD40MnXAAAGQ0lEQVR4nNWbfUxVZRzHP88Fx9G0bHPhHJryUiDMUmhaiNDATUI2G7F8qUxnRcOVmkpmKA7NOWavuFHWgjXNZpabL8wp8yIynYPpFEMHGKv7BzbNXGgnBZ7+uPeeey8qnHPvOZfTd3ec85yd57mf87u/3/c599wHpL/6pDFVC+bc/cBoLzPkwF8C3ZLgEuf75M5h4wz0Mk1CIo3g+qknNWc7sHFGrrlIuuQA4YctDXTd9Wc5QOwkk5F0SfQj... | <image>As shown in the figure, the cross section of a small reservoir dam is a right trapezoid, the width of crest BC is 6.0, the height of dam is 14.0, and the slope of the slope CD is i = 1.0:2.0, then the length of the dam bottom AD is () | 34.0 | 524 | [
"13m",
"34m",
"(6+14\\sqrt{3})m",
"40m"
] | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAI0AAABPCAAAAADzFRnGAAAFs0lEQVR4nMWaTYgcRRTH/68ZpBKQrMFgLtlEFDJewq4IbgKaLBhIvCR78xBiclCC4GFykEzAzG6UFRQzehD2IEmEBASJi172uCsSGIRk1lyyASWT1cjGDUwushXX9PNQH1290/PRH9Pz9qO7q7te/frVe9Wvqhs8KPF95kkAeOMfZl+VeRiUEAGVq+/y2loJIFU2OBoA+G/uEMRBp2BgPcXMfmPPKl/ddsMWDNQ2dP3WNrr/98u2YKA063Pf... | <image>As shown in the figure, the slope of the slope formed by the conveyor belt and the ground is 1.0:2.0, it sends the object from the ground point A to the point B higher than the ground 2.0, then the distance the object travels from A to B is () | 2\sqrt{5} | 525 | [
"4",
"2\\sqrt{5}",
"\\sqrt{5}",
"2\\sqrt{3}"
] | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAHgAAACNCAAAAABZUOGkAAAJoklEQVR4nL1bfWwUxxX/je3KlkJrVJ/LUQ4dMQYdhkgncKoTiUtbkGpFGFOgMn8krSsODMUUR/0gEW2lKqogbSo+YscOENVVXNVVTYOOcA2SU4FUC5BNScLHocQIt6aSKW5iauzeset9/WN37/ZuP25n1ucn2zszO/Pe+735zezs7JgRvMl7UoNQuyIPNgnA9M/VBLf/XgwzAD8qWw0wNT1nhgEc9ksCaL0bHvr0uXllYCK2PRlOdRxARQUg... | <image>As shown in the figure, in triangle ABC, AB = AC = 18.0, BC = 12.0, the vertices E and F of the square DEFG are in triangle ABC, the vertices D and G are on AB and AC respectively, AD = AG, DG = 6.0, then the distance from point F to BC is () | 6\sqrt{2}-6 | 526 | [
"1",
"2",
"12\\sqrt{2}-6",
"6\\sqrt{2}-6"
] | D |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAHoAAAB6CAAAAABVMhg4AAAHJklEQVR4nL1bXWwUVRg931iC1OqDCPUnQPgxNdIHNBB/6sNqSFpMbIlPYAjGgGAoCYaY6ANvRlmNGCBWHjTxQQ0VfBPawoP156k0tJGSIInYasEYHjBx24e27j0+3Jmd2Zk73Zmduftlu7t3Zveee+73nfvd3nsXJFmm+6yo2ADrAwpzhxwAPXeJyMqSQwgElo2YkivkF0sfBEl2j5GHV5QaQ3mubb8iefiMQ2D+vyeAYx1v2acMAJ/f+UgA... | <image>As shown in the figure, in the square ABCD with edge length 9.0, F is a point on AB. Connect CF. Pass point F to draw FE perpendicular CF which intersects AD at point E, if AF = 3.0, then AE is equal to () | 2.0 | 527 | [
"1",
"1.5",
"2",
"2.5"
] | C |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAHMAAABgCAAAAAALahIPAAAJiElEQVR4nL2af0wUZxrHvy+YG+LRYLpLbytrSdRWFM9SgRNwKVa3FXsuIKXa5LxEoim9wxjt2R6e2qWJPTBtKlWp9aCnl5zRq1A8tGhP2gOVgNm1qIBcc5Jq4RJPVt0GxJkK+9wfMzs7Mzu7sLh7T8jOvD/2/bzP8z7zvA/vLEgWPg8AqiniAsU9n1dNTfGNEWdGwSdjt/MR/zgiLkpm6/QE4d1kW8SZUxT3Vz5n8Z/aiEWaqdBTaG+kN9ef... | <image>As shown in the figure, in Rttriangle ABC, angle BAC = 90.0, AB = 2.0, AC = 3.0, D is the midpoint of BC, and moving points E and F are on AB and AC respectively, passing points to draw EG parallel AD parallel FH, and they intersect BC at points G and H, if EF parallel BC, then the value of EF + EG + FH is () | \sqrt{13} | 528 | [
"\\sqrt{10}",
"\\sqrt{13}",
"2\\sqrt{10}",
"2\\sqrt{13}"
] | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAGwAAAB6CAAAAAB/gumXAAAHVElEQVR4nL1abWhUVxp+zkSaglmS0tBYGrbEDDTQ0o51FiMd1x/pJzi20gjuqtAW6wfsj7QwUouwgllWt7QoaOu1oZTWVoMpjR/Qhkn6R0MT1Hb6tebHjMuy6Yc4PyxGqsXcZ3+ce+/cmXtOcu/MGZ+EuWfOeXOfnPec9z3ve84RhHGMdnRSqBpi5rnwBKDkMk1GAtvTnVDrSxhX4+HFT+jeaVyNBXakdW3GyOioztqCrrqTCTkpDr8Ri2tl... | <image>As shown in the figure, in triangle ABC, D and E are points on AB and AC respectively, and DE parallel BC, if AD = 5.0, DB = 3.0, DE = 4.0, then BC is equal to () | \frac{32}{5} | 529 | [
"\\frac{12}{5}",
"\\frac{15}{4}",
"\\frac{20}{3}",
"\\frac{32}{5}"
] | D |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAKYAAABSCAAAAAD74PCkAAAHaklEQVR4nL2aX2gcRRzHfxvE4AnNy4YqTXKttiYvhlh9iNrQlzMoWtqiRbFXc1ZMrffSQi31QS9FhBBfKqagViWC6YtpinCQSxHMQwIn5QwGJCKpvTw0PXoVcr2m29yl+/Vhdm//787sJfnShr29nZnP/b7zm52ZXcKmaYCIiOhymLIP0aYpRUvfYO29Ns7LIZk+NGwEkLuqC6/QD9V9vJgSTB82EXNprmcxFzkk814fLppnJUmSpGMiYFbN... | <image>As shown in the figure, in the parallelogram ABCD, E is the midpoint of DC, the area of triangle DEF is 2.0, then the area of triangle ABF is () | 8.0 | 530 | [
"2",
"4",
"6",
"8"
] | D |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAHsAAAB4CAAAAAD3ONINAAAH0UlEQVR4nL2bf2jc5hnHv/I6uqUF+Q9niPXa60xKlTozpv7Hg4FT6sG1BOoUN8m1K3W6QgrrwJi1mJHmttIStwud1xnqYljP7EdcktYtdb0rTdjdyDIP/2EIXpRClnj46G5JaK84WeT6rG//0Ol+6PTjlXT2F5vT6f3x0fNK76tHj54Dt1YGmQSAOZIQbpXTmsVPzjEHjWyBgAig9LPyRkhVm5Y+7UU7APizCUgAjsbvMjdCqtr07O5v44Vh... | <image>As shown in the figure, AB parallel CD, frac {AO}{OD}=frac {2.0}{3.0}, then the ratio of the perimeter of triangle AOB to the perimeter of triangle DOC is () | \frac{2}{3} | 531 | [
"\\frac{2}{5}",
"\\frac{3}{2}",
"\\frac{4}{9}",
"\\frac{2}{3}"
] | D |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAKEAAAB/CAAAAACiDv01AAAJIklEQVR4nM2cfWwcRxnGn3VjUqUGB+TgbbXJqY5FXQ4FCxMRZKNYIlUuUZACMk1MgpqgUJEYiWKRykVtQCWAERWKwBWugtSr0gYrjQgSqT+kWMSJXSw5wjTEcRH5cHQn5BBDbcWm1/NlH/7YvY+9u/2ancv1J59393Zm7tl535mdmXfvQEHaoQDakmj2YkSB7ckfkiT17LsV8AnN18n2qzq/9dj//Oa3LTeuXKb+ykceAQAouWcEWW4jyfbO... | <image>As shown in the figure, AB parallel CD, AC, BD intersect at O, BO = 6.0, DO = 3.0, AC = 12.0, then the length of AO is () | 8.0 | 532 | [
"4",
"6",
"8",
"10"
] | C |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAIsAAACCCAAAAABTfWTrAAAIH0lEQVR4nMVbf2wbVx3/PKej0qgUEFFrFY90jREpmzIPkCqUIFcq0rLCWJEy0qSVkCBTOyYgqjZVZaHwR4EGOq1AECkrmrcVJaiIjD/aZoJCXGWbJtBcTaiZ1IxtdSq5hIKlZGo6u+/DH/fDZ/vOfu98Z3/Uxvfe3Tt/7vM+7/u+9+4siFBAcXFjt2abSChMAFH8NqF5nWFxwY87OyH0mgTPxRDj+Z5r2i2D5yIAYGn1cxvvbD0XAMAvH+en... | <image>As shown in the figure, in triangle ABC, E and F are the midpoints of AB and AC respectively. If the area of triangle AEF is 1.0, then the area of the quadrilateral EBCF is () | 3.0 | 533 | [
"1",
"2",
"3",
"4"
] | C |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAIoAAABbCAAAAACJjkIyAAAId0lEQVR4nMVabWgcxxl+V07/hEIomHqdrm1sXYiSo6pSCVKqS2xIWp+LCi4IjJr+MI2LA+cQVw1FtIlKi9qqwdAWn0vAP3yGpqhYYP1QrXOJwZfIzZVLq+IqvgafQt1TQfGF9syprZI5z9Mfs7u3HzOze5eT9YCt3dmZuWffd573nY8l6MFRKNsXrf87xhgRkbUuf9hDehjN5+G9jaiuBoiIXjtSBr7Z919pjSgq9JM9e7wkoKmqIyHa32V9... | <image>As shown in the figure, in the trapezoidal ABCD, AD parallel BC, diagonal AC, BD intersect at point O, if S~triangle AOD~:S~triangle OCD~ = 1.0:2.0, then S~triangle AOD~:S~triangle BOC~ = () | \frac{1}{4} | 534 | [
"\\frac{1}{6}",
"\\frac{1}{3}",
"\\frac{1}{4}",
"\\frac{\\sqrt{6}}{6}"
] | C |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAKMAAAB4CAAAAAC7/h2wAAAKDElEQVR4nM2cf3AU5RnHP+9eIIkcvViPAdo44CQIlqhHYUYodMChaDrEHyPQ0dG2OK0/ptAJlFAZLaMzwihVKlMM/mwpLZ0q4lTrr2QsFVuitKaT2AYhJamhxBZMrBcTa2Jy+/SP3b1973KX5OLt3X5nLvs+zz7v7neffX88++y7UYJ/IAqA9bOqE9RGPrikg0IAeqYAmu98xREUQPd5gOKsQ9M/HF3HdZUAcqziX7bsH47KKUg0DLxX+cQM... | <image>As shown in the figure, planting trees on the hillside, it is known that angle A = 30.0, AC = 3.0, the distance of slope AB of two adjacent trees is equal to () | 2\sqrt{3}m | 535 | [
"6m",
"\\sqrt{3}m",
"2\\sqrt{3}m",
"2\\sqrt{2}m"
] | C |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAIUAAACfCAAAAADy/EUdAAAmo0lEQVR4nM18aZQlR3XmjYjcM1++fauta+u9VepWS6IlISEMCBnkgcEs9piZ0cwYozGLWDQIeXTAbAZsZITNOeMf9hzAzAyD7THYLAMSQiCEhNRqulutXlT7XvX2JffMiJgfr6q7qrqqurrlH3NP1YuXkZERX373xs0bSz7EYSvhHG95DoAjAM4BIQBgGIBhYNuV31a2vpAjDABbgkQAgBBCnL0TEYS+j4FdKwYA4FsI2+rE5QXf8T3+JJzl... | <image>As shown in the figure, the elevation angle of the top of a building is 30.0 when viewed from point A in the air by a hot air balloon, and the depression angle of this building is 60.0. The horizontal distance between the hot air balloon and the building is 120.0. The height of this building is () | 160\sqrt{3}m | 536 | [
"160m",
"160\\sqrt{3}m",
"(160-160\\sqrt{3})m",
"360m"
] | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAR0AAACzCAAAAACRYJeNAAAs8UlEQVR4nOW9eZydR3Um/Jyqepe7397VUkuyNsuyZGNsD15YE2BMJnzAjJkhCfABM5PBgInlxGTsHxAMOGMDNijEHswSwPlMBg9mPkPisVnHBowNGK+SraUla++9++7vVlVn/ri3u9VyS2pZrdWPfj/d9623um7d5z11TtWpU1XEeBnil68D7l6y6z1HyidORGVOMSRvf/8Q2yevXH7EnPTyk53kncM/yYLDP/xB95GyqhNRn1ML33r0vixA... | <image>As shown in the figure, a teaching interest group wants to measure the height of a tree CD. They firstly measured the elevation angle of the tree top C at point A as 30.0, and then proceeded 10.0 along the direction of AD to point B, and the elevation angle of tree top C measured at B is 60.0 (the three points ... | 5\sqrt{3}m | 537 | [
"10m",
"5m",
"5\\sqrt{3}m",
"10\\sqrt{3}m"
] | C |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAL0AAACXCAAAAABliwW8AAAWCElEQVR4nO1deXRV1fX+9r4vCQRibRUEoQ4oMklBqXWWwQGwKgXbWhxaXWodFm1djogFTAREQCCA4k8tDlUotBUnEBUFQRFRpCpRUBSJUJmTl4HkvXvP3r8/zr3vvSTvJe8hkGStfouQO5xz7nf33WefffbZ94YUzRjc2AQyh8YF3vzYVy1aH9tuduz1v2MpttPs2JfM7HysBDvNjX3pgq5bnRjp5sJeAQXE2xLp0z43drS5sCeAAOydez2d... | <image>As shown in the figure, in order to measure the height of the TV tower AB, use the goniometer CD with a height of 1.0 at D, and measure the elevation angle of the top A of the TV tower to be 30.0, and then walk 120.0 in the direction of the TV tower to F, and the elevation angle of the top A of the TV tower is 6... | 60\sqrt{3}+1 | 538 | [
"60\\sqrt{3}",
"61",
"60\\sqrt{3}+1",
"121"
] | C |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAJ0AAABwCAAAAAAhly1WAAAKO0lEQVR4nMVbf1AU1x3/vAMkEFQsKCchWJUaFY2AUqlp1cSJxghKm19K6WjVjJ2YsTrpaDoyqBObSRvN2CZVWqzK6CiNTscxJjg6QaOQ+qMGEIXRGKqGBgUjHIfK/dpv/9jbvd27fcud7N59Rtnb977vvc9+f723b3cZIcJoxjhunSWMPDThLNWpjDi7iiHD+ZWRZleVdl+nNsLs2mxZQ2L51ZFl5z68AE/EAQTt4IwsuxNvxKf2AmBgmvUR... | <image>As shown in the figure, in a mathematics extracurricular practice activity, Xiaowen measured the elevation angle of the top A of the tree at point C to be 37.0, BC = 20.0, then the height of the tree AB is () (reference data: sin37^\circ approximate 0.6, cos37^\circ approximate 0.8, tan37^\circ approximate 0.75... | 15.0 | 539 | [
"20m",
"15m",
"12m",
"16m"
] | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAKQAAACJCAAAAACH7Mx1AAAYhUlEQVR4nMV8eXxURbb/t+re7k53Op1OQhJCEhISlrAEAsIAIggPFxBFEB1xdNQZFxzUn85jfM64IA6/p/jQcd4IDOL28TeM44gbMCrIIogsSpwABkiEAIEESMjSSbrT2606vz9ud7qTdKCz4Zfl3lv31qnvPVWn6txTVc0kA4gBACTX/+kIJEaLUEZAes2dyhuOSMUy6rK4dpDgehFEHJBgnXvNjsElIKUAZICtFAARSEpAdkKQJgQgGCQA... | <image>As shown in the figure, to build a highway in a certain place, a tunnel must be built from B to C (B and C are on the same level). In order to measure the distance between B and C, an engineer took a hot air balloon to start from C and rose vertically 100.0 to reach A. Observing the depression angle of B at A is... | 100\sqrt{3}m | 540 | [
"100\\sqrt{3}m",
"50\\sqrt{2}m",
"50\\sqrt{3}m",
"\\frac{100\\sqrt{3}}{3}m"
] | A |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAFMAAABdCAAAAAD80wWsAAAEMUlEQVR4nK2Za0hUQRTHz9oYYoUVhpj0tpCCil6EVBDlh7KiB0L4oYVqyd3MqLRWehCWZYUfogeFvR8WRJgZGb3LCCMyavtgiJTbViRBRK5pO+7tw+7Vu3ceO3fm/oXdnXPm/u45M2funUGHBrYrwX4kILuBbb4OO5k/Xjd//jrkVoZNzODbxo/+rqTRk5aNDRTbwPTdb237nZw2NT8rJRnghSNHndk0fcbK3FnD9Ob7HIcyU8uH2uGGdiik... | <image>In the mathematics practice inquiry class, the teacher arranged for the students to measure the height of the school flagpole. As shown in the figure, Xiao Ming's study group is at a distance of 10.0 from the bottom of the flagpole. The elevation angle of the top of the flagpole is measured with a goniometer as ... | 10\sqrt{3} | 541 | [
"10\\sqrt{2}",
"20",
"\\frac{10\\sqrt{3}}{3}",
"10\\sqrt{3}"
] | D |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAKkAAABkCAAAAADYyE+ZAAAHOElEQVR4nM2bf2xW1RnHP6f18hJt0swVmwVjJ61rjfzRzkUlLKGbGnCLtUaYZOvCtjjWLCzI0CCZxBLN5gbDuVEWZYYYQ9LIiBAladMNZvYjIetsSSCC0lgSNCHDjUo1lLv22R/3vr/63nPfc+6v8k373nvPj3s+ec5znnPued+rhBANNbaHZWeqmrBMd2NWGAYKJX36lpasOKorjHRPx0eZcVRXCOnE5XsW1WVHUk16Utm5hS9lSFJNetLf... | <image>As shown in the figure, to measure the height AB of a tower that cannot be reached at the bottom, two students of A and B took measurements at C and D respectively. Given that the points B, C and D are on the same straight line, and AB perpendicular BD, CD = 12.0, angle ACB = 60.0, angle ADB = 30.0, the height ... | 6\sqrt{3}米 | 542 | [
"12\\sqrt{3}米",
"6\\sqrt{3}米",
"12米",
"6米"
] | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAOIAAACACAAAAAAzR+paAAAU0UlEQVR4nO1de3RU1bn/7XnlqSPUAWORGB5JgYIhiGiogFyiAYG0gM1lFb1cBLyNvYVa0brU3uUC1EplLW2iWOp1UQtLy6tAxaB4efjoNQqJQggSk1AgJiE1hLxzZub87h9nnmfOOXNmMtw+Vn8LM/vs8+39PfY+e++zz/dtBaENCt+f8EQkHTSzBwIdRp7zX1+SrEK2XXPtCD9hBKlGWWGoohqNre2S1etNTht+XQzCDRj87MuqYxebmgOy... | <image>As shown in Figure 1, the clock face of a clock is fixed perpendicularly on the horizontal desktop, and there is a point A on the minute hand, and when the clock face displays 3.0 o'clock 30.0 minutes, the minute hand is perpendicular to the desktop, and the height from point A to the desktop is 10.0 cm. As show... | 19.0 | 543 | [
"22-3\\sqrt{3}",
"16+\\pi",
"18",
"19"
] | D |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAIgAAABbCAAAAACNe5IPAAARCElEQVR4nMVae5yVVbl+1vvtNXtA0DQwr5Hp+dWpU8oggeMoggPewh/eQgnxaKKllRmZkqngPUwys/KClilqKmNeQrzkNTyaBzPzWB0tARVEkJMOM/Pttb73fc4f396z98ye4QhMnff3g733N+tb3/O9t/W+z1qO2FyhQ3rLzM2+vZfI5t/qEGe+N1A4PgAQ9vkVAHDXrbv/E4G4KgjXE8uKt44fMBwf3DSuxwcApGd9afmIfwKQDAaDAjAD... | <image>As shown in the figure, PA and PB are the tangents of circle O, AC is the diameter of circle O, angle P = 50.0, then the degree of angle BOC is () | 50.0 | 544 | [
"50^\\circ",
"25^\\circ",
"40^\\circ",
"60^\\circ"
] | A |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAIYAAABUCAAAAABi5BBpAAAHeElEQVR4nMWaf3BU1RXHvzfJIzO6ndROEGayxVZqs210msBaMiTqamjJKBNLA+0/ToEaQ5hFQWPGMEKTGeOwndARxw0mihaKdtCGkU4KZCkCLdEJQ+pu21DpaJrYWMdUOg0mTpO9sN/+8fbtj2T3/dh9JGcy2ffuj3M/75xzz7vvvicIyxJYVGq9k77kWO8it9kNYRWDALBzyTfmGUMA2Ff2CTLwpJ0YAEYmyhc6xPxiEGh/Ct+E7eaw6pSO... | <image>As shown in the figure, in Rttriangle ABC, AD perpendicular BC at D, DE perpendicular AB at E, if AD = 3.0, DE = 2.0, then AC = () | \frac{9}{2} | 545 | [
"\\frac{21}{2}",
"\\frac{\\sqrt{15}}{2}",
"\\sqrt{15}",
"\\frac{9}{2}"
] | D |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAGsAAAB0CAAAAACnVJOeAAAJAklEQVR4nL1abWxT1xl+bshNKtXIjTAlDLZUJS3eQoQ7jJYqWWO0IsyW0qDB0qmNgIkFJiIlUzMRBBugwUbVVoBmqrGg4QqQWKGDalE+2mwYDYvQpE0YQQFhRhhUS+q0JbLREp/E735cX+f6fh43No+S63vfc859zvtxvi/oUeAI4Ik15CD7GBKuEh3P+4ZAWadipZVHATSVPQK9Wr58GwCeLs6+Xqx003bpLvt6fXazGI+KC5BNl32uBYtv... | <image>As shown in the figure, in triangle ABC, AB = BC = 2.0, circle O with AB as the diameter is tangent to BC at point B, then AC is equal to () | 2\sqrt{2} | 546 | [
"\\sqrt{2}",
"\\sqrt{3}",
"2\\sqrt{2}",
"2\\sqrt{3}"
] | C |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAIQAAABuCAAAAADD8OSfAAAIqklEQVR4nM1ba2wU1xX+jnEmikO7SFklDl1jsRhlnUXEgKNagmAjExXHa9lWKrV2KuUhNfmRtIpoi5CimCZUKkpJflQgRaVVbKkEIlFhxNYmFVZs5FBLgCDEztqqKU13ESRxiymGeB+e0x+zs4/Zndl7526jHq12Xvfc+8055577OGfAWeoFgCH+5gm5Fz1D+hgiEty6UtsZ7gpkKTXTDL9xyrCnXiIiagPA5FCsNBGAM9MM5II421JFu3YG... | <image>Definition: The minimum value of the distance between a fixed point A and any point on circle O is called the distance between point A and circle O. There is a rectangle ABCD (as shown in the figure), AB = 14.0, BC = 12.0, circle K and the edges AB, BC, and CD of the rectangle are respectively tangent to the poi... | 4.0 | 547 | [
"4cm",
"8cm",
"10cm",
"12cm"
] | A |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAH8AAABuCAAAAAArXJPxAAAK30lEQVR4nMWbfVwU1RrHH4iXRDNkAQFXQBIWX0DkSr4gvpKE9tFCyvC1NCGxW9eX7Fof0/RWV03rRkZ6tW4aQqKYKQJ2r+a7YCiKCAuJgJoob5YsLDu7+7t/7LLsy8zuzLJrv392zjnPnO88z5ydc+acMw6gP1WOfy6enLpx7sOau03N7QrGyeVxD5FPoLs1dThYFX/l1cIrpRUdgb6iPj1dnFSKtpam+hqShIWPHO5qbz7K8gsKg0ZGDB0k... | <image>As shown in the figure, circle O is the circumscribed circle of triangle ABC, angle BOC = 3.0 angle AOB, if angle ACB = 20.0, then the degree of angle BAC is () | 60.0 | 548 | [
"120^\\circ",
"80^\\circ",
"60^\\circ",
"30^\\circ"
] | C |
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