images listlengths 1 1 | problem stringlengths 14 525 | answer stringlengths 1 103 | id int64 0 2.82k | choices null | ground_truth stringlengths 1 103 |
|---|---|---|---|---|---|
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAlAAAAHWCAYAAAC447cdAADngUlEQVR4nOz9d3Ab9/3v/z53UQmAIFhAAOykRFIiRfXeJctd7r3X9DhxEp8yd+6Ze8/cM/M738Qtvcdxi3svsmzZ6r2LRaREUmIFewOIjt37ByC5qVFmk/R5zCieUCCwELCffe2nvD9SJBJRNRoNgiAIgiAIwrmRVFVVx/ogBEEQBEEQLiTyWB+AIAiCIAjChUYEKEEQBEEQhCESAUoQBEEQBGGIRIASBEEQBEEYIhGgBEEQBEEQhkgEKEEQ... | <image>Find m \angle P N M. | D | 400 | null | D |
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{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAkoAAAFxCAYAAACMdodqAABncElEQVR4nO3dd3xV9f3H8de5K3vvACGE7ABuce+tOBHcdWtra2tttdZfa6uttnbZ1lFnXSjg1rr33gvIzSAkjEASsndyx7m/P5Lce4MEAgay3s/Ho39UBW5r7rmv+z2f8/0aPp/Ph4iIiIh8h2W0X4CIiIjIWKVQEhERERmCQklERERkCAolERERkSEolERERESGoFASERERGYJCSURERGQICiURERGRISiURERERIagUBIREREZgkJJRERE... | <image>If P R \parallel K L, K N = 9, L N = 16, and P M = 2K P, find K P. | A | 401 | null | A |
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{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAARoAAAECCAYAAAAhNhhMAAAyLklEQVR4nO2de1xUdf7/n4IjICIEiCigCGFKZqBohZe+mrVpRavprv1WM92u7q615X67WlttW7Z+2/S7Xeyime63vmm6kZe2tL6akSkqpSJKICo3ESbkPg4Mvz/GGWZggBmYYc6ZeT8fjx4PsDNnPsyc8zrv+6dXY0NxM4IgCC7Ex90LEATB8xGhEQTB5YjQCILgckRoBEFwOSI0giC4HBEaQRBcjgiNIAguR4RGEASXI0IjCILLEaERBMHl... | <image>In \odot G, m \angle A G B = 30 and C G \perp G D. Find m \widehat C D F. | C | 402 | null | C |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAXgAAADaCAYAAACsPln3AAABRmlDQ1BJQ0MgUHJvZmlsZQAAeJxjYGASSSwoyGFhYGDIzSspCnJ3UoiIjFJgf8LAzCDGwMvAzWCZmFxc4BgQ4ANUwgCjUcG3awyMIPqyLsisayszrE7URYr5bTi99smnzY2Y6lEAV0pqcTKQ/gPE6ckFRSUMDIwpQLZyeUkBiN0BZIsUAR0FZM8BsdMh7A0gdhKEfQSsJiTIGci+AWQLJGckAs1gfAFk6yQhiacjsaH2ggCvi6uPj0Kwq5G5... | <image>Find the area of the parallelogram. Round to the nearest tenth if necessary. | B | 403 | null | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAa0AAAGqCAYAAAC4UxuPAACQ0ElEQVR4nOzddXhc15n48e8d5hnRjNiSBWaGJI7DDTTMnDLjtt1ud7dd+nW32912t8zdUpo4jA465DgcM8i20GLNjKRhnjv398eMRzIksWXJovN5njyJHWskS3fue885L0iKoigIgiAIwjSgmuwvQBAEQRBOlAhagiAIwrQhgpYgCIIwbYigJQiCIEwbImgJgiAI04YIWoIgCMK0IYKWIAiCMG2IoCUIgiBMGyJoCYIgCNOGCFqCIAjCtCGC... | <image>In \odot F, G K = 14 and m \widehat G H K = 142. Find J K. | A | 404 | null | A |
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{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAPsAAADVCAYAAACR1IbgAAArb0lEQVR4nO2dfVyUdbr/3ywQDyIIiIiAPD+IgwKKmmC4nbRsK9TWWq0sf0vtZtbJOrqdrbbaspfp9qhn62y2ZpbVmphtW5puR0tKBYEUlWdBBxERkMeBYJzfH8PczCBPysA998z3/Y/34Nwz18zcn/t7fa/vdV1fO51Op0MgEFg9v5DbAIFAMDwIsQsENoIQu0BgIwixCwQ2ghC7QGAjCLELBDaCELtAYCMIsQsENoIQu0BgIwixCwQ2ghC7... | <image>In \odot F, F H \cong F L and F K = 17. Find J H. | A | 405 | null | A |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAnAAAAFgCAYAAAA7LUSlAAC0/UlEQVR4nOz9d3hcV3rn+3535VyFQhVQyAAJgCTAHCWKpMSk1MqZSt0OY8/MGZ/xeGbs8Zw799xz7nPu5Ojx2O623a1Wt1rqllo5kFRiFDMBEgRAEAzIuXJO+/5RhUiASSRAAOvzPHpaagLFXQAK+1fvu961JFmWZQRBEARBEIRZQzHTFyAIgiAIgiDcHBHgBEEQBEEQZhkR4ARBEARBEGYZEeAEQRAEQRBmGRHgBEEQBEEQZhkR4ARBEARB... | <image>Find x. | C | 406 | null | C |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAVgAAAFcCAYAAACN/aZWAABNKklEQVR4nO2df0BV9f3/nw0cXLygoHhREBAQUa/mD0ALCtfyR63EH7OWS8tF26eFlSvL1bZyy2Y6cyWr75JmPzbdcqK2tkpdk8KmgIp6VUREkIuKN0Au6IV56X7/gAP3/LiX++Oce8859/X4p53DvdczOPd53u/Xj+frJpvNZgNBEAQhOt/y9wUQBEGoFRJYgiAIiSCBJQiCkAgSWIIgCIkggSUIgpAIEliCIAiJIIElCIKQCBJYgiAIiSCB... | <image>Quadrilateral A B C D is inscribed in \odot Z such that m \angle B Z A = 104, m \widehat C B = 94, and A B \parallel D C. Find m \widehat B A. | C | 407 | null | C |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAncAAAIICAYAAAAMvsh2AACwxElEQVR4nOzddZic5fX/8fczbrs76+4SIUJCICTEgeDeUupuv3pLS73QUqGl7t5+a7TFKRICJMRIAkmIZ91dZnfcn98fO5lsQnQjuzN7XtfVi7LsTia7z87zmfvc59yKqqoqQgghhBAiKWgm+gkIIYQQQohzR8KdEEIIIUQSkXAnhBBCCJFEJNwJIYQQQiQRCXdCCCGEEElEwp0QQgghRBKRcCeEEEIIkUQk3AkhhBBCJBEJd0IIIYQQSUTC... | <image>Triangle J K L is circumscribed about \odot R. Find the perimeter of \triangle J K L. | B | 408 | null | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAsUAAAF5CAYAAAB3K1eLAADQ30lEQVR4nOz9V3RcWZbmef5Na23QWgMEtdaadJLu4R4qM7JSVJZoUSO6qh66e2rWvM28zczLPHX3dE9Xd2ZlRUZkKBd0J+nUWisoQmthMK213XkwEASlUwB0iPNbK9byAAGY0Wh2777n7rM/2f/r+l6JOSRJou9ajEffhvGNprHbHPxf/sP/laPHPsFgMCAIgiAIgiAIy4187v95VUH8b//dv2f/wQPo9fof6zkKgiAIgiAIwoJSPv2P2YL4... | <image>\triangle M H J \cong \triangle P Q J. Find y. | C | 409 | null | C |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAQcAAAC+CAYAAAA4GcquAAABRmlDQ1BJQ0MgUHJvZmlsZQAAeJxjYGASSSwoyGFhYGDIzSspCnJ3UoiIjFJgf8LAzCDGIM6gz2CQmFxc4BgQ4ANUwgCjUcG3awyMIPqyLsgs+VNVf877TN/6iLfO3WPuVBNM9SiAKyW1OBlI/wHi9OSCohIGBsYUIFu5vKQAxO4AskWKgI4CsueA2OkQ9gYQOwnCPgJWExLkDGTfALIFkjMSgWYwvgCydZKQxNOR2FB7QYDXxdXHRyHY1cjc... | <image>Find the measure of \angle 6. | B | 410 | null | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAocAAAEvCAYAAAA3s2v8AAABRGlDQ1BJQ0MgUHJvZmlsZQAAeJxjYGASSSwoyGFhYGDIzSspCnJ3UoiIjFJgf8LAzCAIhLwMDInJxQWOAQE+QCUMMBoVfLvGwAiiL+uCzFo004JpwfNI7YUcq///4uaajqkeBXClpBYnA+k/QJyeXFBUwsDAmAJkK5eXFIDYHUC2SBHQUUD2HBA7HcLeAGInQdhHwGpCgpyB7BtAtkByRiLQDMYXQLZOEpJ4OhIbai8I8Lq4+vgoBLsamRta... | <image>Find the measure of \angle 1 if m \angle 4 = m \angle 5. | C | 411 | null | C |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAj8AAAGuCAYAAAB/fmdMAAB+4klEQVR4nO3dZXRc1/X38e+9wyNmsGSmmNmJHWZmdKhJiin+mzxNIaWU27RN2zRlCDXMzIntJE7MzCRmHL70vBhZlmRJlmThzP6sldUqkcZjSXPnd/fZZx/FsiwLIYQQQog4oQ71ExBCCCGEGEwSfoQQQggRVyT8CCGEECKuSPgRQgghRFyR8COEEEKIuCLhRwghhBBxRcKPEEIIIeKKhB8hhBBCxBUJP0IIIYSIKxJ+hBBCCBFXJPwIIYQQ... | <image>Find x. | B | 412 | null | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAm8AAAFSCAYAAACkOjhmAABywUlEQVR4nO3dd3ib53X///eDvQmA4F6iBjWoYcmW5CXLki1v2amTNLNNkybNaka/bdJ0pWnTlfFLm6RJk2a0Sdzs6W3ZlmQNL1mStTf3xiL2xvP7AxCHLNuyBkmA53VdulgppPuQBB58cN/3OUdRVVVFCCGEEEKUBM10X4AQQgghhLhwEt6EEEIIIUqIhDchhBBCiBIi4U0IIYQQooRIeBNCCCGEKCES3oQQQgghSoiENyGEEEKIEiLhTQgh... | <image>The segment is tangent to the circle. Find x. | B | 413 | null | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAc8AAAGwCAYAAADPDO4/AAA/cElEQVR4nO3df3DUd37n+TdYNq2xoNXsyQli9AOEdVksoTYc4x0LI1F7BTbcjOS62ongPIvI7sUYJ3HPuHzsYqosV2GuXLP2tDNjjDNbQdy4jJKqu2mSMg7e3bjBKBVbZ6aNNMotY0FbGomN2ekfCKfbdtvcH7La/f1++9e3f31/9PNRNRV/G3XrG5D61Z9f7/eSW7du3RIAAJC3pUbfAAAAVkN4AgCgE+EJAIBOhCcAADoRngAA6ER4AgCg... | <image>Find P W, if X Z = 18 and P Y = 3. | C | 414 | null | C |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAPgAAAD/CAYAAADc1BuzAAABRmlDQ1BJQ0MgUHJvZmlsZQAAeJxjYGASSSwoyGFhYGDIzSspCnJ3UoiIjFJgf8LAzCDGIMRgyKCfmFxc4BgQ4ANUwgCjUcG3awyMIPqyLsisB/O42vdrVBiX2l66POt2/ANM9SiAKyW1OBlI/wHi9OSCohIGBsYUIFu5vKQAxO4AskWKgI4CsueA2OkQ9gYQOwnCPgJWExLkDGTfALIFkjMSgWYwvgCydZKQxNOR2FB7QYDXxdXHRyHY1cjc... | <image>Find the area of the shaded sector. Round to the nearest tenth, if necessary. | B | 415 | null | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAATAAAAFUCAYAAACjnmC/AAABRWlDQ1BJQ0MgUHJvZmlsZQAAeJxjYGASSSwoyGFhYGDIzSspCnJ3UoiIjFJgf8LAzCDJwMPAyGCWmFxc4BgQ4ANUwgCjUcG3a0B1QHBZF2TWrUbLwmfhj38ssohM0zVmMsBUjwK4UlKLk4H0HyBOTy4oKmFgYEwBspXLSwpA7A4gW6QI6Cggew6InQ5hbwCxkyDsI2A1IUHOQPYNIFsgOSMRaAbjCyBbJwlJPB2JDbUXBHhdXH18FIJdjcwN... | <image>Find x. Round to the nearest tenth. | B | 416 | null | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAwUAAAEwCAYAAADmTd1OAABdc0lEQVR4nO3ddVhcd6L/8fcoM4NrIEDck6ZptLF66r7tbjW1lXq7eu/qb+/q3b1rddvq1t3d49JY48SBQHAbnznn98cAoQkkhBgwn9fz7B/bQJgkcOa8z9cspmmaiIiIiIhI3LIe7RcgIiIiIiJHl6JARERERCTOKQpEREREROKcokBEREREJM4pCkRERERE4pyiQEREREQkzikKRERERETinKJARERERCTOKQpEREREROKcokBEREREJM4p... | <image>Find x. | B | 417 | null | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAi4AAADoCAYAAADIZG9fAABNsElEQVR4nO3de1zUZdr48c8AAwwMKHgAEUVR8BCaqHjEZN3UrDYUO1qrtVG7T6vtti39erLW3F17TGrbTbetXVvL3azWtLCj5RokHlHwgCdABAVBURAYmBmGYX5/jAwgCMPJOXC9X69ejV++35mbw8xcc9/XfV0Kk8lkQgghhBDCAbjYegBCCCGEENaSwEUIIYQQDkMCFyGEEEI4DAlchBBCCOEwJHARQgghhMOQwEUIIYQQDsPN1gMQQggh... | <image>Each pair of polygons is similar. Find A B. | B | 418 | null | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAO8AAAEnCAYAAABBvBTUAAABRmlDQ1BJQ0MgUHJvZmlsZQAAeJxjYGASSSwoyGFhYGDIzSspCnJ3UoiIjFJgf8LAzCDAIMygwMCcmFxc4BgQ4ANUwgCjUcG3awyMIPqyLsgsvtePDO5HT+F5/1nLJXJfz25M9SiAKyW1OBlI/wHi9OSCohIGBsYUIFu5vKQAxO4AskWKgI4CsueA2OkQ9gYQOwnCPgJWExLkDGTfALIFkjMSgWYwvgCydZKQxNOR2FB7QYDXxdXHRyHY1cjc... | <image>In the figure, Q R \parallel T S, Q T \parallel R S, and m \angle 1 = 131. Find the measure of \angle 6. | D | 419 | null | D |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAwUAAAEwCAYAAADmTd1OAABdc0lEQVR4nO3ddVhcd6L/8fcoM4NrIEDck6ZptLF66r7tbjW1lXq7eu/qb+/q3b1rddvq1t3d49JY48SBQHAbnznn98cAoQkkhBgwn9fz7B/bQJgkcOa8z9cspmmaiIiIiIhI3LIe7RcgIiIiIiJHl6JARERERCTOKQpEREREROKcokBEREREJM4pCkRERERE4pyiQEREREQkzikKRERERETinKJARERERCTOKQpEREREROKcokBEREREJM4p... | <image>Find B D. | C | 420 | null | C |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAOsAAADUCAYAAAB9JtStAAAkN0lEQVR4nO2de0AUZffHv+QqLHIRCFYFFbkJuF4o0FBUfl7DN0MxLbS8JJW+oWmGWfpLrSzTfL1RWmJeUnvTRFF/3ispSAUVVEDkFuiS4spVYEEX9/fHurOzXBfYmdmZfT5/zS6zs88u+51znvOccx4zlUqlAoFAMHqe4XoABAJBP4hYCQSeQMRKIPAEIlYCgScQsRIIPIGIlUDgCUSsBAJPIGIlEHgCESuBwBOIWAkEniDiegCmgExehepa... | <image>Find the exact circumference of the circle. | C | 421 | null | C |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAoIAAAIVCAYAAABFk57uAAC6fUlEQVR4nOzddZjc53nv//d3mGeWGcWMFpMtyxwzpeGkadK0obY5aU/b0/akv1NK2mADDbMtU2zHMYrBYmZpGWdhZnYYv78/ZrQkyaJdLd2v6/Kl9dJ8pZ2d+czzPPd9K6qqqgghhBBCiAlHM9IXIIQQQgghRoYEQSGEEEKICUqCoBBCCCHEBCVBUAghhBBigpIgKIQQQggxQUkQFEIIIYSYoCQICiGEEEJMUBIEhRBCCCEmKAmCQgghhBAT... | <image>Find m \angle 4. | D | 422 | null | D |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAgMAAAFTCAYAAACkvQ89AABVCklEQVR4nO3ddZic5dXH8e8zurOzrlnfuCuxDRGg0OIeHEKAlhZatK5v+7Z9aaFICwWKxQgEgjvFEoi7bFzW3Xdcnuf9YzYzuyGByG52Zud8rqtXjdJJMjvPb84597kVTdM0hBBCCBG1dL39AoQQQgjRuyQMCCGEEFFOwoAQQggR5SQMCCGEEFFOwoAQQggR5SQMCCGEEFFOwoAQQggR5SQMCCGEEFFOwoAQQggR5SQMCCGEEFFOwoAQQggR... | <image>Find x. | D | 423 | null | D |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAjoAAAEOCAYAAACAS73mAAABRGlDQ1BJQ0MgUHJvZmlsZQAAeJxjYGASSSwoyGFhYGDIzSspCnJ3UoiIjFJgf8LAzCAIhLwMDInJxQWOAQE+QCUMMBoVfLvGwAiiL+uCzFo004JpwfNI7YUcq///4uaajqkeBXClpBYnA+k/QJyeXFBUwsDAmAJkK5eXFIDYHUC2SBHQUUD2HBA7HcLeAGInQdhHwGpCgpyB7BtAtkByRiLQDMYXQLZOEpJ4OhIbai8I8Lq4+vgoBLsamRta... | <image>Find the measure of \angle 4 in the figure. | D | 424 | null | D |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAVkAAADMCAYAAADZLtCfAAABRmlDQ1BJQ0MgUHJvZmlsZQAAeJxjYGASSSwoyGFhYGDIzSspCnJ3UoiIjFJgf8LAzCDOIMxgxKCQmFxc4BgQ4ANUwgCjUcG3awyMIPqyLsisy9KZZ1r+/9V1aWsTOvyc7xmmehTAlZJanAyk/wBxenJBUQkDA2MKkK1cXlIAYncA2SJFQEcB2XNA7HQIewOInQRhHwGrCQlyBrJvANkCyRmJQDMYXwDZOklI4ulIbKi9IMDr4urjoxDsamRu... | <image>Find y. | C | 425 | null | C |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAK0AAAEPCAYAAAAwDEQSAAABRmlDQ1BJQ0MgUHJvZmlsZQAAeJxjYGASSSwoyGFhYGDIzSspCnJ3UoiIjFJgf8LAzCDOwM8gyyCcmFxc4BgQ4ANUwgCjUcG3awyMIPqyLsis6bce3FrtZzyDZVvGAdHJ7DMw1aMArpTU4mQg/QeI05MLikoYGBhTgGzl8pICELsDyBYpAjoKyJ4DYqdD2BtA7CQI+whYTUiQM5B9A8gWSM5IBJrB+ALI1klCEk9HYkPtBQFeF1cfH4VgVyNz... | <image>Find x. | B | 426 | null | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAgkAAAHTCAYAAACtL4ssAACRD0lEQVR4nOzdd3gU19n38e/M9l31XhCSKBK9GlzA2Ma497jbSZzE6XnSixOnPelxnN6eJG96bIztuMVxx2BwwY3eEUW9d22fnZn3j12tJBAgQKCVdH+uiwtYhLSg3Tn3nPM791FM0zQRQgghhDiMOtJPQAghhBCJSYoEIYQQQgxKigQhhBBCDEqKBCGEEEIMSooEIYQQQgxKigQhhBBCDEqKBCGEEEIMSooEIYQQQgxKigQhhBBCDEqKBCGE... | <image>Find M P. | B | 427 | null | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAXEAAADkCAYAAABuWxTgAAABRWlDQ1BJQ0MgUHJvZmlsZQAAeJxjYGASSSwoyGFhYGDIzSspCnJ3UoiIjFJgf8LAzCDJwMPAyGCWmFxc4BgQ4ANUwgCjUcG3a0B1QHBZF2TWrUbLwmfhj38ssohM0zVmMsBUjwK4UlKLk4H0HyBOTy4oKmFgYEwBspXLSwpA7A4gW6QI6Cggew6InQ5hbwCxkyDsI2A1IUHOQPYNIFsgOSMRaAbjCyBbJwlJPB2JDbUXBHhdXH18FIJdjcwN... | <image>Find x. Round to the nearest tenth. | A | 428 | null | A |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAcwAAAD/CAYAAAB8QuYxAAAdBklEQVR4nO3dX2xc5ZnH8R/U3ZotdGK0uXCoTf4gLqKZJCVykXD+cbFFSS7iXq3DpvKkFyUki3CXZSO5kZqVWLRZltao2xRumonKEt+sakAJYi+KcWIkOiJrsDfSRk0w4zWulFXsg2ltWNPsxeQMZyYznnfsM3Pec873IyGFZBJOG3t+877P8z7vbTdu3LghAACwpNuDfgAAAMKAwAQAwACBCQCAAQITAAADBCYAAAYITAAADBCYAAAYIDAB... | <image>If F K = 3 x - 1, K G = 4 y + 3, J K = 6 y - 2, and K H = 2 x + 3, find y so that the quadrilateral is a parallelogram. | B | 429 | null | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAjQAAAEPCAYAAABV3l7wAAA96ElEQVR4nO3de3zOdePH8ddlxjZDm1PCzGE0yoqkJYc0FUpKP8VGKm6kIla77xDauu8UdYtsbpXDbEqRU6RW7S51ZVIOyZ2RQ1sLYw6za8x2/f7gWjuft+v0fj4eHg/rOn3W3W0vn+/n+/kYzGazGRERERE7VsvaAxARERGpLAWNiIiI2D0FjYiIiNg9BY2IiIjYPQWNiIiI2D0FjYiIiNg9BY2IiIjYPQWNiIiI2D0FjYiIiNg9BY2IiIjY... | <image>Find x. | D | 430 | null | D |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAgEAAAGcCAYAAABA9nNhAACL10lEQVR4nOzddZhk5bnv/e8q13b3Hnc3xnD3QAiBhEASLFhkJ9vOOe8+Z1uyd7ITLCRAICQhhEDwwRnG3d172t3Kda33j6qu7p7p8fa+P9fFNcC0VHdX17rX89zP71Y0TdMQQgghxIijG+gHIIQQQoiBIUWAEEIIMUJJESCEEEKMUFIECCGEECOUFAFCCCHECCVFgBBCCDFCSREghBBCjFBSBAghhBAjlBQBQgghxAglRYAQQggxQkkRIIQQ... | <image>Find m \angle T Q R. | C | 431 | null | C |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAf4AAAHsCAYAAAAzcc+1AACOmElEQVR4nOzdd3hb15nv++9GbwRAgATATqpbXbKqe42dZqc4PXESp0xJTqadzJzJnHPnzJly75RMOZOZSeJUp/fiOIlLYlu2JVnFlmT1QrETAEkQANHL3vcPgCBlq4sFJN/P82gccSRwiyT2b693rfUuRdM0DSGEEEIsCLrZvgAhhBBCzBwJfiGEEGIBkeAXQgghFhAJfiGEEGIBkeAXQgghFhAJfiGEEGIBkeAXQgghFhAJfiGEEGIBkeAX... | <image>H K and I G are diameters of \odot L. Find m \widehat H I. | B | 432 | null | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAkUAAAH0CAYAAAAzAFmMAADepElEQVR4nOzddXxb973/8deRdMSWmSkx22mStmmbMjOso3I77h3T3e7g/sZbt7vdMd/xVtqKKzOlTElD5ji2Y2ZbTOf8/pAsc2I7ThPbn+ce7dpGlhRH1nnr+/18Px9F13UdIYQQQohVznC4n4AQQgghxJFAQpEQQgghBBKKhBBCCCEACUVCCCGEEICEIiGEEEIIQEKREEIIIQQgoUgIIYQQApBQJIQQQggBSCgSQgghhAAkFAkhhBBCABKK... | <image>Find x. | B | 433 | null | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAcoAAAEFCAYAAABjIqe9AAABRmlDQ1BJQ0MgUHJvZmlsZQAAeJxjYGASSSwoyGFhYGDIzSspCnJ3UoiIjFJgf8LAzCDEwMVgyqCVmFxc4BgQ4ANUwgCjUcG3awyMIPqyLsis3Utj/vW8f8nssnDSwp/ruCwx1aMArpTU4mQg/QeI05MLikoYGBhTgGzl8pICELsDyBYpAjoKyJ4DYqdD2BtA7CQI+whYTUiQM5B9A8gWSM5IBJrB+ALI1klCEk9HYkPtBQFeF1cfH4VgVyNz... | <image>Find x if A D is an altitude of \triangle A B C. | D | 434 | null | D |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAQsAAADSCAYAAABdE+UBAAABRWlDQ1BJQ0MgUHJvZmlsZQAAeJxjYGASSSwoyGFhYGDIzSspCnJ3UoiIjFJgf8LAzCDJwMPAyGCWmFxc4BgQ4ANUwgCjUcG3a0B1QHBZF2TWrUbLwmfhj38ssohM0zVmMsBUjwK4UlKLk4H0HyBOTy4oKmFgYEwBspXLSwpA7A4gW6QI6Cggew6InQ5hbwCxkyDsI2A1IUHOQPYNIFsgOSMRaAbjCyBbJwlJPB2JDbUXBHhdXH18FIJdjcwN... | <image>Find x. Round to the nearest degree. | C | 435 | null | C |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAT8AAAD8CAYAAAABraMFAAAYnElEQVR4nO3de1xUdf7H8fcIiFzCQIlsQFERKPECoVZ429K8JaJuW6n109LKRFt/rra/zOxmu3nJEtJaTdK1WrXwJ7vrPVdTVkUTL7SCYKYwyyIKhFzlMvsHHoRhgGHmzJwz830/H48ej3SG4QsPePk9Z2bOR6PX6/UgIhJMO6UXQESkBMaPiITE+BGRkBg/IhIS40dEQmL8iEhIjB8RCYnxIyIhMX5EJCTGj4iExPgRkZAYPyISEuNHREJi... | <image>Find x. | B | 436 | null | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAARIAAAFfCAYAAACC8UORAAABRmlDQ1BJQ0MgUHJvZmlsZQAAeJxjYGASSSwoyGFhYGDIzSspCnJ3UoiIjFJgf8LAzCDEwMVgyqCVmFxc4BgQ4ANUwgCjUcG3awyMIPqyLsis3Utj/vW8f8nssnDSwp/ruCwx1aMArpTU4mQg/QeI05MLikoYGBhTgGzl8pICELsDyBYpAjoKyJ4DYqdD2BtA7CQI+whYTUiQM5B9A8gWSM5IBJrB+ALI1klCEk9HYkPtBQFeF1cfH4VgVyNz... | <image>In \triangle P Q R, Z Q = 3 a - 11, Z P = a + 5, P Y = 2 c - 1, Y R = 4 c - 11, m \angle P R Z = 4 b - 17, m \angle Z R Q = 3 b - 4, m \angle Q Y R = 7 b + 6, and m \angle P X R = 2 a + 10. P X is an altitude of \triangle P Q R. Find a. | D | 437 | null | D |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAYwAAAE4CAYAAABIYsQpAAABRmlDQ1BJQ0MgUHJvZmlsZQAAeJxjYGASSSwoyGFhYGDIzSspCnJ3UoiIjFJgf8LAzMDHIMQgw8CdmFxc4BgQ4ANUwgCjUcG3awyMIPqyLsisy79j76nNu7c/WdpE/GtOzxpM9SiAKyW1OBlI/wHi9OSCohIGBsYUIFu5vKQAxO4AskWKgI4CsueA2OkQ9gYQOwnCPgJWExLkDGTfALIFkjMSgWYwvgCydZKQxNOR2FB7QYDXxdXHRyHY1cjc... | <image>In the figure, m \angle 4 = 104, m \angle 14 = 118. Find the measure of \angle 7. | B | 438 | null | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAlcAAAF5CAYAAACydQ9fAABUwElEQVR4nO3df2xTd94v+Hd3uav0qnCaalmJUrtJQWjL2pCnXabPrdMERrdUcQTxc2euJsnNKKFXD3GaoU2nw2SVh1voiGGVMr1Nh0mT9O5AoubGfjR0rgElEfTZp0Dj7vRBnQnYSiVUfvSYFGmRSE7SfRLpiS77hzkn5xz/to/tY/v9kirhg33yjYuPP+f7/Xw/n0cePHjwAERERERkiP8h3wMgIiIiKiYMroiIiIgMxOCKiIiIyEAMroiI... | <image>Find m \angle D. | A | 439 | null | A |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAZkAAADsCAYAAACmPdsIAAABRWlDQ1BJQ0MgUHJvZmlsZQAAeJxjYGASSSwoyGFhYGDIzSspCnJ3UoiIjFJgf8LAzCDOwMvAxsCemFxc4BgQ4ANUwgCjUcG3awyMIPqyLsgsXtuav29kL2vyZafUn/EoiMBUjwK4UlKLk4H0HyBOTy4oKmFgYEwBspXLSwpA7A4gW6QI6Cggew6InQ5hbwCxkyDsI2A1IUHOQPYNIFsgOSMRaAbjCyBbJwlJPB2JDbUXBHhdXH18FIJdjcwN... | <image>Find x. | C | 440 | null | C |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAZMAAAClCAYAAACZSBBlAAABRmlDQ1BJQ0MgUHJvZmlsZQAAeJxjYGASSSwoyGFhYGDIzSspCnJ3UoiIjFJgf8LAzCDGIM6gz2CQmFxc4BgQ4ANUwgCjUcG3awyMIPqyLsgs+VNVf877TN/6iLfO3WPuVBNM9SiAKyW1OBlI/wHi9OSCohIGBsYUIFu5vKQAxO4AskWKgI4CsueA2OkQ9gYQOwnCPgJWExLkDGTfALIFkjMSgWYwvgCydZKQxNOR2FB7QYDXxdXHRyHY1cjc... | <image>For the pair of similar figures, find the area of the green figure. | D | 441 | null | D |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAUkAAAFHCAYAAAAsgL7YAAABRWlDQ1BJQ0MgUHJvZmlsZQAAeJxjYGASSSwoyGFhYGDIzSspCnJ3UoiIjFJgf8LAzCDOwMvAxsCemFxc4BgQ4ANUwgCjUcG3awyMIPqyLsgsXtuav29kL2vyZafUn/EoiMBUjwK4UlKLk4H0HyBOTy4oKmFgYEwBspXLSwpA7A4gW6QI6Cggew6InQ5hbwCxkyDsI2A1IUHOQPYNIFsgOSMRaAbjCyBbJwlJPB2JDbUXBHhdXH18FIJdjcwN... | <image>Find x. | D | 442 | null | D |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAcIAAAGWCAYAAADrB4OkAAB4t0lEQVR4nO3dd3xV9f3H8de5e2bvBRkQtiAIqCggiOKoo3W2WvurrW21tdZaO2zVWltrl1bb2t0qdW9xoIIIiuJij5AFCdk7uXuc8/vjJjeJgrIybu7n+XhQBIFeyb3nfb6f8/1+PoqmaRpCCCFEnNKN9AsQQgghRpIEoRBCiLgmQSiEECKuSRAKIYSIaxKEQggh4poEoRBCiLgmQSiEECKuSRAKIYSIaxKEQggh4poEoRBCiLgmQSiEECKu... | <image>The segment is tangent to the circle. Find x. | C | 443 | null | C |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAlMAAAD9CAYAAACYyPJfAAAqLElEQVR4nO3df3wU9b3v8U/7OI/bP24LzdkHnFtB6innkAi2NUoS5UgiSWhjCEKCBlMk0CZBjaj5ITHakJCAFtAkWCWKIT0QpEgsAgIppssigYuJAbXaJGrveVxIAj1Xr7fMes/9o/94/+AQdyazye7O7s7Mzuv5Fzv7gy+Q/fKeme/38/nGV1999ZUAAAAgJN80ewAAAAB2RpgCAAAwgDAFAABgAGEKAADAAMIUAACAAYQpAAAAAwhTAAAA... | <image>Quadrilateral A B C D is shown. A C is 40 and B D is \frac { 3 } { 5 } A C. B D bisects A C. For what value of x is A B C D a parallelogram. | C | 444 | null | C |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAWIAAAEPCAYAAAB4Ns7+AABPl0lEQVR4nO2deViU5feHbzbZFQEVARXBBXHJBbUQNUErTTHXtDTTLMvKcinTMjNbzNTKfuVWLmXp1zWXMnPLDTXXXJBEEBAEEZB9EWbm98c4wwzrALMx89zX5dXQvAPPzLzzmfOe55zPsSguuCNDIBAIBAbD0tALEAgEAnNHCLFAIBAYGCHEAoFAYGCEEAsEAoGBEUIsEAgEBkYIsUAgEBgYIcQCgUBgYIQQCwQCgYERQiwQCAQGRgixQCAQ... | <image>Find m \widehat B C A. | D | 445 | null | D |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAANUAAADdCAYAAAAsEzfuAAAo5UlEQVR4nO2dfViUZdr/Py4QoIiCIiIoCCiIaIKibpC4PVr2spJYuVmZbqzbmtb6K33crNV2H3ssMyutts0yrUe3LBRrs9ItTHwDFF9QEUHeBhEREEQGYsb5/THMzfA+wD3v1+c4PI6Z4Z77vpyZ732e13md53n10mg0GgQCgWz8ytwDEAhsDSEqgUBmhKgEApkRohIIZEaISiCQGSEqgUBmhKgEApkRohIIZEaISiCQGSEqgUBmhKgEApkR... | <image>In \odot B, the diameter is 20 units long, and m \angle A C E = 45. Find x. | A | 446 | null | A |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAnMAAAFtCAYAAABshOx4AAChfElEQVR4nOz9V5BcV5buef6Pe7jWKrTWAloTAAEQIARBnazMLJFZVT11+3b3tX5pm26zeRqzeZ3nnrE2655blVW3VGZlUpMASRAgCK1VaK3Dw7XW58yDRwCgAAiACCAisH8PacZIhMcJ4cc/33uvtSRFURQEQRAEQRCEFUn1vC9AEARBEARBeHIizAmCIAiCIKxgIswJgiAIgiCsYCLMCYIgCIIgrGAizAmCIAiCIKxgIswJgiAIgiCsYCLM... | <image>Find m \angle 2. | B | 447 | null | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAc4AAAGZCAYAAAAAbdH/AAChEUlEQVR4nOzdd3jUVdbA8e/0THqHFDop9N47UqRIEVCkSUekY1vru666uipdkI4IigoqUpXee++kUJKQkN5nMpn2/pHkRwIWAmmT3M/z8OwuSyaTzMw995577rkyq9VqRRAEQRCExyIv7ScgCIIgCLZEBE5BEARBKAQROAVBEAShEETgFARBEIRCEIFTEARBEApBBE5BEARBKAQROAVBEAShEETgFARBEIRCEIFTEARBEApBBE5BEARBKAQR... | <image>If m \angle A E D = 95 and m \widehat A D = 120, what is m \angle B A C? | B | 448 | null | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAN8AAAFDCAYAAAC6KtugAAABRGlDQ1BJQ0MgUHJvZmlsZQAAeJxjYGASSSwoyGFhYGDIzSspCnJ3UoiIjFJgf8LAzCAEFGRmEEhMLi5wDAjwAfIYYDQq+HaNgRFEX9YFmXXT7Mim4rkXSq/kTk22YHhQjKkeBXClpBYnA+k/QJyeXFBUwsDAmAJkK5eXFIDYHUC2SBHQUUD2HBA7HcLeAGInQdhHwGpCgpyB7BtAtkByRiLQDMYXQLZOEpJ4OhIbai8I8Lq4+vgoBLsamRta... | <image>\triangle K L N and \triangle L M N are isosceles and m \angle J K N = 130. Find the measure of \angle L N M. | B | 449 | null | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAARMAAAC2CAYAAAD6D2lRAAABRGlDQ1BJQ0MgUHJvZmlsZQAAeJxjYGASSSwoyGFhYGDIzSspCnJ3UoiIjFJgf8LAzCAEFGRmEEhMLi5wDAjwAfIYYDQq+HaNgRFEX9YFmXXT7Mim4rkXSq/kTk22YHhQjKkeBXClpBYnA+k/QJyeXFBUwsDAmAJkK5eXFIDYHUC2SBHQUUD2HBA7HcLeAGInQdhHwGpCgpyB7BtAtkByRiLQDMYXQLZOEpJ4OhIbai8I8Lq4+vgoBLsamRta... | <image>Given right triangle X Y Z with hypotenuse X Y, Y P is equal to Y Z. If m \angle P Y Z = 26, find m \angle X Z P. | A | 450 | null | A |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAVMAAAEACAYAAAAOUZUtAAABRGlDQ1BJQ0MgUHJvZmlsZQAAeJxjYGASSSwoyGFhYGDIzSspCnJ3UoiIjFJgf8LAzCAKhLwMyonJxQWOAQE+QCUMMBoVfLvGwAiiL+uCzOKK+Han7EqwsuVDi8OzwwVXYqpHAVwpqcXJQPoPEKcnFxSVMDAwpgDZyuUlBSB2B5AtUgR0FJA9B8ROh7A3gNhJEPYRsJqQIGcg+waQLZCckQg0g/EFkK2ThCSejsSG2gsCvC6uPj4Kwa5G5oaW... | <image>Rhombus R S T U has an area of 675 square meters. Find S U. | D | 451 | null | D |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAfQAAAFaCAYAAADowK8UAAA3eElEQVR4nO3df1gUV5ov8NdxyIxxxd4A0UAgjA6NCtEM2ASQOBsNRL3JqOvIkBjxB5rrZgfjKrozPnLzuBgzk6iPkUnGjeIPErMGx2ucyUYlUe8YAoSWjBIQgTWLtBCJkDQw6sZel/sHdMOpqqZ/VXdVnfp+/koVdHGeJPCeOue87zust7e3lwAAAEDTvqf0AAAAAMB3COgAAAAcQEAHAADgAAI6AAAABxDQAQAAOICADgAAwAEEdAAAAA4g... | <image>A B C D is a rhombus. If E B = 9, A B = 12 and m \angle A B D = 55. Find A E. | A | 452 | null | A |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAi8AAAFDCAYAAADyCu74AAAr10lEQVR4nO3db2wb953n8a+7voONbTK2u8EhzZF17cIPcuTF2CLAwcPKyfYAQ9LZ0UNJ68LpE4vaXLsKCleA6gcK4DWgGD0o6fpEBQesjQgiH9otLCEGisYO6cMh6KEBiT4w6j8Z4pIDgo08ueKiA7zQPZBnPBySoxlyOH/fr0eSTFETRdJ8+f39fp/vrq2trS0BAACIiW+EfQEAAABeULwAAIBYoXgBAACxQvECAABiheIFAADECsULAACI... | <image>Quadrilateral A B D C is a rectangle. Find m \angle 6 if m \angle 1 = 38. | A | 453 | null | A |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAdwAAAHNCAYAAAC0KcrLAACWwklEQVR4nOzddXhb2bX38e8RS5bMlmQIOZwJwzBksMM8k+G2M7e95fYt8y1zb3uLU5h2OpBhZuZkZsLMHJPMYp2jc877h5zEFDZI9vo8T5/n3tZ2FMc+P+219l5bMU3TRAghhBD9yjLYL0AIIYQYDiRwhRBCiAEggSuEEEIMAAlcIYQQYgBI4AohhBADQAJXCCGEGAASuEIIIcQAkMAVQgghBoAErhBCCDEAJHCFEEKIASCBK4QQQgwACVwh... | <image>Find y. | B | 454 | null | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAnAAAAFzCAYAAAC+bzSQAADAnUlEQVR4nOz913tc+Xnoe35X5ZyrUMiRJAjmzGbsZuesblmSJUtO++wzc54zz8y5nv9hLmfmmZltb1uSbVmS1TknpmbOGSByFVLlnKvWXBQIokgwJ4Tf58KPxQbJIlC11rt+b5JkWZYRBEEQBEEQFgzFs34BgiAIgiAIwoMRAZwgCIIgCMICIwI4QRAEQRCEBUYEcIIgCIIgCAuMCOAEQRAEQRAWGBHACYIgCIIgLDAigBMEQRAEQVhgRAAn... | <image>Use parallelogram J K L M to find m \angle J M L. | C | 455 | null | C |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAhsAAAG+CAYAAAA6HsZ9AADew0lEQVR4nOzddZgc15Xw4V9Vc/cw80galEbMshjMzGzHdhLHcfjLJtnNbnaDm2zAjh2wY46ZUZYssmQxMwwz8zRDVX1/1Ghkx4KRNKz7Po8TW1PdfWvUXX3q3nPPkTRN0xAEQRAEQegn8mAPQBAEQRCEkU0EG4IgCIIg9CsRbAiCIAiC0K9EsCEIgiAIQr8SwYYgCIIgCP1KBBuCIAiCIPQrEWwIgiAIgtCvRLAhCIIgCEK/EsGGIAiCIAj9... | <image>Use parallelogram A B C D to find m \angle A F B. | D | 456 | null | D |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAR8AAAETCAYAAAAPlQI2AAAgBElEQVR4nO3df1CU950H8LdKwpIQlrVHepqygFraU4jG1HYajGB/aNRJoHM3LXj2wPsVo01D28t4Y7xxc6Pe5dIf5Hox2v4hXB3hbqZTSCZavLlzMW6mCXfeJlA7YwRXqCGnLcsDtqxxDffH8jw8u+zvfX4/79dMZhCehUcDb77f7+f5fL8LZmZmZkBEpLGFet8AEdkTw4eIdMHwISJdMHyISBcMHyLSBcOHiHTB8CEiXTB8iEgXDB8i0gXD... | <image>Find W T, if Z X = 20 and T Y = 15. | A | 457 | null | A |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAR0AAAD9CAYAAACBWaNNAAArQElEQVR4nO3de1jUZf7/8acLLKIIAiEeEBERUdFERU0o3VYz2xLTrNUt0w3b3dJ2/e5ibtaa2+qWVpbZaXWztNXMTaVarfRXWnjE1AQNAQUVRERBDjIQ4Pz+GGeYgQEGmPnMfGbej+vqugYZ4I7Da+7T+77babVaLUIIoZCf2bsBQgjXIqEjhFCUhI4QQlESOkIIRUnoCCEUJaEjhFCUhI4QQlESOkIIRUnoCCEUJaEjhFCUhI4QQlESOkII... | <image>In \odot A, m \angle E A D = 42. Find m \widehat E D B. | C | 458 | null | C |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAhAAAAICCAYAAACeHvQZAAC5IElEQVR4nOzdd3hb93Xw8e+92CBAABwANylqS9b23iNxbMfO3klHusfbtE2TprvpbtN0v2m60qZ5M9osJ7YTO957a+9JEeDAILH3uu8fFwRJWbZFihTX+TyPHoWMCF9R4MXB+Z2haJqmIYQQQggxA+pCX4AQQgghlh4JIIQQQggxYxJACCGEEGLGJIAQQgghxIxJACGEEEKIGZMAQgghhBAzJgGEEEIIIWZMAgghhBBCzJgEEEIIIYSYMQkg... | <image>P M is a diameter of \odot R. Find m \widehat M N P. | D | 459 | null | D |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAPoAAADRCAYAAADlh6/IAAAhL0lEQVR4nO3de1xUdf7H8RcC6ShCgkQsmKDgJdHURFth091VUbt417TSLma66uYltdQyW9dfaWVualtieCkvuSWmqXgpTdEUS1MML2BeMCRkVEQHgnF+f+BMAw7IMLcznM/z8ejxKDjgSXjP98z3vM/362EwGAwIIaq1Gq4+ASGE40nQhVABCboQKiBBF0IFJOhCqIAEXQgVkKALoQISdCFUQIIuhApI0IVQAQm6ECogQRdCBSToQqiABF0I... | <image>Use rhombus X Y Z W with m \angle W Y Z = 53, V W = 3, X V = 2 a - 2, and Z V = \frac { 5 a + 1 } { 4 }. Find X Z. | C | 460 | null | C |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAUMAAADKCAYAAAA/+yKjAAAeFklEQVR4nO3de1yUddrH8Q9yEARBQUQFwQMiKrqgoiVs+rip1bpRdrSnNdvssKZ7qGzbfHZb97X2qnzttru2tdv6lOWT1baZdN7aTEoqz67iCVFT8TCOgBwEBIZ5/hgHRoRhBmZkDt/3X6PcM3Ojw5fffd/XfV0BZrPZjIiIn+vW1TsgIuIJFIYiIigMRUQAhaGICKAwFBEBFIYiIoDCUEQEUBiKiAAKQxERQGEoIgIoDEVEAIWhiAigMBQR... | <image>Find the measure of the altitude drawn to the hypotenuse. | D | 461 | null | D |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAVsAAAC8CAYAAADW+Q1jAAAYR0lEQVR4nO3d/1NU570H8Hfv9FdZMgzM1C+IE12+bPQmkRWhmTgKUaS2CfkisUZqtI5Gb6z13sSYxptJc1uNaSmjkehYE4e0N4p6SXtbJARwTC2Ii5qrLiimU1jR3AvDlMU/wPvD2XP2LLt79gDLOYfneb9mmFmXs+4znPP57LPP85zn860HDx48ABERTap/srsBREQyYLIlIrIAky0RkQWYbImILMBkS0RkASZbIiILMNkSEVmAyZaIyAJM... | <image>Parallelogram M N P Q is shown. What is the value of x? | A | 462 | null | A |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAASkAAACcCAYAAAAj6V3wAAABRGlDQ1BJQ0MgUHJvZmlsZQAAeJxjYGASSSwoyGFhYGDIzSspCnJ3UoiIjFJgf8LAzCAOhLoMConJxQWOAQE+QCUMMBoVfLvGwAiiL+uCzFotY9AkXFqv75vflF356eodTPUogCsltTgZSP8B4vTkgqISBgbGFCBbubykAMTuALJFioCOArLngNjpEPYGEDsJwj4CVhMS5Axk3wCyBZIzEoFmML4AsnWSkMTTkdhQe0GA18XVx0ch2NXI3NDS... | <image>Find the area of the triangle. Round to the nearest hundredth. | B | 463 | null | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAcsAAAFeCAYAAADqqTS3AAAsjElEQVR4nO3dXWwb573n8X/OyUUCtJmkRS7cLudIqZELg6y9CbwFQtUvxaI5omBHe0cKMuSeC4uK6212C5VYVkBdwBWgGt2mSWVRuYmFaEXeHdWGKLQXJy9H9EE3SNYpCV8UTZMOkeQiaJ1xAsQ4a6z2QpnRzPBl+DLDITnfDxDA4stwQon8zfM8/+d57tvd3d0VAADQ0N8FfQIAAPQ7whIAABeEJQAALghLAABcEJYAALggLAEAcEFYAgDg... | <image>Find m \angle D. | B | 464 | null | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAokAAAGcCAYAAAC1JDqUAACdGklEQVR4nOzddXyV5/nH8c9xiSsEtxBFIhQJUKh7V6Gd/Npt7VZdt/q6rbJ27VbZ1nVb3Vd3d4NCgsVdCE4g7sef5/z+OOEkQQMFIud6v168WgI5PIGc53zPfV/XdWu8Xq8XIYQQQggh+tAO9gUIIYQQQoihR0KiEEIIIYTYi4REIYQQQgixFwmJQgghhBBiLxIShRBCCCHEXiQkCiGEEEKIvUhIFEIIIYQQe5GQKIQQQggh9iIhUQghhBBC... | <image>What is the value of x if m \widehat N R = 62 and m \widehat N P = 108? | C | 465 | null | C |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAmAAAAE6CAYAAACxlu7cAAABRmlDQ1BJQ0MgUHJvZmlsZQAAeJxjYGASSSwoyGFhYGDIzSspCnJ3UoiIjFJgf8LAzCDIIMbAyKCXmFxc4BgQ4ANUwgCjUcG3a0B1QHBZF2SW9PLvlU2BmXz/GZa+d+u+ex1TPQrgSkktTgbSf4A4PbmgqISBgTEFyFYuLykAsTuAbJEioKOA7DkgdjqEvQHEToKwj4DVhAQ5A9k3gGyB5IxEoBmML4BsnSQk8XQkNtReEOB1cfXxUQh2NTI3... | <image>Find the measure of \angle 1 if m \angle D G F = 53 and m \angle A G C = 40. | B | 466 | null | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAb8AAAEGCAYAAAD11pvPAAAfE0lEQVR4nO3deVyVdaLH8Q8CKgiiuCSuoLgg4I6aS9LiVpk3nWtpqy0zN81p5pbVTKuVM+1NY1NT2i2zUcvU7GZlZVcntVBEU3FFURNJUZBFAQ+Hc/84isdkh3PO85zn+/5L4DzP61cHzvc8v/P7/h4/h8PhQERExEIaeHsAIiIinqbwExERy1H4iYiI5Sj8RETEchR+IiJiOQo/ERGxHIWfiIhYjsJPREQsR+EnIiKWo/ATLzrBmsdHEB0Z... | <image>Find the measure of the altitude drawn to the hypotenuse. | B | 467 | null | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAM8AAACmCAYAAAB9etvNAAAOuUlEQVR4nO3de1xUdcLH8c8Io4aoICKibUoi5kqWZVmrFqZPpmUpq7Zr9+xmW2ZRdntK0yzdUrd1H+1p19Rat7yVWor3NDF1vSylT7y8RSWKCigq4gXwPH+IpqQ4nJk5Z87M9/3PVAfO/BI//M78zpkzLsMwDESkyqrZPQARp1I8IiYpHhGTFI+ISYrHxwpcoylwjbZ7GGIBxSNikuIRMUnxiJikeERMUjwiJikeEZMUj4hJikfEJMUjYpLi... | <image>Find y. | D | 468 | null | D |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAkkAAAF8CAYAAADb3y+3AAAxK0lEQVR4nO3deXwU9eH/8XfchCOEQNCAIeEIJOFIgoRThSpa8a5UarWiqAit+i3aYqs9rN/a2tPWo4r6U7Fo9evFtyhatVq+LSqHcgUh4QokGAIBAoQjEGOy7O+PkL2YTfaY3Z3dfT0fjz4endndyQjMziszn5lJcjgcDgEAAMDDadFeAQAAACsikgAAAAwQSQAAAAaIJAAAAANEEgAAgAEiCQAAwACRBAAAYIBIAgAAMEAkAQAAGCCSAAAA... | <image>If P R \parallel K L, K N = 9, L N = 16, P M = 2 K P, find M L. | C | 469 | null | C |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAtEAAAFyCAYAAAAzqYbaAABdt0lEQVR4nO3dfVjT5f4H8DcBKYioECKCiAiIigYI+AAdPOazHiHNzMqnE9Yv09JTWkcrs9JSM0tJMy1NS1PLxMx8yiMJmqCAAsqTzyBOAgWBiQz3+wM2NtjGNjb29H5dV9fl/WX77sbcvp/vvft+31ZisVgMIiIiIiJS2yOG7gARERERkalhEU1EREREpCEW0UREREREGmIRTURERESkIRbRREREREQaYhFNRERERKQhFtFERERERBpiEU1E... | <image>If \frac { I J } { X J } = \frac { H J } { Y J }, m \angle W X J = 130 and m \angle W Z G = 20, find m \angle J H I. | B | 470 | null | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAmcAAAGRCAYAAAAgkRSIAADqAUlEQVR4nOz9Z5Bc553veX5Pem/Lew/vvSVBL4myLXZL6pbaybW59+5s7NzdiHmzGxs7MRsxd2Z2+t6WWuq+7WRaLe9FEiRBeO9dee8rvbdnX5xEASQMAbCAygL+nwgFu8mqrASqKs8/n/P8np+iqqqKEEIIIYQoC7rFfgJCCCGEEOImGc6EEEIIIcqIDGdCCCGEEGVEhjMhhBBCiDIiw5kQQgghRBmR4UwIIYQQoozIcCaEEEIIUUZkOBNC... | <image>Find m \angle 4. | C | 471 | null | C |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAkkAAAF8CAYAAADb3y+3AAAxK0lEQVR4nO3deXwU9eH/8XfchCOEQNCAIeEIJOFIgoRThSpa8a5UarWiqAit+i3aYqs9rN/a2tPWo4r6U7Fo9evFtyhatVq+LSqHcgUh4QokGAIBAoQjEGOy7O+PkL2YTfaY3Z3dfT0fjz4endndyQjMziszn5lJcjgcDgEAAMDDadFeAQAAACsikgAAAAwQSQAAAAaIJAAAAANEEgAAgAEiCQAAwACRBAAAYIBIAgAAMEAkAQAAGCCSAAAA... | <image>If P R \parallel K L, K N = 9, L N = 16, P M = 2 K P, find K M. | B | 472 | null | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAb4AAAESCAYAAACCU7B8AABIw0lEQVR4nO3deVRTZ94H8C8FKlFECWJUUJBN1OBWwAVanI7WpR1xGWt1qtUp2mWw1bfFcaoz1hmxVmqtlW7Wjq1Ota2Vgrbu00oLdQEFNSqyo0GNkSAIBoZQ3j9ibhJIQgJJ7s3N73OO5yR6CY+Q3O+zPy4tLS0tIIQQQpzEQ2wXgBBCCLEnCj5CCCFOhYKPEEKIU6HgI4QQ4lQo+AghhDgVCj5CCCFOhYKPEEKIU6HgI4QQ4lQo+AghhDgV... | <image>The diameters of \odot A, \odot B, and \odot C are 10, 30 and 10 units, respectively. Find B Y if A Z \cong C W and C W = 2. | B | 473 | null | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAjkAAAF/CAYAAACrAtiBAABiE0lEQVR4nO3dd5xU9b3/8deZPjvbe6XvLioWBEEQe++KJsaYYro1JjfJzS83uTfl5qZ3a6LGVI1G7BqNvSAiKCoibAG2916mz5zfHzM7ix12F3aZeT8fyT95wGYYmHPe8zmf7+djmKZpIiIiIpJkLNP9AkRERET2BoUcERERSUoKOSIiIpKUFHJEREQkKSnkiIiISFJSyBEREZGkpJAjIiIiSUkhR0RERJKSQo6IiIgkJYUcERERSUoKOSIi... | <image>If A C = 14, B C = 8, and A D = 21, find E D. | B | 474 | null | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAuIAAAILCAYAAACtqPl1AAEAAElEQVR4nOz9d3Rc93nv/7739D6YGWAGHSBBAuwUJXb1LstxTdzj3pKc5OTkOKese9dd69z7u+t3T3pyck7iuNux4zhOXGOrS6Qau0RRFIlGEh2YAQbT+8ze9489GIISqwQSAPG81nKcBYPAkAAGn/nuz34eRdM0DSGEEEIIIcQNZVjsByCEEEIIIcRKJEFcCCGEEEKIRSBBXAghhBBCiEUgQVwIIYQQQohFIEFcCCGEEEKIRSBBXAghhBBC... | <image>R P = 3.5 and J P = 9. Find P L. | C | 475 | null | C |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAVcAAAEWCAYAAADSNdTRAAABRGlDQ1BJQ0MgUHJvZmlsZQAAeJxjYGASSSwoyGFhYGDIzSspCnJ3UoiIjFJgf8LAzCAKhLwMyonJxQWOAQE+QCUMMBoVfLvGwAiiL+uCzOKK+Han7EqwsuVDi8OzwwVXYqpHAVwpqcXJQPoPEKcnFxSVMDAwpgDZyuUlBSB2B5AtUgR0FJA9B8ROh7A3gNhJEPYRsJqQIGcg+waQLZCckQg0g/EFkK2ThCSejsSG2gsCvC6uPj4Kwa5G5oaW... | <image>In the figure, the vertices of quadrilateral A B C D intersect square E F G H and divide its sides into segments with measure that have a ratio of 1:2. Find the area of A B C D. | B | 476 | null | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAbMAAADbCAYAAADnPX8EAABLEElEQVR4nO2dd1hUR9uH72UBBUTpIKhBRFTAjg1FIoomFuxGXzUx+hqNRlMsMcWU15io0RSTqCmaWBKNLZ+KRKNBjcTeFeyKIr0qAlKW/f6AxQV2qbuwu8x9XbmCp845Z/b8zsz85nkkmRnRcgQCgUAg0GOMarsAAoFAIBBUF2OpRFLbZRAIBAKBoFoYCy0TCAQCgb5jDELNBAKBQKDfGBsZiWEzgUAgEOg3QskEAoFAoPcIMRMIBAKB3iPE... | <image>Quadrilateral A B C D is a rectangle. Find y. | A | 477 | null | A |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAARMAAAD6CAYAAACClaNGAAAo9UlEQVR4nO3de1yUdfr/8RcgKQKCgIigiCCKiHlCU1LM1N3VWlvL2tx0SytrdX9Wrlu2fbez28lOftdsza9W2sk0dzuYJWq6iZWKloooQpxBhZHzMAIzvz+mGQY5DTDDzNz39Xw8fDwAB705zHs+93197utyq6spMCCEEJ3k7ugDEEIog4SJEMImJEyEEDYhYSKEsAkJEyGETUiYCCFsQsJECGETEiZCCJuQMBFC2ISEiRDCJiRMhBA2IWEi... | <image>Find the perimeter of \triangle Q R S if \triangle Q R S \sim \triangle Q T P. | B | 478 | null | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAOgAAACOCAYAAAA7BEQ/AAAbG0lEQVR4nO2deUAT1/bHv9QoBANKEKMCimyCjVqQRQuKr9W61CeoVZ9rnxW7aav+WqyttthFa2t9tmqtVaxrsWql1b5KRdqnFYqyKCourIIElYYEiGBAgvz+iAmTECCQZWaS+/krJDOTQ2a+99xz7rn32jQ1NTWBQCAwkifoNoBAILQOESiBwGCIQAkEBkMESiAwGCJQAoHBEIESCAyGCJRAYDBEoAQCgyECJRAYDBEogcBgiEAJBAZDBEog... | <image>Find x. Assume that any segment that appears to be tangent is tangent. | D | 479 | null | D |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAATkAAADmCAYAAACu/vK/AAAbKElEQVR4nO3de3iU5bnv8W+cxBASjiEGJJyRY9BwCpSEohZP1IUtHtaiB1BLtxXBbnVjrXRptVvLlrZWpXjtvdhF7epyWxQLRSvgCRtUEiAgIYEEwimAISRqGEggmcz+Iw4dhkkyk8zMe/p9ros/gAl5Apkf7/2+z30/cV6v14uIiE1dYvQCRESiSSEnIramkBMRW1PIiYitKeRExNYUciJiawo5EbE1hZyI2JpCTkRsTSEnIramkBMRW1PI... | <image>If P T = y - 3, P S = y + 2, R S = 12, and Q S = 16 solve for y. | D | 480 | null | D |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAacAAADhCAYAAABsmXpdAAA21ElEQVR4nO3deUCU1frA8S8CsoRsLqiAoCCg4oKKmmBQuZaJStbVyuVme3bzFlxvVmpdu6aV3Sy7FUVWP8trLmiLW6UmargrhiIoIKiIgCACCuP8/sBBkG2AWd4Zns9fOrzvzJnh5X3mnOec81io1Wo1QgghhIK0MnYDhBBCiNtJcBJCCKE4EpyEEEIojgQnIYQQiiPBSQghhOJIcBJCCKE4EpyEEEIojgQnIYQQiiPBSQghhOJIcBJCCKE4... | <image>Find A B. | C | 481 | null | C |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAegAAAHPCAYAAACY+UmCAACbSUlEQVR4nOzddWBbV5r38e8Vy5YsycwYh5mZqczcpkkKM4XpTAcW3t2d2dmBndnpQCdQDjRpysxtmJnZzGzZki2W7vuHZCelcGzZPp//mlrysS3dn8655zyPJMuyjCAIgiAIYUXR2QMQBEEQBOG7REALgiAIQhgSAS0IgiAIYUgEtCAIgiCEIRHQgiAIghCGREALgiAIQhgSAS0IgiAIYUgEtCAIgiCEIRHQgiAIghCGREALgiAIQhgSAS0I... | <image>Find D F. | A | 482 | null | A |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAgQAAAG/CAYAAAAn58+9AACesklEQVR4nOzdd3xV9fnA8c+5++Zm70EWAZIwBBTcEweIWxnWVbfWn62j1Wq1Vltb6657a9U6EcWBijhREQHZZAAJZO95b3L3Ob8/Eu5NEJQRkpvkeb9evmwVYyTnnvOc5/sMRdM0DSGEEEIMa7qB/gaEEEIIMfAkIBBCCCGEBARCCCGEkIBACCGEEEhAIIQQQggkIBBCCCEEEhAIIYQQAgkIhBBCCIEEBEIIIYRAAgIhhBBCIAGBEEIIIZCA... | <image>Find x. | B | 483 | null | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAY4AAAEACAYAAACkvpHUAAABRmlDQ1BJQ0MgUHJvZmlsZQAAeJxjYGASSSwoyGFhYGDIzSspCnJ3UoiIjFJgf8LAzCDNwMvAxcCWmFxc4BgQ4ANUwgCjUcG3awyMIPqyLsgsobSDM7jnPHqnzpEXkd/omY2pHgVwpaQWJwPpP0CcnlxQVMLAwJgCZCuXlxSA2B1AtkgR0FFA9hwQOx3C3gBiJ0HYR8BqQoKcgewbQLZAckYi0AzGF0C2ThKSeDoSG2ovCPC6uPr4KAS7Gpkb... | <image>P Q is tangent to the circle. Find x. Round to the nearest tenth. | B | 484 | null | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAaUAAAFlCAYAAABLOvcaAAABRmlDQ1BJQ0MgUHJvZmlsZQAAeJxjYGASSSwoyGFhYGDIzSspCnJ3UoiIjFJgf8LAzCDOIMxgxKCQmFxc4BgQ4ANUwgCjUcG3awyMIPqyLsisy9KZZ1r+/9V1aWsTOvyc7xmmehTAlZJanAyk/wBxenJBUQkDA2MKkK1cXlIAYncA2SJFQEcB2XNA7HQIewOInQRhHwGrCQlyBrJvANkCyRmJQDMYXwDZOklI4ulIbKi9IMDr4urjoxDsamRu... | <image>In the figure, below, square A B C D is attached to \triangle A D E as shown. If m \angle E A D is 30 and A E is equal to 4 \sqrt { 3 }, then what is the area of square A B C D? | C | 485 | null | C |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAegAAAEpCAYAAABY5LEdAAAmSElEQVR4nO3dT2wUV7r38ScjIhmJTGGkLCByx7ygu3IraEbolaY9QGaRCKN7k6VtMYJ3A2aYSEiveC05SJdFBslhcXlvLmM7K9BYtpcEZFvM4o1h3LNBMyLq1l1chRenLcICyXZDJFsaJO7CPuXT5er/9eecqu9HiuT2n3ZR7fSvnjrnPOetN2/evBEAAGCUn8V9AAAAYCcCGgAAAxHQAAAYiIAGAMBABDQAAAYioAEAMBABDQCAgQhoAAAM... | <image>Find x so that the quadrilateral is a parallelogram. | B | 486 | null | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAi8AAAFDCAYAAADyCu74AAAr10lEQVR4nO3db2wb953n8a+7voONbTK2u8EhzZF17cIPcuTF2CLAwcPKyfYAQ9LZ0UNJ68LpE4vaXLsKCleA6gcK4DWgGD0o6fpEBQesjQgiH9otLCEGisYO6cMh6KEBiT4w6j8Z4pIDgo08ueKiA7zQPZBnPBySoxlyOH/fr0eSTFETRdJ8+f39fp/vrq2trS0BAACIiW+EfQEAAABeULwAAIBYoXgBAACxQvECAABiheIFAADECsULAACI... | <image>Quadrilateral A B D C is a rectangle. Find m \angle 5 if m \angle 1 = 38. | C | 487 | null | C |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAuIAAAILCAYAAACtqPl1AAEAAElEQVR4nOz9d3Rc93nv/7739D6YGWAGHSBBAuwUJXb1LstxTdzj3pKc5OTkOKese9dd69z7u+t3T3pyck7iuNux4zhOXGOrS6Qau0RRFIlGEh2YAQbT+8ze9489GIISqwQSAPG81nKcBYPAkAAGn/nuz34eRdM0DSGEEEIIIcQNZVjsByCEEEIIIcRKJEFcCCGEEEKIRSBBXAghhBBCiEUgQVwIIYQQQohFIEFcCCGEEEKIRSBBXAghhBBC... | <image>R P = 3.5 and J P = 9. Find P S. | B | 488 | null | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAlcAAAF5CAYAAACydQ9fAABUwElEQVR4nO3df2xTd94v+Hd3uav0qnCaalmJUrtJQWjL2pCnXabPrdMERrdUcQTxc2euJsnNKKFXD3GaoU2nw2SVh1voiGGVMr1Nh0mT9O5AoubGfjR0rgElEfTZp0Dj7vRBnQnYSiVUfvSYFGmRSE7SfRLpiS77hzkn5xz/to/tY/v9kirhg33yjYuPP+f7/Xw/n0cePHjwAERERERkiP8h3wMgIiIiKiYMroiIiIgMxOCKiIiIyEAMroiI... | <image>Find m \angle C. | D | 489 | null | D |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAsUAAAHRCAYAAACCZMQIAADacElEQVR4nOzdZ3xUZdrH8d+ZPpPeewiB0JuCioBgb9hWRaUIKqBrr7urj+u6xXXXVey6iqB0Gzawi4WiokivKUAq6T3TZ855XkyYwIpKIJB2fT8fXogpJ2HmnP+5z3Vfl6JpmoYQQgghhBDdmK69D0AIIYQQQoj2JqFYCCGEEEJ0exKKhRBCCCFEtyehWAghhBBCdHsSioUQQgghRLcnoVgIIYQQQnR7EoqFEEIIIUS3J6FYCCGEEEJ0exKK... | <image>Find D E. | A | 490 | null | A |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAASIAAAEjCAYAAACW4gwTAAABRWlDQ1BJQ0MgUHJvZmlsZQAAeJxjYGASSSwoyGFhYGDIzSspCnJ3UoiIjFJgf8LAzCDNwM8gx8CcmFxc4BgQ4ANUwgCjUcG3awyMIPqyLsisnElPEx+k3TodyR1+RnCOTjimehTAlZJanAyk/wBxenJBUQkDA2MKkK1cXlIAYncA2SJFQEcB2XNA7HQIewOInQRhHwGrCQlyBrJvANkCyRmJQDMYXwDZOklI4ulIbKi9IMDr4urjoxDsamRu... | <image>Find x. Assume that segments that appear to be tangent are tangent. | D | 491 | null | D |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAATgAAAErCAYAAABKPZ9fAAAKuWlDQ1BJQ0MgUHJvZmlsZQAAeJyVlgdUU1kax+97L52EFnoNvSNFIICU0ANI76ISkkBCCTEhqFiwMDiCY0FEBJQRUSkKjkqRsSKKbVBs2AdERNRxsCAqKvuAJczsnt09+51zc3/58t2vvPNuzh8A8leWUJgBywOQKcgWRfh70eLiE2j4ZwABcoAKcADLYouFjLCwYIDazP53+3gXQJP7LavJXP/++381BQ5XzAYACkM5mSNmZ6J8HF3P2EJR... | <image>Find y. | A | 492 | null | A |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAU8AAAEPCAYAAADClUaeAAAynklEQVR4nO3de0BUdf7/8acLpNCIgiKiKAioqGjeQBMM65eZXcRL1uqWZVG7a9quu4vrln3LdnVJt6y02jbLS5tdTNN0M9NKCiwF0RRviAoKIiIgiAzEjPP7Y2SY4ToMM8yZmffjrxHOwJGB17w/n/M57087nU6nQwghRIv8yt4nIIQQjkjCUwghLCDhKYQQFpDwFEIIC0h4CiGEBSQ8hRDCAhKeQghhAQlPIYSwgISnEEJYQMJTCCEsIOEp... | <image>Triangle A D C is circumscribed about \odot O. Find the perimeter of \triangle A D C if E C = D E + A F. | D | 493 | null | D |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAhoAAAGRCAYAAAAjJhqgAACsf0lEQVR4nOz9d3ic53Xve3+n94IyqIPCBvYG9k6K6pLVi9Usybbck9hJdnZ29jnnfc/uyU6cxNtO3CVbxZKsYvVGir0T7L2izaCX6X2e88eAINhBEh3rc13OdSnCzDwDDWbW3Pe6f0ulKIqCEEIIIUQ/UA/2BQghhBBi5JJCQwghhBD9RgoNIYQQQvQbKTSEEEII0W+k0BBCCCFEv5FCQwghhBD9RgoNIYQQQvQbKTSEEEII0W+k0BBCCCFE... | <image>Find m \angle 4. | C | 494 | null | C |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAATUAAACsCAYAAAAaATs7AAAjxElEQVR4nO3de1hTV7oG8Dc1yFUQEKMCgtxEGxUU1CkojNWqrQpi1dHOVB3pdGzFlnpgPNqpOlZrYTrWSy/TarGe1p7qiOL0aL20hQqOAgoqIiBQkCCNkTsYkMA+f8RsknAPuW6+3/P4PDGEZAHJu9f69lpr8xiGYUAIIRzxlKEbQAgh2kShRgjhFAo1QginUKgRQjiFQo0QwikUaoQQTqFQI4RwCoUaIYRTKNQIIZxCoUYI4RQKNUIIp1Co... | <image>Find x. Assume that any segment that appears to be tangent is tangent. | A | 495 | null | A |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAARYAAAERCAYAAAC+SIj3AAA+VUlEQVR4nO2deVyU5fr/3zCObLLIJoIigijikguVkkumntLMMrVjv7TUOrZ4jnXMk9W35ZSnso7Hym+rLVra106alplWbmVGpaiYiguCiGziMAIDDOMww++PcYYZGGCAWR5m7vfr5es1I88wNzPP83mu63Nf93V71dYU1iEQCAR2xNvVAxAIBO6HEBaBQGB3hLAIBAK7I4RFIBDYHSEsAoHA7ghhEQgEdkcIi0AgsDtCWAQCgd0RwiIQCOxO... | <image>In \odot R, S U = 20, Y W = 20, and m \widehat Y X = 45. Find m \widehat S U. | D | 496 | null | D |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAXcAAAD7CAYAAACRxdTpAAA9OElEQVR4nO3deVyU5f7/8RcCKoQbqwiyCSiKmihqrlRq5qlIzUpLs5PVaV/157FFrWPnpG3fk2mdNJfUFnPNVs20xAXXFBc2WQQR2WSRRRjm98c4w6DsMsw993yej0ePB8nijTPznuu+7ut63zZarVaLEEIIVWll7gMQQgjR/CTchRBChSTchRBChSTchRBChSTchRBChSTchRBChSTchRBChSTchRBChSTchRBChSTchRBChSTchRBChSTc... | <image>Use parallelogram J K L M to find m \angle J M L if J K = 2 b + 3 and J M = 3 a. | C | 497 | null | C |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAYkAAAD2CAYAAAAj3nsdAAAT60lEQVR4nO3db2gcZ37A8Z8Tw8lw5/H6aoruqrUtHX1hdrlyIFqyqiw3YGOJu/NLyShIfdGLEydBEHIG1S8UsAXGpIjmkth5E4sYSdAXTVos40CIrWpDi2iasCJ90Sp2dmnE4SbyuCkWVLB9Ic94drXP7qy08+d55vt5tZbH5omsPN+d55mZ3VUul8sCAEANT0U9AABAfBEJAIASkQAAKBEJAIASkQAAKBEJAIASkQAAKBEJAIASkQAAKBEJ... | <image>If m \angle Z Y W = 2 x - 7 and m \angle W Y X = 2 x + 5, find m \angle Z Y W. | C | 498 | null | C |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAApAAAAFxCAYAAADERZjqAABqrElEQVR4nO39Z3Bk2Znmef5dwwF3h9aO0FoHRERqzaRKiiSTqlgUTVYr657ptent6e1um+0es1lbs7Xdnp2e3e3qKZLFqiJZZFEkyUym1jIEZGgFEXCH1q713Q/uoTICEfAIIICAPz8z0gyRgPsFcHHvc8973nNMhmEYiIiIiIgskHm5D0BERERE7i0KkCIiIiKSFwVIEREREcmLAqSIiIiI5EUBUkRERETyogApIiIiInlRgBQRERGRvChA... | <image>Find x. | B | 499 | null | B |
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