Datasets:
dle666
/
GeoFocus-test

Dataset card Data Studio Files
xet
 Community
2
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problem
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714
answer
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4 values
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAABLaElEQVR4nO3deZidZX3w8ec5y2QhBCQBIRIQEGRxhUBBuXwtRLSiaFHfUrWCVCQkZGYSVluh9mqtWOsrBFtxYXt5xQXIJQi2yirWKqAoEAmELQsQSFiyL3O294+7eXqcLZNklvPM/fn8kWsymZmczMw1eb7nvn/PnTYajQQAAIhDYaQfAAAAMHwEAAAAREQAAABARAQAAABERAAAAEBEBAAAAEREAAAAQEQEAAAAREQAAABARAQAAABERAAA...
<image>As shown in the diagram, AB=16, AC=12, BA is perpendicular to CA. Find the perimeter of △CBA.
48
936
[ "48", "29.61", "360.5", "51.76" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAACos0lEQVR4nOzdZ3xVZbr//1X23gklnaIoiPQSmg6igOCIdKmCOs6oQHoCxA4BUgggYAUCSQCRHtrYlRZCVefob5oCIR1sowOk05Lstdb/wf13H44gIiTZZX3eD87LCTmwUtbe9/de13VfsmEYEgAAAABzUJx9AQAAAADqDwEAAAAAMBECAAAAAGAiBAAAAADARAgAAAAAgIkQAAAAAAATIQAAAAAAJkIAAAAAAEyEAAAAAACYCAEAAAAAMBEC...
<image>As shown in the diagram, DE=2, DF=3, E bisects segment CD, ABCD is a parallelogram. Find the perimeter of ABCD.
14
6457
[ "14", "126.3", "469.56", "261.32" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAAEAAElEQVR4nOzdd1xT9/4/8HNOEggJU7ZMAUEQBBWQDaK2Wqv1WrV2D9va3i5tVUTFLahV297updXbamtvrba31y17TxFQkSHI3oSRQJJzfn98vs2PG9teB0pCXs8/fChy4ADhc96vz6Q5jqMAAAAAAEA3MCN9AwAAAAAAcP8gAAAAAAAA6BAEAAAAAAAAHYIAAAAAAACgQxAAAAAAAAB0CAIAAAAAAIAOQQAAAAAAANAhCAAAAAAAADoEAQAA...
<image>As shown in the diagram, OA=2, OC=2, ∠CAO=30°, O is the center of ⊙O, the tangent to ⊙O is DC. Find the length of line CD.
2*sqrt(3)
6778
[ "2*sqrt(3)", "176.07", "30.33", "298.33" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAACT50lEQVR4nOzdd3wU1f7/8TM7u6lACL2DYKFIEQW7IEVEFAEVFRVUSoAAoQTS9XclhUDovXmJXkBAgwIiAgqIAlKkI116MZhAQtruzszvj3OZL3otlJDd7L6ef9yHJHE93CQ7n/eZz/mMYhiGAAAAAOAdLK5eAAAAAICiQwAAAAAAvAgBAAAAAPAiBAAAAADAixAAAAAAAC9CAAAAAAC8CAEAAAAA8CIEAAAAAMCLEAAAAAAAL0IAAAAAALwI...
<image>As shown in the diagram, BE=8, DE=4, EC=22, BC⊥AC, BE is perpendicular to DE. Find the length of line AC.
15
4067
[ "15", "491.13", "461.67", "224.44" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAACPhklEQVR4nOzdZ3wUVfv/8TMzuxuS0JsgvYs0QSlSrAgCKgIqtwoWepHQCZ1QQgkldEJQwIJ4gwhSFEVBQURQFFBAUEB6AOmQtjsz/wfnx/5zhxACJNnZnc/7Aa+wu9kcwiZ7feec6xzFNE0BAAAAwB5UXw8AAAAAQPYhAAAAAAA2QgAAAAAAbIQAAAAAANgIAQAAAACwEQIAAAAAYCMEAAAAAMBGCAAAAACAjRAAAAAAABshAAAAAAA2QgAA...
<image>As shown in the diagram, AB=8, ∠DAE=30°, D is the midpoint of segment AB, AC is perpendicular to BC, AE⊥DE. Find the length of line BC.
4
5112
[ "4", "26.77", "480.43", "312.08" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAADqgklEQVR4nOzdd3wU1fo/8DMzu5veGymQkEAqhKqgFGkWEFAUAQGFC0pHeoCABYFQQ5EOAurFgldRiljwIoqCgEB6D0lISC+kZ7M7O78/ni/7y6UGSLKbzOf9x315w7I5IbMzz3POc57DSZLEAAAAAABAHnhDDwAAAAAAAJoOEgAAAAAAABlBAgAAAAAAICNIAAAAAAAAZAQJAAAAAACAjCABAAAAAACQESQAAAAAAAAyggQAAAAAAEBGkAAA...
<image>As shown in the diagram, AC=2*x+9, BD=4*x-5, ∠CAE=42°, ∠DCE=4*y°, ∠EAB=23°, ∠EBD=83°, AC and BD are opposite sides of the parallelogram ABDC. Find the value of y.
8
1872
[ "8", "431.48", "137.92", "236.68" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAADmG0lEQVR4nOzdd3wU5fo28GdmdtMb6UAghBBKaCE0RUAQKVIULAgiIKIgUhQBgRRKQhKa2BBBkCZy8KggTRCkd+k1kISQkN77JtndmXn/uH/smwOICEk2mbm+f5yPJwnJE9idua+n3MPJsswAAAAAAEAdeHMPAAAAAAAAqg8CAAAAAACAiiAAAAAAAACoCAIAAAAAAICKIAAAAAAAAKgIAgAAAAAAgIogAAAAAAAAqAgCAAAAAACAiiAAAAAA...
<image>As shown in the diagram, ∠LPM=65°, P is the center of ⊙P, NP is perpendicular to JP. Find the measure of ∠MPN.
25
2829
[ "25", "184.59", "296.67", "270.28" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAAC3+ElEQVR4nOzdd3yN5//H8es+K8OIEcTe2tp7qxotYtaekQgt1WFvgtrUamkVIfbe1B6ltEatUpvYERJJkHHG/fvj+jq/0yAiMk5yXs8/+pCTc07uk+a+78/7vq/PdSmqqgoAAAAAjkGT0hsAAAAAIPkQAAAAAAAHQgAAAAAAHAgBAAAAAHAgBAAAAADAgRAAAAAAAAdCAAAAAAAcCAEAAAAAcCAEAAAAAMCBEAAAAAAAB0IAAAAAABwIAQAA...
<image>As shown in the diagram, ∠GJC=50°, ∠IAH=x°, ∠JLA=72°, IO∥PL, PL is parallel to CN. Find the value of x.
22
1626
[ "22", "403.26", "354.86", "423.23" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAADhNUlEQVR4nOzdd1wU1/c38Dtb6NKkW8AuCsSGWMCGxm7sHUGwt8SeqDHGGmOisUU0CoJir7HGXhCl2AuY2BBFuvS2uzPPH+fnPHyxRI1Sdj7vP/JCXDaDMztzzr3n3MsJgsAAAAAAAEAaZKV9AAAAAAAAUHKQAAAAAAAASAgSAAAAAAAACUECAAAAAAAgIUgAAAAAAAAkBAkAAAAAAICEIAEAAAAAAJAQJAAAAAAAABKCBAAAAAAAQEKQAAAA...
<image>As shown in the diagram, NM=9, NP=10, QM=8, QP=7, WX=4, QPNM is similar to WZYX. Find the perimeter of quadrilateral WZYX.
17
673
[ "17", "340.98", "20.3", "323.88" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAAB1OklEQVR4nO3dd5xV9Z0//nPuvTN0QUQRQRRU7F2jgFFsGI0KMdiwgBSz39+m7KZsS3a/G9ds2iabzaYpTdHYUBCDDXsvKPYGAoooCEivM/fe8/vj8+P+JjMwzh2BKef5/MPHveeWOTNy73m/PjVOkiQCAADSIdPUJwAAAOw8AgAAAKSIAAAAACkiAAAAQIoIAAAAkCICAAAApIgAAAAAKSIAAABAiggAAACQIgIAAACkiAAAAAApIgAAAECK...
<image>As shown in the diagram, ∠ABC=90°, ∠BCD=1/2∠ABC, ∠DAB=90°. Find the measure of ∠CDA.
135
5148
[ "135", "136.74", "93.32", "351.33" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAADutUlEQVR4nOzdd1xUV/o/8HNnhg6iggV7ix0VG0WK9F4G0CQbo2mrpm2MJpseNW6qMVmTbKpJNj0bYYbeBQQVbBQjYEHEAggiRZA6M/f3x/Pl/m6wASptPu8/8jIwDHfuMOeez7nnnIfjeZ4BAAAAAIB2kPT1AQAAAAAAQO9BAAAAAAAA0CIIAAAAAAAAWgQBAAAAAABAiyAAAAAAAABoEQQAAAAAAAAtggAAAAAAAKBFEAAAAAAAALQIAgAA...
<image>As shown in the diagram, ∠BAF=12*x+4°, ∠FBA=16*x-12°, quadrilateral ADCB is a rectangle. Find the measure of ∠FBA.
52
2099
[ "52", "109.36", "91.9", "388.5" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAAEAAElEQVR4nOzdd3wU9fY//vfMtmzJ7mbTE0IvSehVuqDSxCsIFixcC6h4vSo2BAWVIjbw2sWKXRQEAUVBhUjvPQkt1IT03ZQt2TIzvz/ON/PbTxoBUjbZ1/MPHmGZ7E7C7sw57/c57zcnSRIDAAAAAIDgwDf2CQAAAAAAQMNBAgAAAAAAEESQAAAAAAAABBEkAAAAAAAAQQQJAAAAAABAEEECAAAAAAAQRJAAAAAAAAAEESQAAAAAAABBBAkA...
<image>As shown in the diagram, BA=5*x-1, BC=4*x+3, ∠OBA=85°, ∠OCB=85°, the center of circle O is O. Find the value of x.
4
2116
[ "4", "120.28", "416.56", "464.52" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAADUI0lEQVR4nOzdd1wU1/c38Dvb6B0RrNiw996wNxQrigoCgmhiiUZjjIkxJvlGjbEmVhSpVhB77x177xI7KL2X3Z2d54/zc58NKjak7Hzef/hS3F1m28w59557DycIAgMAAAAAAHGQFPcBAAAAAABA0UECAAAAAAAgIkgAAAAAAABEBAkAAAAAAICIIAEAAAAAABARJAAAAAAAACKCBAAAAAAAQESQAAAAAAAAiAgSAAAAAAAAEUECAAAAAAAg...
<image>As shown in the diagram, AB=12, EB=9, ∠DBA=55°, quadrilateral ADCB is a rhombus. Find the length of line CE.
3*sqrt(7)
1394
[ "3*sqrt(7)", "34.09", "289.45", "372.15" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAACLiElEQVR4nOzdZ3xURd//8Tnn7KYRQugiICLSi9IFpCgKghgEBSlSpPcSQge97j9SQ6/Sq1IERFEUqQpIl14FlCotBFJI2T3n/B/Mzd65qAGS7GbP5/3geuFms5lwsTvznfnNjGKapgAAAABgDaq7GwAAAAAg7RAAAAAAAAshAAAAAAAWQgAAAAAALIQAAAAAAFgIAQAAAACwEAIAAAAAYCEEAAAAAMBCCAAAAACAhRAAAAAAAAshAAAAAAAW...
<image>As shown in the diagram, BA=2*x+4, BC=4*x-8, CA=3*x-1, ∠ABC and ∠BCA are the base angles of the isosceles △ ABC. Find the perimeter of △ABC.
40
606
[ "40", "194.13", "346.7", "261.12" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAAEAAElEQVR4nOzdd1xUx/c38Ln37i4daVIEFcWGYm/YYzeaxJbExBaNvbdYoqgYW+yxxG5iNMbEnth7772jIGJBeu+7e+99/jg/9+GLDRDY9nn/4QuWZRlw79xzZs7McLIsMwAAAAAAMA+8vhsAAAAAAABFBwkAAAAAAIAZQQIAAAAAAGBGkAAAAAAAAJgRJAAAAAAAAGYECQAAAAAAgBlBAgAAAAAAYEaQAAAAAAAAmBEkAAAAAAAAZgQJAAAA...
<image>As shown in the diagram, ∠GKH=122°, the center of ⊙K is K. Find the measure of ⌒KHG.
122
564
[ "122", "87.03", "274.43", "362.18" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAABvxklEQVR4nO3dd7wU1f0//tlC712wK6LS7BULtkgMKnYsESwY8zFqjBVREVuiJsTeIooVVFBj1FixgLHFAoKKShUQaVIv3LI7vz/Ol/3d0LwgcC/M8/kHj8vuzuzszuzuec2c9zmpOI4jAAAgGdKVvQEAAMD6IwAAAECCCAAAAJAgAgAAACSIAAAAAAkiAAAAQIIIAAAAkCACAAAAJIgAAAAACSIAAABAgggAAACQIAIAAAAkiAAAAAAJIgAA...
<image>As shown in the diagram, ∠COB=3∠AOC-20°. Find the measure of ∠AOC.
50
5252
[ "50", "224.11", "361.21", "295.83" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAACptUlEQVR4nOzddVxVyfsH8HNu0GViF4q5dnesa6xda0uqpGJgK9hdhCBlYbdrYqy1dgfYYreE5L3nnN8fz8/7ZSkRgRvn8/7DF94cLufOzDMzzwwrCAIDAAAAAADiIFF3AQAAAAAAoOAgAAAAAAAAEBEEAAAAAAAAIoIAAAAAAABARBAAAAAAAACICAIAAAAAAAARQQAAAAAAACAiCAAAAAAAAEQEAQAAAAAAgIggAAAAAAAAEBEEAAAAAAAA...
<image>As shown in the diagram, BA=7, BC=6, CA=3, EF=9, △DFE is similar to △ACB.. Find the perimeter of triangle DFE.
24
1544
[ "24", "302.75", "186.36", "129.63" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAAEAAElEQVR4nOzdd3xURfs28JlzdpPd9F5ITzYJTbo0QVQUAUEUASs8gBQFBUSBdEJ6KIKgKCqiggIqIvIAooIiiIIiUXp6L6T3bDnnvH/Mj33z0KQk2d3s9f3DDyabZALJ7n3NzD1DJUkiAAAAAABgHjhDDwAAAAAAADoOAgAAAAAAgBlBAAAAAAAAMCMIAAAAAAAAZgQBAAAAAADAjCAAAAAAAACYEQQAAAAAAAAzggAAAAAAAGBGEAAAAAAA...
<image>As shown in the diagram, AB=13, AC=5, BC=12, the center of circle O is O, the tangent to circle O is BM. Find the length of line PQ.
60/13
4624
[ "60/13", "309.8", "217.77", "93.25" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAAD+uklEQVR4nOzdZ3xUxfs+/jllW3olECAQioTeVJoC0gQUBFFQUAFRREVAeu9FehMUVAT1CyqgKEhTKdIhIh1CSSAJECC9bjnl/+D+5/zyCS1Ayu6e6/2AV0i2nE327Jlr5p4ZTlVVBgAAAAAA+sCX9AEAAAAAAEDxQQAAAAAAANARBAAAAAAAAB1BAAAAAAAA0BEEAAAAAAAAHUEAAAAAAADQEQQAAAAAAAAdQQAAAAAAANARBAAAAAAAAB1B...
<image>As shown in the diagram, ∠AMD=100°, ∠DAM=30°, the center of ⊙O is O. Find the measure of ∠CBM.
50
3953
[ "50", "326.07", "427.05", "328.42" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAAEAAElEQVR4nOzdd1xT9/c/8Huz2CgKDpYLcA+0LsQNim0V956ATNHWUavIco9aBRQVFRduUeuq4qgDUGvrbl1oFSeoKCiQhCT398f5kh8fB6ICSW5ezz/6sCEJ9yaXe895v8/7XJbjOAYAAAAAAPSDQNMbAAAAAAAA5QcJAAAAAACAHkECAAAAAACgR5AAAAAAAADoESQAAAAAAAB6BAkAAAAAAIAeQQIAAAAAAKBHkAAAAAAAAOgRJAAAAAAA...
<image>As shown in the diagram, ∠AGK=60°, ∠MJB=50°, HA is parallel to CG, MH is parallel to EN, WD∥BT. Find the measure of ∠ORP.
60
1480
[ "60", "366.17", "292.52", "481.24" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAABpJUlEQVR4nO3deXjsWV0n/vOtJfue3ORe6IaGaWgURG0VtX8M2Aoq4zwMKosLgoIjzsgi6GODLYvQoyDzuCvqCIg+jAtM4waDuDAjigMqI04jiy2C3XRSlX1Pavv+/jh0GZLc3C1JJTmv1x95qr6pJCd1c6vO+5zPOSfL8zwAAABpKHS6AQAAwPERAAAAICECAAAAJEQAAACAhAgAAACQEAEAAAASIgAAAEBCBAAAAEiIAAAAAAkRAAAAICEC...
<image>As shown in the diagram, CB∥DE. Prove that ∠TCB+∠EDG=180°.
0
184
[ "0", "284.02", "170.55", "145.44" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAAEAAElEQVR4nOzdZ1xUV9c//DMz9N6bgCBNFESxi733Lkq1t9hiSVFzJXdyGZNo7IpdQYoo9t5jQRHsDRAFQXrvfcrzYj2Zv5cxCgqcmTm/74v7c90EdTPncM5aa6+9N08ikTAAAAAAAMANfLYHAAAAAAAATQcJAAAAAAAAhyABAAAAAADgECQAAAAAAAAcggQAAAAAAIBDkAAAAAAAAHAIEgAAAAAAAA5BAgAAAAAAwCFIAAAAAAAAOAQJAAAA...
<image>As shown in the diagram, ∠BCD=120°, the center of ⊙O is O. Find the measure of ∠DAB.
60
4520
[ "60", "259.34", "480.63", "449.64" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAAC2Y0lEQVR4nOzdd1xc5533/XNmhg4STQU1BKgLUKEJNRAwDLjE3bHjlHXq5s66x7E32bilbOw4tpPcm+ze2ZQnzU4s2bJliV4kUUWXQKKDQIWO6GXKef64VrNEzWqUmfN5/+GXPMwMZxjK73u1n6woigQAAABAHTSzfQEAAAAAZg4BAAAAAFARAgAAAACgIgQAAAAAQEUIAAAAAICKEAAAAAAAFSEAAAAAACpCAAAAAABUhAAAAAAAqAgBAAAA...
<image>As shown in the diagram, AB=AC, BC=5, the perimeter of triangle ABC is 21, ED is the perpendicular bisector of AB, ED is perpendicular to BD. Find the perimeter of triangle BCE.
13
2860
[ "13", "115.44", "249.81", "103.22" ]
A
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<image>As shown in the diagram, ∠DEA=95°, ∠FAD=120°, the center of ⊙F is F. Find the measure of ∠BAC.
35
1377
[ "35", "247.72", "248.23", "29.62" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAACG1ElEQVR4nO3dd3xUVf7/8XPv1EwgJHQQadKkCyhShEWkiCC9l9hdFlAQEERXXdeVsihFxVUXlYQqIB0EBEGRohQRRKSDIFUgIaRMuff3x/lmfrNJiAFSZua8nn/wCJOZyc0kMJ/3OZ9zjmaapgAAAACgBr2gLwAAAABA/iEAAAAAAAohAAAAAAAKIQAAAAAACiEAAAAAAAohAAAAAAAKIQAAAAAACiEAAAAAAAohAAAAAAAKIQAAAAAACiEA...
<image>As shown in the diagram, ML=3*x+1, MN=4*x-2, ∠LPM=5*y°, triangle MLN is an equilateral triangle, MP is the median of triangle MLN. Find the value of y.
18
2358
[ "18", "488.67", "485.54", "15.33" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAABfM0lEQVR4nO3dd5zU5Z0H8N9vZhaQXhUbUtQYc7EmFkBFvWgsMecRE6KmXM6oUdL0TGxREwsqPSJqYtQYbIhgSSwXzRkbyhm72EUFxa502J2Z3/3xnHN7SxFhd2d3n/f7D1+wO7v7W9yd+X6e3/f7PGmWZQkAABCHXLUvAAAAaD4CAAAAREQAAACAiAgAAAAQEQEAAAAiIgAAAEBEBAAAAIiIAAAAABERAAAAICICAAAAREQAAACAiAgAAAAQ...
<image>As shown in the diagram, ∠DAE=∠ABC, ∠EAC=75°. Find the measure of ∠BCA.
75
3510
[ "75", "173.48", "51.36", "401.4" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAAEAAElEQVR4nOzdZ3xURfv/8Tlnd9M7gQChh4QuSJeqSBFEUURUFAFRkV6kShOpUqWKYAFE8UYBAW+lqfTeS+gEQoCQQhppW875P5gf+88dikjbTfbzfsArWXaTQ8juXt+Za2YUXdcFAAAAANegOvoCAAAAADw5BAAAAADAhRAAAAAAABdCAAAAAABcCAEAAAAAcCEEAAAAAMCFEAAAAAAAF0IAAAAAAFwIAQAAAABwIQQAAAAAwIUQAAAAAAAX...
<image>As shown in the diagram, ∠BOC=50°, O is the center of circle O, OB is parallel to AC. Find the measure of ∠OAB.
25
4246
[ "25", "109.62", "159.81", "461.27" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAAEAAElEQVR4nOzdZXwU5/428HtmVrJxd1csECzB3QotbgUi1E6hVOmpn9qpy2mhLYcqJCEEp1DcKRIkSIBA3N1ddndmnhf3n332AKUhJNkkc31f8EnCJrmz2cz8rlsZURQJAAAAAABIA2voBgAAAAAAQMdBAAAAAAAAkBAEAAAAAAAACUEAAAAAAACQEAQAAAAAAAAJQQAAAAAAAJAQBAAAAAAAAAlBAAAAAAAAkBAEAAAAAAAACUEAAAAAAACQ...
<image>As shown in the diagram, ∠CBA=120°, O is the center of ⊙O. Find the measure of ∠CDE.
120
4528
[ "120", "130.5", "152.11", "67.53" ]
A
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<image>As shown in the diagram, the area of BDAC is 177, AD=11, AE=13, BC=x, AE⊥BE, quadrilateral BDAC is a trapezoid. Find the value of x.
211/13
446
[ "211/13", "447.44", "273.53", "13.98" ]
A
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<image>As shown in the diagram, ∠HGB=100°, BA is parallel to DC. Find the measure of ∠CHF.
80
3095
[ "80", "377.82", "426.13", "94.76" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAABCiUlEQVR4nO3deZxU5Z3o4VNdVeyLCIgrOCoTFY1boiQaNSSIUVFxX27imGicSWJyr+OYaNSJTMxN4s3NjHMnycREJ5nRGEFExRWNDqgoEQTiltGg7AjIKtDQXXXuH++lLmFpGgS6m9/z/MGnl1PVpzldVe/31HvOKeR5ngEAADHUtfQKAAAAO48AAACAQAQAAAAEIgAAACAQAQAAAIEIAAAACEQAAABAIAIAAAACEQAAABCIAAAAgEAEAAAA...
<image>As shown in the diagram, AB=10, C is the midpoint of segment AO, D is the midpoint of segment OB. Find the length of line CD.
5
5230
[ "5", "449.74", "5.8", "330.58" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAAEAAElEQVR4nOzdd3xT9fc/8Pe9N2matE0HqzOdgCgFWjZlbxWhxfVxf9SPIqKyd0FlCgruhfpxbzZFVmnZSwQBWdq9995J7v39cX7NN58CpSNt1uv5hw+NaftOe9uc877nfQ4nSRIDAAAAAAD7wJt7AQAAAAAA0H6QAAAAAAAA2BEkAAAAAAAAdgQJAAAAAACAHZGZ8HNJknTbI8Ucxxn+afJPflM8b3FJjlSvweMcx1ngagEAAADAlnBm6QKk...
<image>As shown in the diagram, BE=9, Q is the centroid of △BAC. Find the length of line QE.
3
1089
[ "3", "488.75", "41.2", "161.44" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAACe2klEQVR4nOzdeXxUVZ7//3PvrZA94NJASAio3fNtW1kSEkCd6ZnpVlnCrnbP/Ga6R8UEwqJtS5ZKbVkqSyUsgs0ii+IuKG6MosiiICB0KyIIArIJyL6Ttere+/vjtBnaFTCk6qZezz98aBLw+riSnPf5fM7nKKZpCgAAAADhQQ32AwAAAABoOQQAAAAAIIwQAAAAAIAwQgAAAAAAwggBAAAAAAgjBAAAAAAgjBAAAAAAgDBCAAAAAADCCAEA...
<image>As shown in the diagram, PQ=25, RS=10, RT=x, SQ=5, PQ is parallel to TS, TR is perpendicular to SR. Find the length of line ST.
50/3
1755
[ "50/3", "326.98", "61.2", "208.41" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAAEAAElEQVR4nOzdd1wU1/o/8DMzWyhLWXoHFaTZAAERQaPRqClqTPTGdGNMND253lRNbnrUJPfGJDcxzRRTrkmMKUYTFUVBioJgoUjvnaXsLuzuzPz+OD/3uxeNUYMs7Hzef/hCZHFEmHk+55znHEYURQIAAAAAANLAWvsCAAAAAABg6CAAAAAAAABICAIAAAAAAICEIAAAAAAAAEgIAgAAAAAAgIQgAAAAAAAASAgCAAAAAACAhCAAAAAAAABI...
<image>As shown in the diagram, ∠COA=130°, the center of circle O is O. Find the measure of ∠DBA.
65
4618
[ "65", "119.44", "11.9", "354.94" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAACLQElEQVR4nOzdZ3wU5fr/8XtmdkkBAqF3kCpIkQ6KgggKgoJIk04CHMux0QmhQ2gBjx5FjyQUaVKkiBSRLqKIVAVEqhTpLYSQZHfm/j+4f+SPlBBCkt3NfN4PfCXLZneEzcz1vcs1mpRSAAAAALAH3dMHAAAAACDjEAAAAAAAGyEAAAAAADZCAAAAAABshAAAAAAA2AgBAAAAALARAgAAAABgIwQAAAAAwEYIAAAAAICNEAAAAAAAGyEAAAAA...
<image>As shown in the diagram, AD=1, DB=2, DE∥BC. Find the ratio of the length of line DE to the length of line BC.
1/3
5701
[ "1/3", "248.03", "87.21", "308.81" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAAEAAElEQVR4nOzdd1wVd7o/8O/MnF4A6UURURSxK3bsihWxpGfTbvZuNskvudlNMW1jsjF90252s7nJrqlreiLYjQ27iBWVIiCgqPR2+jkz8/vjuZ7LYokictrn/UdeBgFHPDPn+Xyfb+FkWWYAAAAAABAYeE9fAAAAAAAAdB0EAAAAAACAAIIAAAAAAAAQQBAAAAAAAAACCAIAAAAAAEAAQQAAAAAAAAggCAAAAAAAAAEEAQAAAAAAIIAgAAAA...
<image>As shown in the diagram, ∠BDO=25°, the center of ⊙O is O, the diameter of ⊙O is DC, C bisects arc OAB. Find the measure of ∠COA.
50
6563
[ "50", "121.53", "467.87", "425.83" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAAD+c0lEQVR4nOzdd1yV5/3/8es+iw2yBVFx4t574t57RhHTZu+0ab9J2qZJ+kvTNG2apNlN0yYiatwaY1y4996oIIjI3hsO55z798f19XxP1BgXHOB+Pf/ow+IRbsjhvj/va3wuRVVVAQAAAEAbdM6+AAAAAAC1hwAAAAAAaAgBAAAAANAQAgAAAACgIQQAAAAAQEMIAAAAAICGEAAAAAAADSEAAAAAABpCAAAAAAA0hAAAAAAAaAgBAAAAANAQ...
<image>As shown in the diagram, ∠CAB=52°, O is the center of circle O. Find the measure of ∠ABC.
38
6140
[ "38", "93.26", "438.72", "232.79" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAABxe0lEQVR4nO3deZhVVX4v/L3PqSqGYp5HAVFQUdF2wFlpcUBlksnZbrvzmHSSTt/3ptNJ3r5JJ510J7m37/s+9+3kebqTTqe7AZVBQVBBFESkEVScEBQVEGWmGIuhhnP2+8cKJ9VMMtep2p/PHzyndu1T7IJ91l7f315r7ThJkggAAEiHTH0fAAAAcPYIAAAAkCICAAAApIgAAAAAKSIAAABAiggAAACQIgIAAACkiAAAAAApIgAAAECKCAAA...
<image>As shown in the diagram, the sum of the measure of ∠ABC and the measure of ∠CDA is 120, AB=DC, AD=BC. Find the measure of ∠DAB.
120
3152
[ "120", "178.6", "444.0", "248.99" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAAC5uElEQVR4nOzdd1yV5f/H8XschqCIK0UxtdyrrCxHNi1zZdq34Z65UKYKCsgQRJHlTDP3zp0tLTXLMtPM3Fqae+IAROBw7vv+/XF95efXzAkczjmv5x898GZ4JXDuz/u6Ptd1y4ZhSAAAAAAcg2LtAQAAAAAoPAQAAAAAwIEQAAAAAAAHQgAAAAAAHAgBAAAAAHAgBAAAAADAgRAAAAAAAAdCAAAAAAAcCAEAAAAAcCAEAAAAAMCBEAAAAAAA...
<image>As shown in the diagram, AD/AB=1/3, DE is parallel to BC. Find the ratio of the length of line AE to the length of line AC.
1/3
5079
[ "1/3", "32.77", "385.42", "453.37" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAAB+xklEQVR4nO3dZ3yUxfr/8bnvezedEpAqTaWJcBBFCT0IgqAoiByKiIBdECkJ5YAVUCAgiGIDG3oEFVGkKb0EQlMBRQFRQOk1kLbt3vk/mMP+8g9FSpJNdj7vB75gs0kGiLvzneuaGUNKKQAAAADowQz2AAAAAADkHwIAAAAAoBECAAAAAKARAgAAAACgEQIAAAAAoBECAAAAAKARAgAAAACgEQIAAAAAoBECAAAAAKARAgAAAACgEQIAAAAA...
<image>As shown in the diagram, JK=JL, JK=KL, JK=x+7, JL=4*x-8. Find the measure of ∠KJL.
60
140
[ "60", "220.07", "117.07", "355.27" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAABYiElEQVR4nO3deZzWZaHw/++9zT0zLCaJpqhZilku5VZ2Ork8uWaltJw0hZ6OmIkLsq+yIyCraIuVenrKOMcyjx5PVrYXJzXX0sokHxV3UFFgZu7998f14v7NwyYCcw9wvd9/8BqGe4YvzLzg+ny/15Kq1WoJAAAQh3R3XwAAANA4AgAAACIiAAAAICICAAAAIiIAAAAgIgIAAAAiIgAAACAiAgAAACIiAAAAICICAAAAIiIAAAAgIgIAAAAi...
<image>As shown in the diagram, ∠YZX=a/2°, ∠ZXY=2*a°, XY is perpendicular to ZY. Find the measure of ∠YZX.
18
1333
[ "18", "99.83", "414.97", "175.74" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAAC+D0lEQVR4nOzdZ3xVVfr//V3OSScdSEghIQFRUEGpUqQK0kSqIyUQegfBNpZx1LEgDL2GhI4ookjvvYiAIE1aek8IgQCBlHPO/WD92Xd+oQxScpJ9Pu8H83KSk2QnJHuv71rXtZZssVgkAAAAALZBsfYFAAAAACg5BAAAAADAhhAAAAAAABtCAAAAAABsCAEAAAAAsCEEAAAAAMCGEAAAAAAAG0IAAAAAAGwIAQAAAACwIQQAAAAAwIYQAAAA...
<image>As shown in the diagram, the sum of the measure of ∠EAB and the measure of ∠CDE is 90, AE is the angle bisector of ∠DAB, AF bisects ∠MAE, DF bisects ∠EDN, AB is perpendicular to EB, AE is perpendicular to DE. Find the measure of ∠DFA.
135
3020
[ "135", "375.47", "323.53", "286.06" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAACCOklEQVR4nO3dd3xUVfrH8XPvlHQSSui9IyLSVUAEpHekhABWZFEREBBFV9d1XZUmiIjYVlBJoRfpCggRBASkI713CC115t77++Ms88sGCAGSTCbn8/6D12Qy5QKZ3Od77nPO0SzLEgAAAADUoHv7AAAAAADkHAIAAAAAoBACAAAAAKAQAgAAAACgEAIAAAAAoBACAAAAAKAQAgAAAACgEAIAAAAAoBACAAAAAKAQAgAAAACgEAIAAAAAoBAC...
<image>As shown in the diagram, YX=4, ZX=4, ∠XYZ=60°, ∠YZX=60°. Find the length of line YZ.
4
1931
[ "4", "225.72", "289.1", "2.09" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAADU3ElEQVR4nOzdd5wUVb7//1OduyfnTFSCkjOSTIhZ9yqGVVjRdffu6u41EAVRkgioqxu86zUgohgwLGFdxVUkDFFAkiAqw+Qce2Z6erq7+vfH+VK/WbIwMx3q9fyDBwwDUz3TVXXepz6fcxS/3y8AAAAA6IMh0AcAAAAAoP0QAAAAAAAdIQAAAAAAOkIAAAAAAHSEAAAAAADoCAEAAAAA0BECAAAAAKAjBAAAAABARwgAAAAAgI4QAAAAAAAd...
<image>As shown in the diagram, the perimeter of ABCD is 18, FE perpendicular bisects AC, BA and CD are opposite sides of the parallelogram ABCD. Find the perimeter of triangle CDF.
9
6584
[ "9", "192.36", "377.63", "80.02" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAAEAAElEQVR4nOzdd1wU1/c//juzhV5ElCLYe+9RjCV2Y4kxscUaC1jQKNh7V2wxiAVrElvsmrexxxIVe6/YUAREkN53d2Z+f5yv8+OD0RgjbJnX8488CCwwrLt3zrn3nHs5SZIYAAAAAAAoA2/sCwAAAAAAgIKDBAAAAAAAQEGQAAAAAAAAKAgSAAAAAAAABUECAAAAAACgIEgAAAAAAAAUBAkAAAAAAICCIAEAAAAAAFAQJAAAAAAAAAqCBAAA...
<image>As shown in the diagram, ∠AOC=80°, O is the center of ⊙O, DA∥BC. Find the measure of ∠BAD.
40
6219
[ "40", "383.39", "296.81", "272.55" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAAEAAElEQVR4nOzdd1gc17k/8DM725e+IHqHBYQsS8hFQg1JNCHbiX0jO7FTbpybasdOsx07cRInN3mS+BfbSZzEKb65LolT7dixRFPvEmqoAUtZOiy9bmF3dn5/vFeTzQISQsDuwvfzhx9pNcwekAznnXO+5+VEUWQAAAAAALA0yLw9AAAAAAAAWDgoAAAAAAAAlhAUAAAAAAAASwgKAAAAAACAJQQFAAAAAADAEoICAAAAAABgCUEBAAAAAACw...
<image>As shown in the diagram, ∠ADE=68°, ∠CBD=28°, ∠CBE=28°, ∠ECB=82°. Find the measure of ∠EAD.
42
1101
[ "42", "169.6", "276.51", "61.78" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAACyV0lEQVR4nOzdZ3wU1fs+/jNld1MhCaGE3kvoPdRQ0qjWj4qK9CKIFOkdlC699yKioigIhJDQe0da6CAQioSWnuxO+T+4f8w/3wgYIMnszl7vB74kJGRgNzPnOue+z+FUVWUAAAAAAOAceL0vAAAAAAAAcg4CAAAAAACAE0EAAAAAAABwIggAAAAAAABOBAEAAAAAAMCJIAAAAAAAADgRBAAAAAAAACeCAAAAAAAA4EQQAAAAAAAAnAgCAAAA...
<image>As shown in the diagram, ∠FEA=115°, EABF is mirror congruent to EFGH, quadrilateral ABCD is a rectangle. Find the measure of ∠GFC.
50
3227
[ "50", "6.97", "119.09", "219.09" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAACBFklEQVR4nO3dd3xVVb7//7X3PieFhBJ6VRQEqdJEijiooNJFRYpIE+lNZfTO3Dszt/zuzDhWIPQOClKk2UBBRLo0AUF6k14CIZB2zt7798fn5nxjGqEkJ8l6Pf/gcVpOdkLOWp/32muvZbiuqwAAAADowQz2AQAAAADIPQQAAAAAQCMEAAAAAEAjBAAAAABAIwQAAAAAQCMEAAAAAEAjBAAAAABAIwQAAAAAQCMEAAAAAEAjBAAAAABAIwQA...
<image>As shown in the diagram, ∠DAB=150°, ABCD is a parallelogram. Find the measure of ∠BCD.
150
6825
[ "150", "177.37", "423.34", "424.9" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAABcj0lEQVR4nO3dd3wVVeLw4bklELoIKuAudkFdEdsqFuyii11X10ILoiA2VtdeUNeCBUWsIB27iA0r9t5WV0FRQIoFEZAOgeTe+/4xr/eXBUTEQELO8/zhhyRzbya5STzfmXNmErlcLgIAAMKQrOgdAAAA1h4BAAAAAREAAAAQEAEAAAABEQAAABAQAQAAAAERAAAAEBABAAAAAREAAAAQEAEAAAABEQAAABAQAQAAAAERAAAAEBABAAAAAREA...
<image>As shown in the diagram, AC=20, BA=48, BC=x, CA⊥BA. Find the value of x.
52
366
[ "52", "33.9", "67.5", "87.5" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAADNoklEQVR4nOzdZ3wU1dvG8TMzu2m00Lv0JmAB6V0pUkQQUEHphA6KlZLspoEURSCEXhQUFSuKWBEUUECagFIUlSK9hvTszDwvzp99Is0ASbbM7/vCT9hskonZcl/n3OccxTRNAQAAAMAaVE9fAAAAAIDcQwAAAAAALIQAAAAAAFgIAQAAAACwEAIAAAAAYCEEAAAAAMBCCAAAAACAhRAAAAAAAAshAAAAAAAWQgAAAAAALIQAAAAAAFgIAQAA...
<image>As shown in the diagram, PX=4, WX=6, XWZY is a kite. Find the length of line WP.
2*sqrt(5)
2676
[ "2*sqrt(5)", "140.76", "342.72", "488.43" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAACZhElEQVR4nOzdZ3xUVbv38bXLTHoPRarSQRQQRSyoWBAVROUoKqIoWAAFRHpJI6F3EJUiiiB6gwrcAnbsgoqoIFKkKEgnvc8uz4t1mJOHXpLMZPbv+8IPhplkJxlmr/9a17WWYtu2AAAAAOAMqq8vAAAAAED5IQAAAAAADkIAAAAAAByEAAAAAAA4CAEAAAAAcBACAAAAAOAgBAAAAADAQQgAAAAAgIMQAAAAAAAHIQAAAAAADkIAAAAAAByE...
<image>As shown in the diagram, ∠ABD=44°, ∠DCE=54°, AD bisects ∠CAB, ED∥AB. Find the measure of ∠ADE.
41
3182
[ "41", "265.17", "315.72", "149.57" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAAClfElEQVR4nOzdZ3wUVfv/8TMzu6mkEwi9SO8IAopIlSIqiCCE4q0ICgiotNBCCSRAKIKiNyKCSFcUKYJIR5p0QVR6hwAhIY203Zn/g/Nj/3sHCAHS9/N+4CtsNtkJkuT6nrmucxTDMAQAAAAAx6Dm9AUAAAAAyD4EAAAAAMCBEAAAAAAAB0IAAAAAABwIAQAAAABwIAQAAAAAwIEQAAAAAAAHQgAAAAAAHAgBAAAAAHAgBAAAAADAgRAAAAAA...
<image>As shown in the diagram, AC=AY, AD=x+2, CB=5/3*x+11, DB=3*y-9, DB=YD, YD=2*y+6. Find the value of x.
21
243
[ "21", "436.93", "379.71", "30.54" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAAEAAElEQVR4nOzdd3wU1fo/8DMz25JNNr33AqH3XqQroGADFLkUQZo0KYLl6i2Wq4I0pUhVEK+FIiJKEaSXgPSWkL7pve0m2d2Z+f3xfNlfboAQILBJ9vP+474wWZaBm505n3Oe5xxOlmUGAAAAAAD2gbf1BQAAAAAAwOODAAAAAAAAYEcQAAAAAAAA7AgCAAAAAACAHUEAAAAAAACwIwgAAAAAAAB2BAEAAAAAAMCOIAAAAAAAANgRBAAAAAAA...
<image>As shown in the diagram, ∠EAD=42°, A is the center of circle A. Find the measure of arc AEC.
180
174
[ "180", "333.16", "450.65", "258.22" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAACetklEQVR4nOzdd3xU953v/1NmVJBAEiC6qcZU0w2YajDd9CKqQA1EtbPZm02cu/d3b5JN2WSTTdY2CFTpvWMQ3Zjem2mmd9FBXTNzzvn98Q0KoQghjTTlvJ5/+CFGw+iLJc35vD/fcmTDMCQAAAAA5qC4egAAAAAASg8BAAAAADARAgAAAABgIgQAAAAAwEQIAAAAAICJEAAAAAAAEyEAAAAAACZCAAAAAABMhAAAAAAAmAgBAAAAADARAgAA...
<image>As shown in the diagram, DE=14, D bisects segment OA, E is the midpoint of segment OB. Find the length of line AB.
28
3085
[ "28", "51.36", "243.45", "17.69" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAACDDElEQVR4nO3dZ3wUVf/38TMzm4QEQglVAQEB6QICAiqgoigCFixICaETWiCEjoVLROm9t4QuggpKEUGaiBWBSynSq3QIJIEkuzNzPzh/5s5Fk5Jkkz2f9wNfye7s5hA3u+f7O02zbVsAAAAAUIPu7QYAAAAASD8EAAAAAEAhBAAAAABAIQQAAAAAQCEEAAAAAEAhBAAAAABAIQQAAAAAQCEEAAAAAEAhBAAAAABAIQQAAAAAQCEEAAAAAEAh...
<image>As shown in the diagram, AO=BO, DO=BO, ∠OAC=28°. Find the measure of ∠BOD.
56
5399
[ "56", "302.23", "149.65", "209.83" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAADwjklEQVR4nOzdd3wU1fc38Dvb0zaVVEhAeu9IR6QoKCAgIl2BUARRQEFFEBEFAREUpAihSAcFpIqAoFIFQXpLIIX0tpu6ZWaeP86T+e03CSFAkk12Pu8/eEHYbGY3szPn3HvuuZwoigwAAAAAAORBYe8DAAAAAACAsoMEAAAAAABARpAAAAAAAADICBIAAAAAAAAZQQIAAAAAACAjSAAAAAAAAGQECQAAAAAAgIwgAQAAAAAAkBEkAAAAAAAA...
<image>As shown in the diagram, ∠OPA=40°, O is the center of circle O, AB is the diameter of circle O, the tangent to ⊙O is PA. Find the measure of ∠ABC.
25
4867
[ "25", "229.76", "309.42", "310.6" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAABa30lEQVR4nO3daXxdVaHw4b3POUlnBMrUllkUkEGkUC6IFEHLrCAXvAgKyOvVQm3TiaGUuQMUWjpQ5BUFlJcrCIjMCgqiQK9YRmUqIFihIkNpS4c0OWfv98O6nBvTNpTSZlrP86G/k+Qk2U3TZP33XmuvNM/zBAAAiEOhrQ8AAABoPQIAAAAiIgAAACAiAgAAACIiAAAAICICAAAAIiIAAAAgIgIAAAAiIgAAACAiAgAAACIiAAAAICICAAAA...
<image>As shown in the diagram, the area of triangle ABC is 4, the ratio of similar △ABC and △DEF is 1/2, triangle ABC is similar to triangle DEF.. Find the area of triangle DEF.
16
5345
[ "16", "317.1", "288.41", "48.55" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAAB5T0lEQVR4nO3dd3wU1f7/8ZnZ3ZCQQOi9SUeqgIAFREUuFkCRi3IVkTQSSkKTEkho0pEikE5oNgRFFMQCqIBS5IoC0iEU6QQSSkKSnZnfH+fH3HypAZJskvN6/uEj2Ww2s1ncnPc5n885qmmaCgAAAAA5aK6+AAAAAAC5hwAAAAAASIQAAAAAAEiEAAAAAABIhAAAAAAASIQAAAAAAEiEAAAAAABIhAAAAAAASIQAAAAAAEiEAAAAAABIhAAA...
<image>As shown in the diagram, the perimeter of quadrilateral ABCD is 8, E bisects segment AB, quadrilateral ABCD is a rhombus. Find the length of line OE.
1
6340
[ "1", "345.69", "252.65", "81.91" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAACSWElEQVR4nOzdd3wUdf7H8e/M7GYTSOi99ypdlCKIFAsgRUGKNOkt9OKpd+f97jyRmkYv0jtSBAVERFDAk9577zWkkLK7M78/vsdcpBkgyWZ3Xs8/fJjNZBnY7Ozn/Z3P9/tVDMMQAAAAAKxB9fQJAAAAAEg7BAAAAADAQggAAAAAgIUQAAAAAAALIQAAAAAAFkIAAAAAACyEAAAAAABYCAEAAAAAsBACAAAAAGAhBAAAAADAQggAAAAAgIUQ...
<image>As shown in the diagram, AD=8, DB=22, ED=3, DE∥BC. Find the length of line BC.
45/4
3037
[ "45/4", "492.32", "105.68", "49.3" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAAEAAElEQVR4nOzdd3yN5/8/8Ou+73NO9hAhm5hJI2YSsUKrlFKjRou2VO1Vq/betBS1R21tqaJaiupAJEhirxBiRIbsdZIz7vv+/fH+OD9fq0FOzknO6/mHR0TG5dznnPv9vq739b44WZYZAAAAAABYBt7UAwAAAAAAgJKDBAAAAAAAwIIgAQAAAAAAsCBIAAAAAAAALAgSAAAAAAAAC4IEAAAAAADAgiABAAAAAACwIEgAAAAAAAAsCBIAAAAA...
<image>As shown in the diagram, ∠CAB=58°, the center of ⊙O is O. Find the measure of ∠COB.
116
4569
[ "116", "88.74", "123.33", "100.97" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAAC+tUlEQVR4nOzdZXwU1/v38TMzu3EhaAjuVqBFihWKFHeKBw0WrEDdW9pS+7XQ4h4SvLRIcQoUaXF3d5eQEM/uzNwPzp+9UwgeI/t5P+C12Uw2k2TZvb5nrnOOYpqmAAAAAOAc1PQ+AQAAAABphwAAAAAAOBECAAAAAOBECAAAAACAEyEAAAAAAE6EAAAAAAA4EQIAAAAA4EQIAAAAAIATIQAAAAAAToQAAAAAADgRAgAAAADgRAgAAAAAgBMh...
<image>As shown in the diagram, AB=2*x, AC=12, BC=20, DE=y+4, EF=15, FD=12, ∠ACB=∠DEF, ∠BAC=∠FDE, ∠CBA=∠EFD, triangle ACB is similar to triangle DEF.. Find the value of y.
5
2594
[ "5", "197.26", "354.11", "376.98" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAACQnElEQVR4nOzdZ1xVWZr3/X04h4wJUREFFYxomUvMOZQ5gKKAJBUlo3b39PT0c8/d93RPT3eXAhJFlChiTihqGcpcljnnHBAVAUXiCc+LPbX7tJUM5P37vpjPNJ7CXRaec/3Xda21FDqdTgAAAAAgDwY1/QAAAAAAqg8BAAAAAJARAgAAAAAgIwQAAAAAQEYIAAAAAICMEAAAAAAAGSEAAAAAADJCAAAAAABkhAAAAAAAyAgBAAAAAJARAgAA...
<image>As shown in the diagram, ∠DCF=53°. Find the measure of ∠ECB.
53
711
[ "53", "433.48", "181.22", "157.22" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAACk3ElEQVR4nOzdZ3xURfv/8TnnbDaNFBIgBAi9NwFBEBCliaKCNPH2pvcmvQkiYAEERAQpghAEEREUBKWJIEWKdOm9QwgE0uvuOf8Hc7P//BCQkmSzez7vB75iSMKQbHav78w1M4phGAIAAACAOajOHgAAAACArEMAAAAAAEyEAAAAAACYCAEAAAAAMBECAAAAAGAiBAAAAADARAgAAAAAgIkQAAAAAAATIQAAAAAAJkIAAAAAAEyEAAAAAACY...
<image>As shown in the diagram, ∠DCA=122°, D is the center of ⊙D. Find the measure of ∠ABC.
61
2363
[ "61", "384.31", "494.46", "248.48" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAAEAAElEQVR4nOzddVxU2f8/8Hun6G4UJAzExsbAzrULJW1ca+211lq711aUtLsT28VCsRVEERFR6Rom7szvj/fX+c3HWoOe1/MPHzDO3LnM3Hi/z3mfc1ilUskAAAAAAIBm4BX3DgAAAAAAQNFBAgAAAAAAoEGQAAAAAAAAaBAkAAAAAAAAGgQJAAAAAACABkECAAAAAACgQZAAAAAAAABoECQAAAAAAAAaBAkAAAAAAIAGQQIAAAAAAKBBkAAA...
<image>As shown in the diagram, BC=6, BC=CD, ∠ABD=30°, ∠BEO=90°, O is the center of ⊙O. Find the area of the ⊙O.
36*pi
6087
[ "36*pi", "250.82", "50.97", "427.51" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAAEAAElEQVR4nOzdd1wU1/c38Dszu0uvUkTAhiKiIMVeo8bYjTUm9i5qbLHFWFFjjV0pNhRjolGTWBKNNRZApdiwIAhKE5AivezOzPPH/TkPX1sswC7s5/2HL4RluQuzM+fcOfdcRhRFAgAAAAAA2oFV9wAAAAAAAKDiIAEAAAAAANAiSAAAAAAAALQIEgAAAAAAAC2CBAAAAAAAQIsgAQAAAAAA0CJIAAAAAAAAtAgSAAAAAAAALYIEAAAAAABA...
<image>As shown in the diagram, AD=24, the center of ⊙N is N, AD is the diameter of ⊙N. Find the length of line CN.
12
495
[ "12", "441.66", "259.06", "91.68" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAABr90lEQVR4nO3dZ5yVxf0/7vuUXZqCUkQE7A1ULChgoibGqLE3sMeuWBGlCFgSG12sWGOLLYqxRJMoYsGCNTFF6VXBEqWswFJ2z7n/D+bn/vlaUGnL7lzXA15w9nCYXc6573nPfGYmk6ZpAgAAxCFb3Q0AAADWHAEAAAAiIgAAAEBEBAAAAIiIAAAAABERAAAAICICAAAAREQAAACAiAgAAAAQEQEAAAAiIgAAAEBEBAAAAIiIAAAAABERAAAA...
<image>As shown in the diagram, ∠CAD=47°, DA is perpendicular to BA. Find the measure of ∠BAE.
43
1880
[ "43", "407.52", "150.92", "333.67" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAABOC0lEQVR4nO3deZxVZeH48XPuvTPsKKCIKPpVEzVRzH3XytISMbVMTTL9mmAuKaGIiOCCAqKUpoZmZt/MStHUtDRRExdwJzcEF1LcQJB9m3vv+f3xxP1NLCPCMAM87/cfvmbunLlzZuY6PJ9znvOcNMuyBAAAiEOusXcAAABoOAIAAAAiIgAAACAiAgAAACIiAAAAICICAAAAIiIAAAAgIgIAAAAiIgAAACAiAgAAACIiAAAAICICAAAAIiIA...
<image>As shown in the diagram, ∠EDH=x°, ∠HDA=3*x°. Find the value of x.
45
889
[ "45", "73.74", "456.56", "451.67" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAACdxklEQVR4nOzdZ3wU1fv38TMzu2kQINIFadK7IE0ULIgKoogNC4pURUooIYGEJCSBBEJHqqgolh/YsCEoig0VBalKF6RJDwnpuzNzPzh/9o5ppJedz/sBr81mszsJW67vnHOdo5imKQAAAABYg1raBwAAAACg5BAAAAAAAAshAAAAAAAWQgAAAAAALIQAAAAAAFgIAQAAAACwEAIAAAAAYCEEAAAAAMBCCAAAAACAhRAAAAAAAAshAAAAAAAW...
<image>As shown in the diagram, AD=10, BA=x-2, BC=5, ED=4, EB∥DC. Find the value of x.
19/2
2418
[ "19/2", "60.91", "132.41", "91.86" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAACJtklEQVR4nOzdZ3xU1fr28V1mUkgIoVfpvSigFGlHQQGlqGABCzVA6IL0DgEElY6EloRmQfpBUEQEFQSRroA0kSIlECAkIWVm7/28WH/myQkkBsiQTNbv+4JPMjOZ7AxT7muve62lWpalAAAAAJCDltkHAAAAAODxIQAAAAAAEiEAAAAAABIhAAAAAAASIQAAAAAAEiEAAAAAABIhAAAAAAASIQAAAAAAEiEAAAAAABIhAAAAAAASIQAAAAAA...
<image>As shown in the diagram, AB=8, AD=6, EO=OF, EO perpendicular bisects DB, FO is the perpendicular bisector of BD, quadrilateral DABC is a rectangle. Find the length of line EF.
15/2
6316
[ "15/2", "470.5", "303.97", "451.2" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAACM/ElEQVR4nOzdeXxdVb3//7WHMybpROe5aelA53Ru0xYKXC44AKLo9YrTVdSviOJF8aL3x0VUEFGQrxN+lauAIopIxYuIQ2mbJk2azvM8z1OaJicn55y99++Pjzk3ZmrS5ozr9fyjj+Rkn5OdNPvs9V7rs9YyPM9TAAAAAPRgZvoEAAAAAKQPAQAAAADQCAEAAAAA0AgBAAAAANAIAQAAAADQCAEAAAAA0AgBAAAAANAIAQAAAADQCAEAAAAA...
<image>As shown in the diagram, AC=19, BN=10, EF=2, NC=20, the height of AEBC is AF, AF is perpendicular to NF, FN⊥CN, AE and BC are the non-parallel sides (legs) of trapezoid AEBC. Find the area of quadrilateral AEBC.
500
1889
[ "500", "176.81", "30.65", "374.49" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAAEAAElEQVR4nOzdZ1xUR/s38DlbYGkCKqIUERDFrihgwQL2EmOsQQFrTEyMxqixYBRLNJrYEu9EY2yAYu9dhIhIFUREwEJHiiC97u7Z87yYP/tsLAQVWGB/3xd+cDm7zMKec65r5poZhuM4AgAAAAAAqoGn7AYAAAAAAED9QQIAAAAAAKBCkAAAAAAAAKgQJAAAAAAAACoECQAAAAAAgApBAgAAAAAAoEKQAAAAAAAAqBAkAAAAAAAAKgQJAAAA...
<image>As shown in the diagram, AB=3*y-8, AD=13, CB=2*x+7, CD=10, ∠ADF=59°, ∠BFC=49°, ∠FBA=20°, AB and DC are opposite sides of the ▱ ADCB. Find the measure of ∠CAD.
72
2699
[ "72", "137.31", "238.51", "433.82" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAAB6s0lEQVR4nO3dd3yUZb7//+u+75kUQkLohBoBlSIWkCLYEReVZmMF6RJ61T2ex9l2dvec/a17zipSQpMAgoUOK0VFURBEEKyAFJHeW4QUksxdfn98DvPNJoABUmbmej3/4DGZTJI7M+Gez/u6Ptd1G57nKQAAAAB6MMv6AAAAAACUHgIAAAAAoBECAAAAAKARAgAAAACgEQIAAAAAoBECAAAAAKARAgAAAACgEQIAAAAAoBECAAAAAKARAgAA...
<image>As shown in the diagram, AC=5, AD=9, ∠DAC=60°, quadrilateral DACB is a ▱, AC⊥DC. Find the area of DACB.
45*sqrt(3)/2
844
[ "45*sqrt(3)/2", "131.06", "206.29", "199.49" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAACkgElEQVR4nOzdd3xUVd7H8XPvnQkp9N6lg/TeiyJiQ0AQCKCUIDUQqu7us/vsqqgo0ouU0EsSEGyrUkPvTZqdKk06JLRk5t77/HGWeWYTSoAkM3Pv5/2HL5xMwk1IJud7zu/3u4ppmgIAAACAPai+vgAAAAAAmYcAAAAAANgIAQAAAACwEQIAAAAAYCMEAAAAAMBGCAAAAACAjRAAAAAAABshAAAAAAA2QgAAAAAAbIQAAAAAANgIAQAAAACw...
<image>As shown in the diagram, ∠AGE=115°, ∠CAB=30°, DE is parallel to FC, ∠BCA is the right angle of the right triangle BCA. Find the measure of ∠DFC.
85
3259
[ "85", "471.51", "28.01", "306.6" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAAEAAElEQVR4nOzdd3xUVf4//nPvlPTeSe8VCEkIKfQOgjQVRQWpgrrLWnZ1F113VXbX3bWtZREExAJLFWnSQSCNkB5IQvokmfTeZ+be+/vjfLm/+YQWIMkkmdfzDx+KyeQCM/ee1znv8z6MIAgEAAAAAAD0A6vrCwAAAAAAgIGDAAAAAAAAoEcQAAAAAAAA9AgCAAAAAACAHkEAAAAAAADQIwgAAAAAAAB6BAEAAAAAAECPIAAAAAAAAOgRBAAA...
<image>As shown in the diagram, AB=AC, AC=AD, ∠EAB=44°, ∠EBC=2∠CDE, the center of ⊙A is A. Find the measure of ∠DAE.
88
2997
[ "88", "472.43", "455.03", "188.85" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAACuV0lEQVR4nOzdZ3wU5f738ZnZ3fRGAoHQe0d6pAmIIKAgvXcQqSJFsB3LsRyPiIIKItKLhdA7SAugIB2C9NBrEtJ7dnfmfnD9mXtPgNASkux83g94hc2WazfZ7O97VVnTNAkAAACAMSi53QAAAAAAzw4BAAAAADAQAgAAAABgIAQAAAAAwEAIAAAAAICBEAAAAAAAAyEAAAAAAAZCAAAAAAAMhAAAAAAAGAgBAAAAADAQAgAAAABgIAQAAAAA...
<image>As shown in the diagram, CB=CD, ∠BCA=90°, ∠CAB=26°, the center of circle C is C. Find the measure of ∠BCD.
52
4344
[ "52", "112.91", "306.68", "159.6" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAAEAAElEQVR4nOzdd1wU1/c38Dszu/QOUlTsDewVjb23xFhiTGKKHbBhwwb2LvYKahJ7TGJJ7MaOJfaOBREVFZHey+7OzPPH+bkPX1BjAXaX/bz/8LUuyzK7sDPn3HvuuZwsywwAAAAAAIwDr+sDAAAAAACAooMEAAAAAADAiCABAAAAAAAwIkgAAAAAAACMCBIAAAAAAAAjggQAAAAAAMCIIAEAAAAAADAiSAAAAAAAAIwIEgAAAAAAACOCBAAA...
<image>As shown in the diagram, ∠BAD=36°, the center of ⊙O is O, AB∥CD. Find the measure of ∠COA.
72
6180
[ "72", "22.98", "386.45", "222.3" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAACGO0lEQVR4nO3dd1yV9f//8WscNqighjtniStn7iy1NDPTMtMsVw6QXLgH7oEzxa1lWmppZdlQUzPNcuYoLU1z74kooMC5ruv3x/vr+fEBJFTgHHg/7n94wzPgAi7OeT+v9+v9equWZSkAAAAA5KA5+wAAAAAAZB0CAAAAACARAgAAAAAgEQIAAAAAIBECAAAAACARAgAAAAAgEQIAAAAAIBECAAAAACARAgAAAAAgEQIAAAAAIBECAAAAACAR...
<image>As shown in the diagram, ∠DCA=56°, ∠EBD=44°, AD bisects ∠CAB, DE is parallel to CA. Find the measure of ∠EDA.
40
3593
[ "40", "105.69", "193.17", "261.77" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAABQR0lEQVR4nO3deZxd8+H4/3PuvTPZCZGFhIRGEal9bRukqKV2VXyU+tD6FpEdSUQIIiKyivp8ilap6kKUqJTaiti+PmILsYdEkJB9JJmZe8/vj/fPfPNJIkgmmcm8n88/PO7c9czIvff9Oud9zkmzLEsAAIA45Op6AQAAgA1HAAAAQEQEAAAAREQAAABARAQAAABERAAAAEBEBAAAAEREAAAAQEQEAAAAREQAAABARAQAAABERAAAAEBEBAAA...
<image>As shown in the diagram, ∠AOC=35°. Find the measure of ∠COB.
145
3437
[ "145", "60.61", "281.89", "252.29" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAADqV0lEQVR4nOzdZ1xU1/o24LWnADN0RcWu2LFXBFRUFAGlm1hSThJzzrH33sWGimIvyTE5SU6iidIVRGygoth7bygqICC9Tdnvh+dl/ycoiEif+/rgbxz2HjYwZd1rPWstjud5BgAAAAAA2kFU1RcAAAAAAACVBwEAAAAAAECLIAAAAAAAAGgRBAAAAAAAAC2CAAAAAAAAoEUQAAAAAAAAtAgCAAAAAACAFkEAAAAAAADQIggAAAAAAABaBAEA...
<image>As shown in the diagram, ∠WZY=4*x°, ∠XWZ=10*x°, ∠YXW=120°, XWZY is a kite. Find the measure of ∠ZYX.
100
700
[ "100", "190.84", "78.04", "452.14" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAABwrklEQVR4nO3dd5xUVZ43/ltV3U1GlGRCQcGsmJAZEyrqGMaMIEpSsjizO/PM89swsz66O447zuy6u6OSGhRQwUExgCNiFiOCGBBMgBgJSm5Cd1fV748z3O1pAcldcN/vP3gV1berbit963zu+Z7vSeXz+QgAAEiGdE2fAAAAsOsIAAAAkCACAAAAJIgAAAAACSIAAABAgggAAACQIAIAAAAkiAAAAAAJIgAAAECCCAAAAJAgAgAAACSIAAAA...
<image>As shown in the diagram, AB=1, OB=2, ∠AOB=a°, ∠OBA=90°. Find tan(a).
1/2
4135
[ "1/2", "26.49", "340.86", "51.65" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAACSCElEQVR4nOzdZ1yUV/7//+uaQkdQQY099t67YkER6W0AuyYmu5u+2c0mm7KJyea7aZtqsqkbjZ1eRFBEEBEQrFgAsRfEgmJXYMr/xvk7v1lbNFHKXK/njTxkuGY4swvXnPcpnyObTCYJAAAAgDKo6rsBAAAAAOoOAQAAAABQEAIAAAAAoCAEAAAAAEBBCAAAAACAghAAAAAAAAUhAAAAAAAKQgAAAAAAFIQAAAAAACgIAQAAAABQEAIAAAAA...
<image>As shown in the diagram, AB=3, BE=50, EC=30, DE is parallel to AB. Find the length of line DE.
9/8
3533
[ "9/8", "136.91", "81.98", "216.46" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAACiXUlEQVR4nOzdZ3wU1fv38TMzu6mkQKihhd67FAERERFQkCqIilhAUVGKdAHpRUAUUbFgAQuIAoIgCIhIFem9BAiEEkjv2d3ZuR+cP3vnR4kIIbub+bwf8AphEwayO3t9z7nOOYphGAIAAACAOajuvgAAAAAAeYcAAAAAAJgIAQAAAAAwEQIAAAAAYCIEAAAAAMBECAAAAACAiRAAAAAAABMhAAAAAAAmQgAAAAAATIQAAAAAAJgIAQAAAAAw...
<image>As shown in the diagram, ∠CAB=45°, the radius of circle A is 2, A is the center of circle A. Find the area of the sector ABC.
pi/2
4913
[ "pi/2", "208.92", "215.93", "61.12" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAACDR0lEQVR4nO3dd3xUVf7/8XPvTDIJJEBCFZQiCApYEURwaQnsqkgHFQsdFIUAQgTL1911VSCEEqlKkSpKE0RsgCAoVUFdFVACKFUSWnpm7r2/P86X+5tvaElIMuW8nn/sAyeT5MJmMp/3uZ/POZplWQIAAACAGnRfXwAAAACAkkMAAAAAABRCAAAAAAAUQgAAAAAAFEIAAAAAABRCAAAAAAAUQgAAAAAAFEIAAAAAABRCAAAAAAAUQgAAAAAA...
<image>As shown in the diagram, AB=y, AD=x, BC=z, BD=8, ∠BAC=45°, ∠BDA=60°, AC⊥BC, DA is perpendicular to BA. Find the value of z.
2*sqrt(6)
508
[ "2*sqrt(6)", "319.23", "7.24", "237.74" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAAEAAElEQVR4nOzdZ3wUVdsG8DOzLb03AgkQICRA6L33DpoGoogVC9IFxEcBCypNQMTyKIKi9ARCi/ReQg09BEKANNLbpm2beT/cD/OuNAOkz/X/wA+W3c0kmd29rzP3OYcTRZEBAAAAAIA88JV9AAAAAAAAUHEQAAAAAAAAZAQBAAAAAABARhAAAAAAAABkBAEAAAAAAEBGEAAAAAAAAGQEAQAAAAAAQEYQAAAAAAAAZAQBAAAAAABARhAAAAAA...
<image>As shown in the diagram, ∠BOA=60°, the center of circle O is O, AB is the diameter of ⊙O. Find the measure of ∠BCA.
30
6717
[ "30", "393.03", "132.69", "55.72" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAACUnUlEQVR4nOzdZ3xUZfr/8fucKekhkEASQgpJSKEpIChFUZGVJmLXtay6urqou7JrXV2xr7u6q669r64FkGIBbCgqioiIdEJJLyQhCZCezMw5/wfXj/nPppFAQiDn837Aa3LmzOSeYQau733uopmmqQAAAABYg97dDQAAAABw9BAAAAAAAAshAAAAAAAWQgAAAAAALIQAAAAAAFgIAQAAAACwEAIAAAAAYCEEAAAAAMBCCAAAAACAhRAAAAAA...
<image>As shown in the diagram, AB=26, AD=12, DG=9/2, EF=8, GF=14, ∠AGF=108°, quadrilateral AGFE is similar to quadrilateral ADCB. Find the perimeter of quadrilateral AGFE.
183/4
372
[ "183/4", "467.37", "131.02", "259.61" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAABGrElEQVR4nO3dZ5hV5b3477XLDAOIFLEEFUVE1AiJnRgLWDF2jUfT1PwTjdEktiRi19gSjhoTNbH8InJMNCqCmCN2Y48lionYAAWUpqCC9Jld/i+ei7nmUEY0wOB87/uF17Bn75k1sNzzfNZ61rNy1Wo1AwAAYsi39AYAAACrjwAAAIBABAAAAAQiAAAAIBABAAAAgQgAAAAIRAAAAEAgAgAAAAIRAAAAEIgAAACAQAQAAAAEIgAAACAQAQAA...
<image>As shown in the diagram, AB=14, AD=DC, DC=4. Find the length of line CB.
6
5287
[ "6", "101.84", "125.11", "19.49" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAADFhUlEQVR4nOzdd3xUVfo/8HPLTHqB9N4JoQriKiiiKy7qKoquCooillVXei8h9N6rXRSQtaEINkRFRUXFgoT0XknvdeaW3x/Pj/lmEwghJJlyP+8/eCWTkNwkM/eez7nPcw6nqioDAAAAAABt4M19AAAAAAAA0HMQAAAAAAAANAQBAAAAAABAQxAAAAAAAAA0BAEAAAAAAEBDEAAAAAAAADQEAQAAAAAAQEMQAAAAAAAANAQBAAAAAABAQxAA...
<image>As shown in the diagram, AD=6, DE=3, quadrilateral ABCD is a ▱. Find the ratio of the length of line AM to the length of line MC.
1/2
5895
[ "1/2", "111.58", "479.86", "495.98" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAACiA0lEQVR4nOzdeZyN5f/48eu+73Nms+9kjZAlpVBpQUqJlJCkLJFdGOuMfZmFWYjIFmUpe0VFRAuFQpGE7DtZhjHMzDn3ff/+uL7Obz4zZowxM2e5X88/PM6cOWfmxrnOeb+v6329L8U0TQEAAADAGlR3XwAAAACA3EMCAAAAAFgICQAAAABgISQAAAAAgIWQAAAAAAAWQgIAAAAAWAgJAAAAAGAhJAAAAACAhZAAAAAAABZCAgAAAABYCAkA...
<image>As shown in the diagram, ∠ACD=35°, ∠BCA=90°, BA∥CD. Find the measure of ∠ABC.
55
3256
[ "55", "331.94", "28.18", "109.64" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAACQDUlEQVR4nOzdd3xUZdr/8VNmJg1CSwi9V6nSVJoIAWlJKLquYldWrCAKKu76PBYQUbDr2tF1WVECBELvRTrSkd5CCZ0QQpKZOef8/riezC8bIIQwySQ5n/cfvCbDZHICM2eu732u+75Vy7IUAAAAAPagBfoAAAAAABQeAgAAAABgIwQAAAAAwEYIAAAAAICNEAAAAAAAGyEAAAAAADZCAAAAAABshAAAAAAA2AgBAAAAALARAgAAAABgIwQA...
<image>As shown in the diagram, AC=9, BA=9, ∠BAC=60°. Find the length of line BC.
9
2793
[ "9", "253.09", "394.99", "250.13" ]
A
[ { "bytes": "iVBORw0KGgoAAAANSUhEUgAABAAAAAQACAIAAADwf7zUAADNVklEQVR4nOzdd1yU17Y38P2UYZCiFLEgkBgBo2JDY8ECFqSrKZ4kppnENGMJds097z0t9hajJibR1BNNM4nSUWygEdBEsWEUUSOg0jsz8zz7/WMd5nKMGlRgZpjf94/7CeMwbM7VZ6+199prC5xzBgAAAAAA1kE09QAAAAAAAKDlIAEAAAAAALAiSAAAAAAAAKwIEgAAAAAAACuCBAAAAAAAwIogAQAAAAAAsCJIAAAAAAAArAgSAAAAAAAA...
<image>As shown in the diagram, AB=8, CA=10, CB=a, ∠BAC=60°. Find the value of a.
2*sqrt(21)
61
[ "2*sqrt(21)", "243.27", "463.0", "477.39" ]
A
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<image>As shown in the diagram, AF=EA, CF=DC, FT=12, QD=EQ. Find the length of line TQ.
6
659
[ "6", "372.4", "145.2", "415.17" ]
A
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<image>As shown in the diagram, BQ=6, QE=8, ∠BDQ=∠EAQ, ∠DQB=∠AQE, ∠QEA=∠QBD. Find the ratio of similar triangles AQE and DQB.
4/3
2632
[ "4/3", "488.72", "310.11", "205.88" ]
A
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<image>As shown in the diagram, ∠NEB=36°, AB∥CD, GF is perpendicular to EF. Find the measure of ∠CFG.
54
3168
[ "54", "182.06", "458.88", "410.22" ]
A
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<image>As shown in the diagram, RT=13, XY=7, ∠ZXY=124°, XZ is the midsegment of triangle SRT, YX is the midsegment of △ RTS. Find the length of line XZ.
13/2
1685
[ "13/2", "75.52", "53.05", "365.96" ]
A
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<image>As shown in the diagram, AC=8, AD=11, BE=2, BF=3, CH=6, EG=2, FD=5, HG=1, BE⊥GE, BN⊥DN, CA⊥MA, DF is perpendicular to BF, GH is perpendicular to CH, GM is perpendicular to NM, HC is perpendicular to AC, ND⊥FD. Find the sum of the area of quadrilateral HCAM, the area of quadrilateral GMNE and the area of quadrilateral FBND.
77
1125
[ "77", "69.15", "452.4", "38.7" ]
A
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<image>As shown in the diagram, ∠ABC=70°, the center of ⊙O is O. Find the measure of ∠AOC.
140
4302
[ "140", "26.24", "321.14", "336.37" ]
A
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<image>As shown in the diagram, the radius of ⊙O is 2, Sin(ABC)=3/4, O is the center of ⊙O. Find the length of line AC.
3
4617
[ "3", "163.79", "30.98", "401.6" ]
A
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<image>As shown in the diagram, AB=8, OP=2, O is the center of circle O, BP⊥OP. Find the length of line BC.
4*sqrt(3)
6247
[ "4*sqrt(3)", "286.13", "345.86", "169.14" ]
A
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<image>As shown in the diagram, AB=10, BC=16, BF is the angle bisector of ∠ABC, D bisects segment AB, BF⊥AF. Find the length of line EF.
3
5761
[ "3", "57.93", "43.16", "367.01" ]
A
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<image>As shown in the diagram, ∠BCD=140°, O is the center of ⊙O. Find the measure of ∠DOB.
80
4509
[ "80", "144.57", "429.56", "450.89" ]
A