id int64 0 399 | depth stringclasses 4 values | problem_version stringclasses 1 value | answer_type stringclasses 2 values | conversations listlengths 2 2 | prompt_pre stringclasses 4 values | image dict | prompt_post stringclasses 2 values | language stringclasses 2 values |
|---|---|---|---|---|---|---|---|---|
200 | depth0 | text_lite | multi_choice | [
{
"from": "human",
"value": "首先进行推理，然后从选项中选出正确的答案，按照这种格式：答案：xxx。\n<image>\nABC是一个等腰三角形，其中两条边AB和BC的长度相等。角CBA等于120°。等腰三角形ABC中，角BAC和角ACB的角度各是多少度？\n选项：\nA.10\nB.30\nC.90\nD.7.5"
},
{
"from": "gpt",
"value": "已知等腰三角形ABC的顶角B为120°，可得底角BAC和ACB为 (180° - 120°) / 2 = 30°。答案：B"
}
] | 首先进行推理，然后从选项中选出正确的答案，按照这种格式：答案：xxx。
<image>
| {
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"path": "depth0_zh/0/1_text.jpg"
} | 答案： | Chinese |
201 | depth0 | text_lite | multi_choice | [
{
"from": "human",
"value": "首先进行推理，然后从选项中选出正确的答案，按照这种格式：答案：xxx。\n<image>\n圆弧CD是一个半圆。AB等于13。请计算图形ABCD中弧CD的长度。\n选项：\nA.65*π/6\nB.39*π/10\nC.13*π/2\nD.13*√(3)*π/8"
},
{
"from": "gpt",
"value": "CD是AB的对边，所以它的长度为13。从C到D的半圆以CD为直径，长度为 13 * π/2 = 13*π/2。答案：C"
}
] | 首先进行推理，然后从选项中选出正确的答案，按照这种格式：答案：xxx。
<image>
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"path": "depth0_zh/1/2_text.jpg"
} | 答案： | Chinese |
202 | depth0 | text_lite | multi_choice | [
{
"from": "human",
"value": "首先进行推理，然后从选项中选出正确的答案，按照这种格式：答案：xxx。\n<image>\n角ACB等于30°。如何求ABC的周长？\n选项：\nA.66*√(3) + 198\nB.66\nC.33 + 33*√(3)\nD.55*√(3) + 165"
},
{
"from": "gpt",
"value": "因为AB = 66且角 ACB = 30°，BC = AB / tan(30°) = 66 / (√(3)/3) = 66*√(3)。斜边 AC = AB / sin(30°) = 66 / (1/2) = 132，故周长为 AB +BC + AC = 66*√(3) + 198。答案：A"
}
] | 首先进行推理，然后从选项中选出正确的答案，按照这种格式：答案：xxx。
<image>
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"path": "depth0_zh/10/11_text.jpg"
} | 答案： | Chinese |
203 | depth0 | text_lite | multi_choice | [
{
"from": "human",
"value": "首先进行推理，然后从选项中选出正确的答案，按照这种格式：答案：xxx。\n<image>\nABC是一个等腰三角形，其中AB = BC。AB=55。图形ABC的周长有多长？\n选项：\nA.3025*√(2)/4\nB.55*√(6)*(√(2 - √(2)) + 2)/3\nC.275*√(2 - √(2))/3 + 550/3\nD.55*√(2 - √(2)) + 110"
},
{
"from": "gpt",
"value": "可知ABC是一个顶角为45°的等腰三角形。则底边的一半为 AB * sin(45°/2) = 55 * (√(2 - √(2))/2) = 55*√(2 - √(2))/2，故底边总长度为 2 * (55*√(2 - √(2))/2) = 55*√(2 - √(2))，计算可得周长为AB * 2 + AC = 55 * 2 + 55*√(2 - √(2)) = 55*√(2 - √(2)) + 110。答案：D"
}
] | 首先进行推理，然后从选项中选出正确的答案，按照这种格式：答案：xxx。
<image>
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"path": "depth0_zh/11/12_text.jpg"
} | 答案： | Chinese |
204 | depth0 | text_lite | multi_choice | [
{
"from": "human",
"value": "首先进行推理，然后从选项中选出正确的答案，按照这种格式：答案：xxx。\n<image>\nCDE构成一个等边三角形。AD等于55*√(3)。请计算ABCED的周长。\n选项：\nA.165*√(3) + 396\nB.44*√(3)\nC.55*√(3) + 132\nD.110*√(3) + 264"
},
{
"from": "gpt",
"value": "矩形ABCD的对边CD长度等于AB，因此CD = 88。CDE是一个等边三角形，故CE和ED均等于88。因此，周长为 AB + AD + BC + ED + CE = 88 + 55*√(3) + 55*√(3) + 88 + 88 = 110*√(3) + 264。答案：D"
}
] | 首先进行推理，然后从选项中选出正确的答案，按照这种格式：答案：xxx。
<image>
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"path": "depth0_zh/12/13_text.jpg"
} | 答案： | Chinese |
205 | depth0 | text_lite | multi_choice | [
{
"from": "human",
"value": "首先进行推理，然后从选项中选出正确的答案，按照这种格式：答案：xxx。\n<image>\nABCD是平行四边形。AB=4。你知道如何计算ABCD的周长吗？\n选项：\nA.24 + 18*√(3)\nB.20/3 + 5*√(3)\nC.8 + 6*√(3)\nD.32*√(3)/3 + 24"
},
{
"from": "gpt",
"value": "鉴于ABCD是对边相等的平行四边形，因此其周长为 (AB + AD) * 2 = (4 + 3*√(3)) * 2 = 8 + 6*√(3)。答案：C"
}
] | 首先进行推理，然后从选项中选出正确的答案，按照这种格式：答案：xxx。
<image>
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"path": "depth0_zh/13/14_text.jpg"
} | 答案： | Chinese |
206 | depth0 | text_lite | multi_choice | [
{
"from": "human",
"value": "首先进行推理，然后从选项中选出正确的答案，按照这种格式：答案：xxx。\n<image>\n角ACB等于45°。如何求ABC的周长？\n选项：\nA.2 + 2*√(2)\nB.2*√(2)/5 + 4/5\nC.√(6)*(√(2) + 2)\nD.2*√(2) + 4"
},
{
"from": "gpt",
"value": "已知AB = 2且角 ACB 为 45°，BC可以表示为 AB / tan(45°) = 2 / 1 = 2。斜边 AC = AB / sin(45°) = 2 / (√(2)/2) = 2*√(2)，所以周长为 AB +BC + AC = 2*√(2) + 4。答案：D"
}
] | 首先进行推理，然后从选项中选出正确的答案，按照这种格式：答案：xxx。
<image>
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"path": "depth0_zh/14/15_text.jpg"
} | 答案： | Chinese |
207 | depth0 | text_lite | multi_choice | [
{
"from": "human",
"value": "首先进行推理，然后从选项中选出正确的答案，按照这种格式：答案：xxx。\n<image>\nCDE是等边三角形。AB=24。你知道图形ABCED的总面积吗？\n选项：\nA.432*√(2)*(√(3) + 2)\nB.144*√(3)/5 + 288/5\nC.24*√(2)*(√(3) + 2)\nD.144*√(3) + 288"
},
{
"from": "gpt",
"value": "根据已知条件，CD是AB的对边，则 CD = AB = 24。CDE是等边三角形，所以它的高为 CD * √(3)/2 = 12*√(3)。三角形CDE的面积为 CD * 高度/2 = 144*√(3)。矩形ABCD的面积为 24 * 12 = 288。因此，ABCED的总面积为 144*√(3) + 288 = 144*√(3) + 288。答案：D"
}
] | 首先进行推理，然后从选项中选出正确的答案，按照这种格式：答案：xxx。
<image>
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"path": "depth0_zh/15/16_text.jpg"
} | 答案： | Chinese |
208 | depth0 | text_lite | multi_choice | [
{
"from": "human",
"value": "首先进行推理，然后从选项中选出正确的答案，按照这种格式：答案：xxx。\n<image>\n边CD向内延伸为矩形内的等边三角形。AD等于64。求出图形ABCED的面积。\n选项：\nA.3840 - 750*√(3)\nB.1280 - 250*√(3)\nC.-625*√(6)/2 + 1600*√(2)\nD.3200 - 625*√(3)"
},
{
"from": "gpt",
"value": "考虑到CD是AB的对边，所以 CD = AB = 50。而CDE是等边三角形，三角形的高为 CD * √(3)/2 = 25*√(3)。该三角形CDE的面积为 CD * 高度/2 = 625*√(3)。矩形ABCD的面积为 50 * 64 = 3200。所以，ABCED的总面积为 3200 - 625*√(3) = 3200 - 625*√(3)。答案：D"
}
] | 首先进行推理，然后从选项中选出正确的答案，按照这种格式：答案：xxx。
<image>
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"path": "depth0_zh/16/17_text.jpg"
} | 答案： | Chinese |
209 | depth0 | text_lite | multi_choice | [
{
"from": "human",
"value": "首先进行推理，然后从选项中选出正确的答案，按照这种格式：答案：xxx。\n<image>\n正方形ABCD内部有一个与之内切的圆。AB=11。你能告诉我内切圆的面积是多少吗？\n选项：\nA.121*√(6)*π/8\nB.121*π/10\nC.121*√(3)*π/12\nD.121*π/4"
},
{
"from": "gpt",
"value": "已知圆内接于正方形ABCD，因此其半径 AB/2 = 11/2，由此可得其面积为 (11/2)^2 * π = 121*π/4。答案：D"
}
] | 首先进行推理，然后从选项中选出正确的答案，按照这种格式：答案：xxx。
<image>
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"path": "depth0_zh/17/18_text.jpg"
} | 答案： | Chinese |
210 | depth0 | text_lite | multi_choice | [
{
"from": "human",
"value": "首先进行推理，然后从选项中选出正确的答案，按照这种格式：答案：xxx。\n<image>\nCD边向内部延伸成矩形内的半圆。AD=45。求ABCD的周长。\n选项：\nA.88*π/5 + 536/5\nB.22*π + 134\nC.44*π/3 + 268/3\nD.44*π + 268"
},
{
"from": "gpt",
"value": "CD为AB的对边，长度也为44。从C到D的半圆，以CD为直径，长度为 44 * π/2 = 22*π。因此，形状的总周长为 AB、AD、BC 和半圆 CD 的长度之和，即 44 + 45 + 45 + 22*π = 22*π + 134。答案：B"
}
] | 首先进行推理，然后从选项中选出正确的答案，按照这种格式：答案：xxx。
<image>
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"path": "depth0_zh/18/19_text.jpg"
} | 答案： | Chinese |
211 | depth0 | text_lite | multi_choice | [
{
"from": "human",
"value": "首先进行推理，然后从选项中选出正确的答案，按照这种格式：答案：xxx。\n<image>\n正方形ABCD包含一个内切圆。AB等于1。请问整个圆的面积是多少？\n选项：\nA.π/4\nB.√(3)*π/3\nC.π/2\nD.√(2)*π/24"
},
{
"from": "gpt",
"value": "圆内接于正方形ABCD，半径 AB/2 = 1/2，其面积为 (1/2)^2 * π = π/4。答案：A"
}
] | 首先进行推理，然后从选项中选出正确的答案，按照这种格式：答案：xxx。
<image>
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"path": "depth0_zh/19/20_text.jpg"
} | 答案： | Chinese |
212 | depth0 | text_lite | multi_choice | [
{
"from": "human",
"value": "首先进行推理，然后从选项中选出正确的答案，按照这种格式：答案：xxx。\n<image>\nAB等于60。在图形ABC中，CB的具体长度是多少？\n选项：\nA.24*√(3)\nB.60\nC.20*√(3)\nD.15"
},
{
"from": "gpt",
"value": "已知AB长度为60且角ACB = 60°，BC的长度为AB / tan(60°)，等于 60 / √(3)=20*√(3)。答案：C"
}
] | 首先进行推理，然后从选项中选出正确的答案，按照这种格式：答案：xxx。
<image>
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"path": "depth0_zh/2/3_text.jpg"
} | 答案： | Chinese |
213 | depth0 | text_lite | multi_choice | [
{
"from": "human",
"value": "首先进行推理，然后从选项中选出正确的答案，按照这种格式：答案：xxx。\n<image>\nABCD是平行四边形。AB=80。请计算ABCD的周长。\n选项：\nA.310\nB.75\nC.155*√(2)/3\nD.62*√(2)"
},
{
"from": "gpt",
"value": "已知ABCD为平行四边形，对边相等。所以其周长为 (AB + AD) * 2 = (80 + 75) * 2 = 310。答案：A"
}
] | 首先进行推理，然后从选项中选出正确的答案，按照这种格式：答案：xxx。
<image>
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"path": "depth0_zh/20/21_text.jpg"
} | 答案： | Chinese |
214 | depth0 | text_lite | multi_choice | [
{
"from": "human",
"value": "首先进行推理，然后从选项中选出正确的答案，按照这种格式：答案：xxx。\n<image>\nABCD是一个正方形。AB=12。在图形ABCD中，CB的长度是多少？\n选项：\nA.12\nB.12*√(3)/5\nC.144\nD.24*√(3)"
},
{
"from": "gpt",
"value": "AB的长度等于12。ABCD是一个正方形，因此其所有边的长度都相等。因此，CB = AB = 12。答案：A"
}
] | 首先进行推理，然后从选项中选出正确的答案，按照这种格式：答案：xxx。
<image>
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"path": "depth0_zh/21/22_text.jpg"
} | 答案： | Chinese |
215 | depth0 | text_lite | multi_choice | [
{
"from": "human",
"value": "首先进行推理，然后从选项中选出正确的答案，按照这种格式：答案：xxx。\n<image>\nABC构成一个扇形。角CBA=45°。你能计算扇形ABC中弧AC的长度吗？\n选项：\nA.11*√(3)*π/4\nB.33*π/10\nC.33*√(2)*π/2\nD.33*π/2"
},
{
"from": "gpt",
"value": "已知扇形的圆心角为45°，相当于π/4，半径AB等于66。由此推出，弧长 AC = 66 * π/4 = 33*π/2。答案：D"
}
] | 首先进行推理，然后从选项中选出正确的答案，按照这种格式：答案：xxx。
<image>
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"path": "depth0_zh/22/23_text.jpg"
} | 答案： | Chinese |
216 | depth0 | text_lite | multi_choice | [
{
"from": "human",
"value": "首先进行推理，然后从选项中选出正确的答案，按照这种格式：答案：xxx。\n<image>\nABC是一个等腰三角形，其中两条边AB和BC的长度相等。AB等于5。能否计算出ABC的周长是多少？\n选项：\nA.25 + 25*√(2)\nB.√(2) + 2\nC.5*√(2) + 10\nD.20*√(2)/3 + 40/3"
},
{
"from": "gpt",
"value": "ABC是一个顶角为90°的等腰三角形。因此，底边长度的一半为 AB * sin(90°/2) = 5 * (√(2)/2) = 5*√(2)/2，底边长度为 2 * (5*√(2)/2) = 5*√(2)。因此，周长为 AB * 2 + AC = 5 * 2 + 5*√(2) = 5*√(2) + 10。答案：C"
}
] | 首先进行推理，然后从选项中选出正确的答案，按照这种格式：答案：xxx。
<image>
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"path": "depth0_zh/23/24_text.jpg"
} | 答案： | Chinese |
217 | depth0 | text_lite | multi_choice | [
{
"from": "human",
"value": "首先进行推理，然后从选项中选出正确的答案，按照这种格式：答案：xxx。\n<image>\nABC是一个等腰三角形，其中AB = BC。角CBA等于120°。等腰三角形ABC中底边AC的长度是多少？\n选项：\nA.50*√(3)\nB.20*√(3)/3\nC.15\nD.10*√(3)"
},
{
"from": "gpt",
"value": "已知等腰三角形ABC的顶角为120°，所以底边的一半为 AB * sin(120°/2)，即 10 * (√(3)/2) = 5*√(3)，则底边全长为 2 * (5*√(3)) = 10*√(3)。答案：D"
}
] | 首先进行推理，然后从选项中选出正确的答案，按照这种格式：答案：xxx。
<image>
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"path": "depth0_zh/24/25_text.jpg"
} | 答案： | Chinese |
218 | depth0 | text_lite | multi_choice | [
{
"from": "human",
"value": "首先进行推理，然后从选项中选出正确的答案，按照这种格式：答案：xxx。\n<image>\n正方形ABCD内部有一个与之内切的圆。AB等于72。请计算圆的周长。\n选项：\nA.72*√(3)*π\nB.96*π\nC.72*π\nD.18*√(3)*π"
},
{
"from": "gpt",
"value": "圆内接于正方形 ABCD，其直径为 AB = 72，所以其周长为 72 * π，得到 72*π。答案：C"
}
] | 首先进行推理，然后从选项中选出正确的答案，按照这种格式：答案：xxx。
<image>
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"path": "depth0_zh/25/26_text.jpg"
} | 答案： | Chinese |
219 | depth0 | text_lite | multi_choice | [
{
"from": "human",
"value": "首先进行推理，然后从选项中选出正确的答案，按照这种格式：答案：xxx。\n<image>\n正方形ABCD内部有一个与之内切的圆。AB等于9。内切圆的周长有多长？\n选项：\nA.3*√(2)*π/2\nB.15*π\nC.9*π/2\nD.9*π"
},
{
"from": "gpt",
"value": "根据正方形ABCD内接的圆的直径 AB = 9，其周长为 9 * π，得 9*π。答案：D"
}
] | 首先进行推理，然后从选项中选出正确的答案，按照这种格式：答案：xxx。
<image>
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"path": "depth0_zh/26/27_text.jpg"
} | 答案： | Chinese |
220 | depth0 | text_lite | multi_choice | [
{
"from": "human",
"value": "首先进行推理，然后从选项中选出正确的答案，按照这种格式：答案：xxx。\n<image>\n边CD在矩形外形成一个半圆。AD等于17。ABCD的周长是多少？\n选项：\nA.17\nB.5*√(2)*(11*π + 90)/4\nC.√(2)*(11*π + 90)/2\nD.11*π/2 + 45"
},
{
"from": "gpt",
"value": "AB的对边是CD，因此CD长度为11。半圆从C到D，其直径是CD，长度为 11 * π/2 = 11*π/2。总周长包括 AB、AD、BC 和半圆 CD，总长度为 11 + 17 + 17 + 11*π/2 = 11*π/2 + 45。答案：D"
}
] | 首先进行推理，然后从选项中选出正确的答案，按照这种格式：答案：xxx。
<image>
| {
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"path": "depth0_zh/27/28_text.jpg"
} | 答案： | Chinese |
221 | depth0 | text_lite | multi_choice | [
{
"from": "human",
"value": "首先进行推理，然后从选项中选出正确的答案，按照这种格式：答案：xxx。\n<image>\nABC是一个等腰三角形，其中AB = BC。角CBA等于60°。在图形ABC中，CB的长度是多少？\n选项：\nA.88\nB.132*√(2)\nC.88*√(2)/5\nD.44*√(2)/3"
},
{
"from": "gpt",
"value": "已知AB的长度为88，ABC是等腰三角形，所以BC长度也是88。答案：A"
}
] | 首先进行推理，然后从选项中选出正确的答案，按照这种格式：答案：xxx。
<image>
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"path": "depth0_zh/28/29_text.jpg"
} | 答案： | Chinese |
222 | depth0 | text_lite | multi_choice | [
{
"from": "human",
"value": "首先进行推理，然后从选项中选出正确的答案，按照这种格式：答案：xxx。\n<image>\n边CD在矩形内延伸，形成等边三角形。AD等于9/2。求ABCED的周长。\n选项：\nA.21/4\nB.21\nC.63/2\nD.63/5"
},
{
"from": "gpt",
"value": "我们有矩形ABCD，CD是AB的对边，所以CD = 4。CDE是一个等边三角形，因此CE = ED = 4。因此，周长为 AB + AD + BC + ED + CE，即 4 + 9/2 + 9/2 + 4 + 4 = 21。答案：B"
}
] | 首先进行推理，然后从选项中选出正确的答案，按照这种格式：答案：xxx。
<image>
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"path": "depth0_zh/29/30_text.jpg"
} | 答案： | Chinese |
223 | depth0 | text_lite | multi_choice | [
{
"from": "human",
"value": "首先进行推理，然后从选项中选出正确的答案，按照这种格式：答案：xxx。\n<image>\n正方形ABCD包含一个内切圆。AB等于72。如何获得图形ABCD中DC的长度？\n选项：\nA.360\nB.72*π\nC.1296*π\nD.72"
},
{
"from": "gpt",
"value": "AB = 72。鉴于ABCD是一个正方形，故其所有边长相等。因此，DC = AB = 72。答案：D"
}
] | 首先进行推理，然后从选项中选出正确的答案，按照这种格式：答案：xxx。
<image>
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"path": "depth0_zh/3/4_text.jpg"
} | 答案： | Chinese |
224 | depth0 | text_lite | multi_choice | [
{
"from": "human",
"value": "首先进行推理，然后从选项中选出正确的答案，按照这种格式：答案：xxx。\n<image>\n边CD向内延伸为矩形内的等边三角形。AB=1。如何得出图形ABCED的面积？\n选项：\nA.3*√(3)/4\nB.9*√(3)/16\nC.√(3)/4\nD.3/4"
},
{
"from": "gpt",
"value": "根据已知条件，CD是AB的对边，所以 CD = AB = 1。由于CDE是等边三角形，故三角形的高为 CD * √(3)/2 = √(3)/2。该三角形CDE的面积为 CD * 高度/2 = √(3)/4。矩形ABCD的面积为 1 * √(3) = √(3)。因此，ABCED的总面积为 √(3) - √(3)/4 = 3*√(3)/4。答案：A"
}
] | 首先进行推理，然后从选项中选出正确的答案，按照这种格式：答案：xxx。
<image>
| {
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"path": "depth0_zh/30/31_text.jpg"
} | 答案： | Chinese |
225 | depth0 | text_lite | open_ended | [
{
"from": "human",
"value": "首先进行推理，然后给出正确的答案，按照这种格式：答案：xxx。\n<image>\n正方形ABCD有一个内切圆。AB等于7。在图形ABCD中，DC的长度是多少？"
},
{
"from": "gpt",
"value": "AB长度为7。鉴于ABCD是正方形，得出其所有边长相等。因此，DC = AB = 7。答案：7"
}
] | 首先进行推理，然后给出正确的答案，按照这种格式：答案：xxx。
<image>
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"path": "depth0_zh/31/32_text.jpg"
} | 答案： | Chinese |
226 | depth0 | text_lite | open_ended | [
{
"from": "human",
"value": "首先进行推理，然后给出正确的答案，按照这种格式：答案：xxx。\n<image>\n正方形ABCD包含一个内切圆。AB=1。求图形ABCD中DC的长度。"
},
{
"from": "gpt",
"value": "AB等于1。ABCD是一个正方形，因此其所有边的长度都相等。因此，DC = AB = 1。答案：1"
}
] | 首先进行推理，然后给出正确的答案，按照这种格式：答案：xxx。
<image>
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"path": "depth0_zh/32/33_text.jpg"
} | 答案： | Chinese |
227 | depth0 | text_lite | open_ended | [
{
"from": "human",
"value": "首先进行推理，然后给出正确的答案，按照这种格式：答案：xxx。\n<image>\n圆弧CD是一个半圆。AD等于6。请计算图形ABCD中弧CD的长度。"
},
{
"from": "gpt",
"value": "CD是AB的对边，因此其长度也是11。从C到D的半圆以CD为直径，它的长度为 11 * π/2 = 11*π/2。答案：11*π/2"
}
] | 首先进行推理，然后给出正确的答案，按照这种格式：答案：xxx。
<image>
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"path": "depth0_zh/33/34_text.jpg"
} | 答案： | Chinese |
228 | depth0 | text_lite | open_ended | [
{
"from": "human",
"value": "首先进行推理，然后给出正确的答案，按照这种格式：答案：xxx。\n<image>\nCD边在矩形内构成了一个向内的半圆。AB=3。整个图形ABCD的面积是多少？"
},
{
"from": "gpt",
"value": "矩形ABCD的面积为 AB * AD = 3 * 4*√(2) = 12*√(2)。以CD为直径的半圆面积为 (AB /2)^2 * π /2 = 9*π/8。总面积为 12*√(2) - 9*π/8 = -9*π/8 + 12*√(2)。答案：-9*π/8 + 12*√(2)"
}
] | 首先进行推理，然后给出正确的答案，按照这种格式：答案：xxx。
<image>
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"path": "depth0_zh/34/35_text.jpg"
} | 答案： | Chinese |
229 | depth0 | text_lite | open_ended | [
{
"from": "human",
"value": "首先进行推理，然后给出正确的答案，按照这种格式：答案：xxx。\n<image>\n边CD向外延伸，构成了矩形外的等边三角形。AB=40。图形ABCED的面积是多少？"
},
{
"from": "gpt",
"value": "考虑到CD是AB的对边，所以 CD = AB = 40。而CDE是等边三角形，三角形的高为 CD * √(3)/2 = 20*√(3)。该三角形CDE的面积为 CD * 高度/2 = 400*√(3)。矩形ABCD的面积为 40 * 44 = 1760。所以，ABCED的总面积为 400*√(3) + 1760 = 400*√(3) + 1760。答案：400*√(3) + 1760"
}
] | 首先进行推理，然后给出正确的答案，按照这种格式：答案：xxx。
<image>
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"path": "depth0_zh/35/36_text.jpg"
} | 答案： | Chinese |
230 | depth0 | text_lite | open_ended | [
{
"from": "human",
"value": "首先进行推理，然后给出正确的答案，按照这种格式：答案：xxx。\n<image>\nCD边向内部延伸成矩形内的半圆。AD=12。如何求图形ABCD的面积？"
},
{
"from": "gpt",
"value": "矩形ABCD的面积可以表示为AB乘以AD，即 6 * 12 = 72。以CD为直径的半圆面积为 (AB /2)^2 * π /2 = 9*π/2。总面积为 72 - 9*π/2 = 72 - 9*π/2。答案：72 - 9*π/2"
}
] | 首先进行推理，然后给出正确的答案，按照这种格式：答案：xxx。
<image>
| {
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"path": "depth0_zh/36/37_text.jpg"
} | 答案： | Chinese |
231 | depth0 | text_lite | open_ended | [
{
"from": "human",
"value": "首先进行推理，然后给出正确的答案，按照这种格式：答案：xxx。\n<image>\nCD边在矩形内构成了一个向内的半圆。AB=36。ABCD的周长是多少？"
},
{
"from": "gpt",
"value": "根据AB是CD的对边，得CD长度为36。从C到D的半圆，以CD为直径，长度为 36 * π/2 = 18*π。因此，形状的总周长是 AB + AD + BC 和半圆 CD 的长度之和，即 36 + 32 + 32 + 18*π = 18*π + 100。答案：18*π + 100"
}
] | 首先进行推理，然后给出正确的答案，按照这种格式：答案：xxx。
<image>
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"path": "depth0_zh/37/38_text.jpg"
} | 答案： | Chinese |
232 | depth0 | text_lite | open_ended | [
{
"from": "human",
"value": "首先进行推理，然后给出正确的答案，按照这种格式：答案：xxx。\n<image>\nABCD是一个正方形。AB等于4。计算图形ABCD中CB的长度。"
},
{
"from": "gpt",
"value": "AB = 4。因为ABCD是一个正方形且所有边都相等，所以 CB = AB = 4。答案：4"
}
] | 首先进行推理，然后给出正确的答案，按照这种格式：答案：xxx。
<image>
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"path": "depth0_zh/38/39_text.jpg"
} | 答案： | Chinese |
233 | depth0 | text_lite | open_ended | [
{
"from": "human",
"value": "首先进行推理，然后给出正确的答案，按照这种格式：答案：xxx。\n<image>\nABCD是一个正方形。AB等于91。请问ABCD的周长是多少？"
},
{
"from": "gpt",
"value": "根据已知，ABCD是正方形，推出周长为 AB * 4 = 91 * 4 = 364。答案：364"
}
] | 首先进行推理，然后给出正确的答案，按照这种格式：答案：xxx。
<image>
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"path": "depth0_zh/39/40_text.jpg"
} | 答案： | Chinese |
234 | depth0 | text_lite | open_ended | [
{
"from": "human",
"value": "首先进行推理，然后给出正确的答案，按照这种格式：答案：xxx。\n<image>\n角ACB等于30°。图形ABC中，CB的长度有多长？"
},
{
"from": "gpt",
"value": "由于AB的长度是49时，在C处的角为30°，所以相邻边 BC为AB / tan(30°)，即 49 / (√(3)/3)=49*√(3)。答案：49*√(3)"
}
] | 首先进行推理，然后给出正确的答案，按照这种格式：答案：xxx。
<image>
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"path": "depth0_zh/4/5_text.jpg"
} | 答案： | Chinese |
235 | depth0 | text_lite | open_ended | [
{
"from": "human",
"value": "首先进行推理，然后给出正确的答案，按照这种格式：答案：xxx。\n<image>\nABCD是平行四边形。AB等于84。你能告诉我图形ABCD中DC的长度吗？"
},
{
"from": "gpt",
"value": "给定AB是84。因为ABCD是平行四边形，对边必然相等，所以DC也是84。答案：84"
}
] | 首先进行推理，然后给出正确的答案，按照这种格式：答案：xxx。
<image>
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"path": "depth0_zh/40/41_text.jpg"
} | 答案： | Chinese |
236 | depth0 | text_lite | open_ended | [
{
"from": "human",
"value": "首先进行推理，然后给出正确的答案，按照这种格式：答案：xxx。\n<image>\n圆弧CD是一个半圆。AB=3。请问图形ABCD的面积是多少？"
},
{
"from": "gpt",
"value": "可得，矩形ABCD的面积是AB乘以AD，即 3 * √(3) = 3*√(3)。半圆以CD为直径，其面积为 (AB /2)^2 * π /2 = 9*π/8。由此，总面积为 3*√(3) - 9*π/8 = -9*π/8 + 3*√(3)。答案：-9*π/8 + 3*√(3)"
}
] | 首先进行推理，然后给出正确的答案，按照这种格式：答案：xxx。
<image>
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"path": "depth0_zh/41/42_text.jpg"
} | 答案： | Chinese |
237 | depth0 | text_lite | open_ended | [
{
"from": "human",
"value": "首先进行推理，然后给出正确的答案，按照这种格式：答案：xxx。\n<image>\nAB等于3。在图形ABC中，CB的具体长度是多少？"
},
{
"from": "gpt",
"value": "鉴于AB的长度为3且角ACB = 45°，则BC的长度为AB / tan(45°)，也就是 3 / 1=3。答案：3"
}
] | 首先进行推理，然后给出正确的答案，按照这种格式：答案：xxx。
<image>
| {
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"path": "depth0_zh/42/43_text.jpg"
} | 答案： | Chinese |
238 | depth0 | text_lite | open_ended | [
{
"from": "human",
"value": "首先进行推理，然后给出正确的答案，按照这种格式：答案：xxx。\n<image>\n角ACB=45°。请问ABC的周长是多少？"
},
{
"from": "gpt",
"value": "因为AB = 1且角 ACB = 45°，BC = AB / tan(45°) = 1 / 1 = 1。斜边 AC = AB / sin(45°) = 1 / (√(2)/2) = √(2)，故周长为 AB +BC + AC = √(2) + 2。答案：√(2) + 2"
}
] | 首先进行推理，然后给出正确的答案，按照这种格式：答案：xxx。
<image>
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"path": "depth0_zh/43/44_text.jpg"
} | 答案： | Chinese |
239 | depth0 | text_lite | open_ended | [
{
"from": "human",
"value": "首先进行推理，然后给出正确的答案，按照这种格式：答案：xxx。\n<image>\n角ACB=45°。你知道图形ABC中，CB的长度吗？"
},
{
"from": "gpt",
"value": "由于AB的长度是6时，在C处的角度为45°，BC的长度是AB / tan(45°)，即 6 / 1=6。答案：6"
}
] | 首先进行推理，然后给出正确的答案，按照这种格式：答案：xxx。
<image>
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"path": "depth0_zh/44/45_text.jpg"
} | 答案： | Chinese |
240 | depth0 | text_lite | open_ended | [
{
"from": "human",
"value": "首先进行推理，然后给出正确的答案，按照这种格式：答案：xxx。\n<image>\nCDE是等边三角形。AD等于1。你知道ABCED的周长是多少吗？"
},
{
"from": "gpt",
"value": "ABCD是一个矩形，CD为AB的对边，因此CD等于1。CDE是一个等边三角形，所以CE等于ED，长度均为1。周长为 AB + AD + BC + ED + CE，即 1 + 1 + 1 + 1 + 1 = 5。答案：5"
}
] | 首先进行推理，然后给出正确的答案，按照这种格式：答案：xxx。
<image>
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"path": "depth0_zh/45/46_text.jpg"
} | 答案： | Chinese |
241 | depth0 | text_lite | open_ended | [
{
"from": "human",
"value": "首先进行推理，然后给出正确的答案，按照这种格式：答案：xxx。\n<image>\n正方形ABCD包含一个内切圆。AB=3。内切圆的面积是多少？"
},
{
"from": "gpt",
"value": "由于圆内接于正方形ABCD，故其直径为 AB = 3，从而其面积为 (3/2)^2 * π = 9*π/4。答案：9*π/4"
}
] | 首先进行推理，然后给出正确的答案，按照这种格式：答案：xxx。
<image>
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"path": "depth0_zh/46/47_text.jpg"
} | 答案： | Chinese |
242 | depth0 | text_lite | open_ended | [
{
"from": "human",
"value": "首先进行推理，然后给出正确的答案，按照这种格式：答案：xxx。\n<image>\n边CD向外延伸，构成了矩形外的等边三角形。AB=1。请问整个图形ABCED的面积是多少？"
},
{
"from": "gpt",
"value": "鉴于CD是AB的对边，意味 CD = AB = 1。又知CDE是等边三角形，其高为 CD * √(3)/2 = √(3)/2。三角形CDE的面积为 CD * 高度/2 = √(3)/4。矩形ABCD的面积为 1 * 2 = 2。由此，总面积为 √(3)/4 + 2 = √(3)/4 + 2。答案：√(3)/4 + 2"
}
] | 首先进行推理，然后给出正确的答案，按照这种格式：答案：xxx。
<image>
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"path": "depth0_zh/47/48_text.jpg"
} | 答案： | Chinese |
243 | depth0 | text_lite | open_ended | [
{
"from": "human",
"value": "首先进行推理，然后给出正确的答案，按照这种格式：答案：xxx。\n<image>\n正方形ABCD内部有一个与之内切的圆。AB等于13。请问内切圆的周长有多长？"
},
{
"from": "gpt",
"value": "内接于正方形ABCD的圆直径 AB = 13，计算出周长为 13 * π，得 13*π。答案：13*π"
}
] | 首先进行推理，然后给出正确的答案，按照这种格式：答案：xxx。
<image>
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"path": "depth0_zh/48/49_text.jpg"
} | 答案： | Chinese |
244 | depth0 | text_lite | open_ended | [
{
"from": "human",
"value": "首先进行推理，然后给出正确的答案，按照这种格式：答案：xxx。\n<image>\nABCD是一个正方形。AB=3。如何获得图形ABCD的周长？"
},
{
"from": "gpt",
"value": "由于ABCD是正方形，因此ABCD的周长为 AB * 4 = 3 * 4 = 12。答案：12"
}
] | 首先进行推理，然后给出正确的答案，按照这种格式：答案：xxx。
<image>
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"path": "depth0_zh/49/50_text.jpg"
} | 答案： | Chinese |
245 | depth0 | text_lite | open_ended | [
{
"from": "human",
"value": "首先进行推理，然后给出正确的答案，按照这种格式：答案：xxx。\n<image>\nCB等于39/2。你能计算出整个图形ABCD的面积吗？"
},
{
"from": "gpt",
"value": "通过计算可得，矩形ABCD的面积等于AB与CB的乘积，即 13 * 39/2 = 507/2。答案：507/2"
}
] | 首先进行推理，然后给出正确的答案，按照这种格式：答案：xxx。
<image>
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"path": "depth0_zh/5/6_text.jpg"
} | 答案： | Chinese |
246 | depth0 | text_lite | open_ended | [
{
"from": "human",
"value": "首先进行推理，然后给出正确的答案，按照这种格式：答案：xxx。\n<image>\nABC是一个扇形。AB=12。你知道ABC的周长是多少吗？"
},
{
"from": "gpt",
"value": "由扇形的圆心角120°和半径AB = 12 可得，弧长 AC = 12 * 2*π/3 = 8*π，故周长为 12 * 2 + 8*π = 24 + 8*π。答案：24 + 8*π"
}
] | 首先进行推理，然后给出正确的答案，按照这种格式：答案：xxx。
<image>
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"path": "depth0_zh/50/51_text.jpg"
} | 答案： | Chinese |
247 | depth0 | text_lite | open_ended | [
{
"from": "human",
"value": "首先进行推理，然后给出正确的答案，按照这种格式：答案：xxx。\n<image>\n边CD在矩形内延伸成等边三角形。AD等于1。如何获得图形ABCED的周长？"
},
{
"from": "gpt",
"value": "ABCD是一个矩形，CD是AB的对边，因此CD = 1。CDE是一个等边三角形，因此CE = ED = 1。因此，周长为 AB + AD + BC + ED + CE = 1 + 1 + 1 + 1 + 1 = 5。答案：5"
}
] | 首先进行推理，然后给出正确的答案，按照这种格式：答案：xxx。
<image>
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"path": "depth0_zh/51/52_text.jpg"
} | 答案： | Chinese |
248 | depth0 | text_lite | open_ended | [
{
"from": "human",
"value": "首先进行推理，然后给出正确的答案，按照这种格式：答案：xxx。\n<image>\n正方形ABCD内部有一个与之内切的圆。AB=81。如何获得图形ABCD中AD的长度？"
},
{
"from": "gpt",
"value": "AB = 81。因为ABCD是正方形，显然其所有边长相等。因此，AD = AB = 81。答案：81"
}
] | 首先进行推理，然后给出正确的答案，按照这种格式：答案：xxx。
<image>
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"path": "depth0_zh/52/53_text.jpg"
} | 答案： | Chinese |
249 | depth0 | text_lite | open_ended | [
{
"from": "human",
"value": "首先进行推理，然后给出正确的答案，按照这种格式：答案：xxx。\n<image>\n圆弧CD构成一个半圆。AB=11。你知道图形ABCD的总面积吗？"
},
{
"from": "gpt",
"value": "通过计算，矩形ABCD的面积为AB乘以AD，即 11 * 11 = 121。以CD为直径的半圆，其面积为 (AB /2)^2 * π /2 = 121*π/8。所以，总面积为 121 + 121*π/8，结果是 121*π/8 + 121。答案：121*π/8 + 121"
}
] | 首先进行推理，然后给出正确的答案，按照这种格式：答案：xxx。
<image>
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"path": "depth0_zh/53/54_text.jpg"
} | 答案： | Chinese |
250 | depth1 | text_lite | multi_choice | [
{
"from": "human",
"value": "首先进行推理，然后从选项中选出正确的答案，按照这种格式：答案：xxx。\n<image>\nABC是一个等腰三角形，其中两条边AB和BC的长度相等。边DE向内延展成矩形内的等边三角形。CE=7/2。请计算CBDFE的周长。\n选项：\nA.3/2\nB.9*√(3)/4\nC.16\nD.80/3"
},
{
"from": "gpt",
"value": "AB长为3，由于ABC是等腰三角形，故BC的长度也是3。矩形CBDE中的DE是CB的对边，因此DE等于3。由于 DEF是一个等边三角形，故DF和FE均等于3。因此，周长为 CB + CE + BD + FE + DF，即 3 + 7/2 + 7/2 + 3 + 3 = 16。答案：C"
}
] | 首先进行推理，然后从选项中选出正确的答案，按照这种格式：答案：xxx。
<image>
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"path": "depth1_zh/0/1_text.jpg"
} | 答案： | Chinese |
251 | depth1 | text_lite | multi_choice | [
{
"from": "human",
"value": "首先进行推理，然后从选项中选出正确的答案，按照这种格式：答案：xxx。\n<image>\nABC是一个等腰三角形，其中两条边AB和BC的长度相等。DB等于9/2。请计算图形CBDE的面积。\n选项：\nA.4*√(3)\nB.108/5\nC.108\nD.18"
},
{
"from": "gpt",
"value": "AB长为4，ABC是等腰三角形，因此可以推出BC长度也是4。矩形CBDE的面积根据公式为 CB * DB，即 4 * 9/2，得出 18。答案：D"
}
] | 首先进行推理，然后从选项中选出正确的答案，按照这种格式：答案：xxx。
<image>
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"path": "depth1_zh/1/2_text.jpg"
} | 答案： | Chinese |
252 | depth1 | text_lite | multi_choice | [
{
"from": "human",
"value": "首先进行推理，然后从选项中选出正确的答案，按照这种格式：答案：xxx。\n<image>\nABCD是平行四边形。AB=2。请问图形DCE中，DE的长度是多少？\n选项：\nA.4*√(3)/3\nB.8*√(3)/15\nC.16*√(3)/3\nD.8/3"
},
{
"from": "gpt",
"value": "因为AB是2，并且ABCD是平行四边形，所以DC作为对边，也是2。由于在E处的角度为60°，DE的长度是DC / sin(60°)，即 2 / (√(3)/2) = 4*√(3)/3。答案：A"
}
] | 首先进行推理，然后从选项中选出正确的答案，按照这种格式：答案：xxx。
<image>
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"path": "depth1_zh/10/11_text.jpg"
} | 答案： | Chinese |
253 | depth1 | text_lite | multi_choice | [
{
"from": "human",
"value": "首先进行推理，然后从选项中选出正确的答案，按照这种格式：答案：xxx。\n<image>\n正方形DCEF包含一个内切圆。AB=1。请问圆的面积是多少？\n选项：\nA.π/2\nB.√(2)*π/2\nC.π/4\nD.√(3)*π/24"
},
{
"from": "gpt",
"value": "考虑到AB为1并且ABCD是矩形，所以对边相等。因此，DC也是1。根据条件，圆内接于正方形DCEF，因此其半径 DC/2 = 1/2，可见其面积为 (1/2)^2 * π = π/4。答案：C"
}
] | 首先进行推理，然后从选项中选出正确的答案，按照这种格式：答案：xxx。
<image>
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"path": "depth1_zh/11/12_text.jpg"
} | 答案： | Chinese |
254 | depth1 | text_lite | multi_choice | [
{
"from": "human",
"value": "首先进行推理，然后从选项中选出正确的答案，按照这种格式：答案：xxx。\n<image>\nABCD是一个正方形。EFG是等边三角形。AB等于1。图形ADEGF的面积是多少？\n选项：\nA.√(2)*(√(3) + 4)/20\nB.√(3)/4 + 1\nC.√(3)/8 + 1/2\nD.3*√(3)/16 + 3/4"
},
{
"from": "gpt",
"value": "AB = 1。鉴于ABCD是一个正方形，故其所有边长相等。因此，AD = AB = 1。考虑到EF是AD的对边，所以 EF = AD = 1。而EFG是等边三角形，三角形的高为 EF * √(3)/2 = √(3)/2。该三角形EFG的面积为 EF * 高度/2 = √(3)/4。矩形ADEF的面积为 1 * 1 = 1。所以，ADEGF的总面积为 √(3)/4 + 1 = √(3)/4 + 1。答案：B"
}
] | 首先进行推理，然后从选项中选出正确的答案，按照这种格式：答案：xxx。
<image>
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"path": "depth1_zh/12/13_text.jpg"
} | 答案： | Chinese |
255 | depth1 | text_lite | multi_choice | [
{
"from": "human",
"value": "首先进行推理，然后从选项中选出正确的答案，按照这种格式：答案：xxx。\n<image>\nABCD是一个正方形。CBE是一个等腰三角形，其中CB = BE。AB=1。等腰三角形CBE中，角BCE和角CEB分别是多少度？\n选项：\nA.30\nB.45\nC.60\nD.180"
},
{
"from": "gpt",
"value": "AB的长度是1。根据ABCD为正方形，得所有边相等。所以，CB = AB = 1。对于等腰三角形CBE，顶角B的角度是 60°，因此其底角BCE和CEB分别为 (180° - 60°) / 2 = 60°。答案：C"
}
] | 首先进行推理，然后从选项中选出正确的答案，按照这种格式：答案：xxx。
<image>
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"path": "depth1_zh/13/14_text.jpg"
} | 答案： | Chinese |
256 | depth1 | text_lite | multi_choice | [
{
"from": "human",
"value": "首先进行推理，然后从选项中选出正确的答案，按照这种格式：答案：xxx。\n<image>\nAB等于48。请问DCE的周长是多少？\n选项：\nA.67\nB.48*√(2) + 48*√(6)\nC.48*√(3) + 144\nD.48 + 48*√(3)"
},
{
"from": "gpt",
"value": "显然，由于AB是48并且ABCD是矩形，因此对边相等。所以，DC也是48。因为角 DEC = 60°，CE = DC / tan(60°) = 48 / √(3) = 16*√(3)。斜边 DE = DC / sin(60°) = 48 / (√(3)/2) = 32*√(3)，故周长为 DC +CE + DE = 48 + 48*√(3)。答案：D"
}
] | 首先进行推理，然后从选项中选出正确的答案，按照这种格式：答案：xxx。
<image>
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"path": "depth1_zh/14/15_text.jpg"
} | 答案： | Chinese |
257 | depth1 | text_lite | multi_choice | [
{
"from": "human",
"value": "首先进行推理，然后从选项中选出正确的答案，按照这种格式：答案：xxx。\n<image>\nABC是一个等腰三角形，其中两条边AB和BC的长度相等。CBDE是平行四边形。角CBD等于30°，DB=4。你能计算出整个图形CBDE的面积吗？\n选项：\nA.9*√(3)/4\nB.6\nC.24/5\nD.18*√(2)"
},
{
"from": "gpt",
"value": "AB长为3，由于ABC是等腰三角形，故BC的长度也是3。平行四边形CBDE的角CBD为30°，则面积为 CB * DB * sin(30°) = 3 * 4 * 1/2 = 6。答案：B"
}
] | 首先进行推理，然后从选项中选出正确的答案，按照这种格式：答案：xxx。
<image>
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"path": "depth1_zh/15/16_text.jpg"
} | 答案： | Chinese |
258 | depth1 | text_lite | multi_choice | [
{
"from": "human",
"value": "首先进行推理，然后从选项中选出正确的答案，按照这种格式：答案：xxx。\n<image>\nABCD是一个正方形。DCEF是一个正方形。AB等于66。你知道图形DCEF中，EC的长度吗？\n选项：\nA.11*√(2)\nB.66\nC.11\nD.132/5"
},
{
"from": "gpt",
"value": "AB的长度是66。由于ABCD是一个正方形并且所有四个边都相等，因此 DC = AB = 66。由于DCEF为正方形，因此其所有边长相同。所以，EC = DC = 66。答案：B"
}
] | 首先进行推理，然后从选项中选出正确的答案，按照这种格式：答案：xxx。
<image>
| {
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"path": "depth1_zh/16/17_text.jpg"
} | 答案： | Chinese |
259 | depth1 | text_lite | multi_choice | [
{
"from": "human",
"value": "首先进行推理，然后从选项中选出正确的答案，按照这种格式：答案：xxx。\n<image>\nDCE是一个等腰三角形，其中两条边DC和CE的长度相等。角ECD=60°。你能告诉我图形DCE中EC的长度吗？\n选项：\nA.1\nB.4/5\nC.5*√(3)/3\nD.5/6"
},
{
"from": "gpt",
"value": "已知AB的长度为1，并且ABCD是矩形，可知相对的边相等。所以，DC也是1。DCE是等腰三角形，因此CE长度也是1。答案：A"
}
] | 首先进行推理，然后从选项中选出正确的答案，按照这种格式：答案：xxx。
<image>
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"path": "depth1_zh/17/18_text.jpg"
} | 答案： | Chinese |
260 | depth1 | text_lite | multi_choice | [
{
"from": "human",
"value": "首先进行推理，然后从选项中选出正确的答案，按照这种格式：答案：xxx。\n<image>\n由边CD外延，得到矩形外的等边三角形。通过延长边FG，得矩形外的等边三角形。EG=85。请计算图形ECFHG的面积。\n选项：\nA.17787*√(3)/20 + 3927\nB.5775\nC.5929*√(3)/16 + 6545/4\nD.5929*√(3)/4 + 6545"
},
{
"from": "gpt",
"value": "因为AB为77，矩形对边相等，使得CD也为77。已知CDE是等边三角形，故EC = CD = 77。FG是EC的对边，故 FG = EC = 77。FGH是等边三角形，因此三角形的高为 FG * √(3)/2 = 77*√(3)/2。三角形FGH的面积为 FG * 高度/2 = 5929*√(3)/4。矩形ECFG的面积为 77 * 85 = 6545。因此，ECFHG的总面积为 5929*√(3)/4 + 6545 = 5929*√(3)/4 + 6545。答案：D"
}
] | 首先进行推理，然后从选项中选出正确的答案，按照这种格式：答案：xxx。
<image>
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"path": "depth1_zh/18/19_text.jpg"
} | 答案： | Chinese |
261 | depth1 | text_lite | multi_choice | [
{
"from": "human",
"value": "首先进行推理，然后从选项中选出正确的答案，按照这种格式：答案：xxx。\n<image>\n圆弧EF是一个半圆。DF=8。你能计算出整个图形DCEF的面积吗？\n选项：\nA.88 - 121*π/8\nB.121*π/8\nC.8\nD.352/3 - 121*π/6"
},
{
"from": "gpt",
"value": "显然，由于AB是11并且ABCD是矩形，因此对边相等。所以，DC也是11。可得，矩形DCEF的面积是DC乘以DF，即 11 * 8 = 88。半圆以EF为直径，其面积为 (DC /2)^2 * π /2 = 121*π/8。由此，总面积为 88 - 121*π/8 = 88 - 121*π/8。答案：A"
}
] | 首先进行推理，然后从选项中选出正确的答案，按照这种格式：答案：xxx。
<image>
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"path": "depth1_zh/19/20_text.jpg"
} | 答案： | Chinese |
262 | depth1 | text_lite | multi_choice | [
{
"from": "human",
"value": "首先进行推理，然后从选项中选出正确的答案，按照这种格式：答案：xxx。\n<image>\nEFG是等边三角形。AB等于13。你知道如何计算DCEGF的周长吗？\n选项：\nA.65*√(3)\nB.65\nC.130*√(2)\nD.325*√(2)/2"
},
{
"from": "gpt",
"value": "已知AB的长度为13，并且ABCD是矩形，可知相对的边相等。所以，DC也是13。DCEF为一个矩形，其中EF为DC的对边，故EF = 13。EFG是一个等边三角形，所以EG等于GF，其长度均为13。因此，周长为 DC + DF + CE + GF + EG = 13 + 13 + 13 + 13 + 13 = 65。答案：B"
}
] | 首先进行推理，然后从选项中选出正确的答案，按照这种格式：答案：xxx。
<image>
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"path": "depth1_zh/2/3_text.jpg"
} | 答案： | Chinese |
263 | depth1 | text_lite | multi_choice | [
{
"from": "human",
"value": "首先进行推理，然后从选项中选出正确的答案，按照这种格式：答案：xxx。\n<image>\nABCD是平行四边形。正方形DCEF内部有一个与之内切的圆。AB等于7。你知道圆的面积是多少吗？\n选项：\nA.49*π/10\nB.245*π/12\nC.245*π/16\nD.49*π/4"
},
{
"from": "gpt",
"value": "由于AB长度为7，并且ABCD是平行四边形，因此DC作为对边，也是7。圆内接于正方形DCEF，因此其直径为 DC = 7，所以其面积为 (7/2)^2 * π = 49*π/4。答案：D"
}
] | 首先进行推理，然后从选项中选出正确的答案，按照这种格式：答案：xxx。
<image>
| {
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"path": "depth1_zh/20/21_text.jpg"
} | 答案： | Chinese |
264 | depth1 | text_lite | multi_choice | [
{
"from": "human",
"value": "首先进行推理，然后从选项中选出正确的答案，按照这种格式：答案：xxx。\n<image>\nEFG是等边三角形。DF等于82。图形DCEGF中，GE的长度有多长？\n选项：\nA.104\nB.156*√(2)\nC.52\nD.4940"
},
{
"from": "gpt",
"value": "由于AB是52并且ABCD是矩形，因此相对边的长度相同。故，DC也是52。矩形对边相等，使得EF也为52。已知EFG是等边三角形，故GE = EF = 52。答案：C"
}
] | 首先进行推理，然后从选项中选出正确的答案，按照这种格式：答案：xxx。
<image>
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"path": "depth1_zh/21/22_text.jpg"
} | 答案： | Chinese |
265 | depth1 | text_lite | multi_choice | [
{
"from": "human",
"value": "首先进行推理，然后从选项中选出正确的答案，按照这种格式：答案：xxx。\n<image>\nDCE呈扇形。AB等于7。扇形DCE的弧DE长度是多少？\n选项：\nA.35*π/4\nB.7*π/2\nC.21*π/5\nD.7*π/3"
},
{
"from": "gpt",
"value": "显然，由于AB为7，并且ABCD是矩形，所以对边相等。因此，DC也是7。已知扇形的圆心角为90°，即π/2，半径DC为7。由此可知，弧长DE等于7 * π/2 = 7*π/2。答案：B"
}
] | 首先进行推理，然后从选项中选出正确的答案，按照这种格式：答案：xxx。
<image>
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"path": "depth1_zh/22/23_text.jpg"
} | 答案： | Chinese |
266 | depth1 | text_lite | multi_choice | [
{
"from": "human",
"value": "首先进行推理，然后从选项中选出正确的答案，按照这种格式：答案：xxx。\n<image>\nABC呈扇形。DB等于91。图形CBDE的周长有多长？\n选项：\nA.181\nB.362\nC.1448/3\nD.543"
},
{
"from": "gpt",
"value": "AB = 90。由于扇形半径恒定，所以BC也是90。通过公式 (CB + DB) * 2 ，CBDE的周长为 (90 + 91) * 2 = 362。答案：B"
}
] | 首先进行推理，然后从选项中选出正确的答案，按照这种格式：答案：xxx。
<image>
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"path": "depth1_zh/23/24_text.jpg"
} | 答案： | Chinese |
267 | depth1 | text_lite | multi_choice | [
{
"from": "human",
"value": "首先进行推理，然后从选项中选出正确的答案，按照这种格式：答案：xxx。\n<image>\nABC是一个等腰三角形，其中两条边AB和BC的长度相等。DE边向内部延伸成矩形内的半圆。AB等于11。你能计算出整个图形CBDE的面积吗？\n选项：\nA.√(2)*(198 - 121*π/8)\nB.198 - 121*π/8\nC.297 - 363*π/16\nD.792 - 121*π/2"
},
{
"from": "gpt",
"value": "AB的长度是11，ABC是等腰三角形，因此BC长也为11。可知矩形CBDE的面积为CB乘以CE，即 11 * 18 = 198。以DE为直径的半圆，其面积计算为 (CB /2)^2 * π /2 = 121*π/8。组合面积为 198 - 121*π/8 = 198 - 121*π/8。答案：B"
}
] | 首先进行推理，然后从选项中选出正确的答案，按照这种格式：答案：xxx。
<image>
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"path": "depth1_zh/24/25_text.jpg"
} | 答案： | Chinese |
268 | depth1 | text_lite | multi_choice | [
{
"from": "human",
"value": "首先进行推理，然后从选项中选出正确的答案，按照这种格式：答案：xxx。\n<image>\nABC是一个扇形。CBD是一个等腰三角形，其中CB = BD。AB=1。你能告诉我图形CBD中DB的长度吗？\n选项：\nA.1\nB.1/2\nC.√(2)/6\nD.√(6)/2"
},
{
"from": "gpt",
"value": "AB = 1。由于扇形的半径保持恒定，因此BC = 1。由于CBD是等腰三角形，故BD的长度也是1。答案：A"
}
] | 首先进行推理，然后从选项中选出正确的答案，按照这种格式：答案：xxx。
<image>
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"path": "depth1_zh/25/26_text.jpg"
} | 答案： | Chinese |
269 | depth1 | text_lite | multi_choice | [
{
"from": "human",
"value": "首先进行推理，然后从选项中选出正确的答案，按照这种格式：答案：xxx。\n<image>\nABCD构成一个正方形。DCEF是一个正方形。AB等于9。你能告诉我图形DCEF的面积是多少吗？\n选项：\nA.135\nB.81*√(3)/2\nC.81\nD.27*√(3)/2"
},
{
"from": "gpt",
"value": "AB的长度是9。由ABCD是正方形并且四边相等可知，DC = AB = 9。正方形DCEF的面积等于边长 9 的平方，计算得 81。答案：C"
}
] | 首先进行推理，然后从选项中选出正确的答案，按照这种格式：答案：xxx。
<image>
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"path": "depth1_zh/26/27_text.jpg"
} | 答案： | Chinese |
270 | depth1 | text_lite | multi_choice | [
{
"from": "human",
"value": "首先进行推理，然后从选项中选出正确的答案，按照这种格式：答案：xxx。\n<image>\n由边CD外延，得到矩形外的等边三角形。角EFC等于30°。能否计算出ECF的周长是多少？\n选项：\nA.12 + 12*√(3)\nB.8*√(3) + 24\nC.2*√(3) + 6\nD.2"
},
{
"from": "gpt",
"value": "因为AB是2，矩形的对边相等，因此CD也是2。鉴于CDE是等边三角形，EC = CD = 2。由角 EFC = 30°，CF可以计算为 EC / tan(30°) = 2 / (√(3)/3) = 2*√(3)。斜边 EF = EC / sin(30°) = 2 / (1/2) = 4，故此周长为 EC +CF + EF = 2*√(3) + 6。答案：C"
}
] | 首先进行推理，然后从选项中选出正确的答案，按照这种格式：答案：xxx。
<image>
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"path": "depth1_zh/27/28_text.jpg"
} | 答案： | Chinese |
271 | depth1 | text_lite | multi_choice | [
{
"from": "human",
"value": "首先进行推理，然后从选项中选出正确的答案，按照这种格式：答案：xxx。\n<image>\nABC是一个等腰三角形，其中两条边AB和BC的长度相等。CBDE是平行四边形。角CBD=30°，DB等于7*√(2)。请问CBDE的周长是多少？\n选项：\nA.16 + 56*√(2)/3\nB.12 + 14*√(2)\nC.12*√(2)/5 + 28/5\nD.2 + 7*√(2)/3"
},
{
"from": "gpt",
"value": "因为AB长为6，ABC是等腰三角形，所以BC的长度也是6。鉴于CBDE是平行四边形，所以对边相等。因此，其周长为 (CB + DB) * 2 = (6 + 7*√(2)) * 2 = 12 + 14*√(2)。答案：B"
}
] | 首先进行推理，然后从选项中选出正确的答案，按照这种格式：答案：xxx。
<image>
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"path": "depth1_zh/28/29_text.jpg"
} | 答案： | Chinese |
272 | depth1 | text_lite | multi_choice | [
{
"from": "human",
"value": "首先进行推理，然后从选项中选出正确的答案，按照这种格式：答案：xxx。\n<image>\nABC是一个扇形。AB=7。在图形CBD中，CD的具体长度是多少？\n选项：\nA.7*√(6)\nB.35*√(2)/2\nC.28*√(2)/5\nD.7*√(2)"
},
{
"from": "gpt",
"value": "AB = 7。因为扇形半径是恒定的，BC也是7。给定角CDB为45°，那么CD的长度为CB / sin(45°)，也就是 7 / (√(2)/2) = 7*√(2)。答案：D"
}
] | 首先进行推理，然后从选项中选出正确的答案，按照这种格式：答案：xxx。
<image>
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"path": "depth1_zh/29/30_text.jpg"
} | 答案： | Chinese |
273 | depth1 | text_lite | multi_choice | [
{
"from": "human",
"value": "首先进行推理，然后从选项中选出正确的答案，按照这种格式：答案：xxx。\n<image>\nACDE构成一个正方形。AB等于1。请问图形ACDE中，AE的长度是多少？\n选项：\nA.4*√(3)/3\nB.2*√(6)/3\nC.2\nD.2*√(3)/3"
},
{
"from": "gpt",
"value": "由于AB的长度是1时，在C处的角为60°，所以AC为AB / sin(60°)，即 1 / (√(3)/2) = 2*√(3)/3。由ACDE是正方形并且四边相等可知，AE = AC = 2*√(3)/3。答案：D"
}
] | 首先进行推理，然后从选项中选出正确的答案，按照这种格式：答案：xxx。
<image>
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"path": "depth1_zh/3/4_text.jpg"
} | 答案： | Chinese |
274 | depth1 | text_lite | multi_choice | [
{
"from": "human",
"value": "首先进行推理，然后从选项中选出正确的答案，按照这种格式：答案：xxx。\n<image>\nABCD构成一个正方形。正方形CBEF包含一个内切圆。AB等于2。请计算内切圆的面积。\n选项：\nA.π\nB.√(2)*π/2\nC.π/4\nD.5*π/6"
},
{
"from": "gpt",
"value": "AB长度为2。鉴于ABCD是正方形，得出其所有边长相等。因此，CB = AB = 2。根据条件，圆内接于正方形CBEF，因此其半径 CB/2 = 1，可见其面积为 (2/2)^2 * π = π。答案：A"
}
] | 首先进行推理，然后从选项中选出正确的答案，按照这种格式：答案：xxx。
<image>
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"path": "depth1_zh/30/31_text.jpg"
} | 答案： | Chinese |
275 | depth1 | text_lite | open_ended | [
{
"from": "human",
"value": "首先进行推理，然后给出正确的答案，按照这种格式：答案：xxx。\n<image>\nABCD是一个正方形。EF边在矩形内构成了一个向内的半圆。DF=11。你能告诉我图形DCEF的面积是多少吗？"
},
{
"from": "gpt",
"value": "AB = 6。鉴于ABCD是一个正方形，故其所有边长相等。因此，DC = AB = 6。已知矩形DCEF的面积是DC乘以DF，即 6 * 11 = 66。以EF为直径的半圆面积为 (DC /2)^2 * π /2 = 9*π/2。由此可知，总面积为 66 - 9*π/2 = 66 - 9*π/2。答案：66 - 9*π/2"
}
] | 首先进行推理，然后给出正确的答案，按照这种格式：答案：xxx。
<image>
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"path": "depth1_zh/31/32_text.jpg"
} | 答案： | Chinese |
276 | depth1 | text_lite | open_ended | [
{
"from": "human",
"value": "首先进行推理，然后给出正确的答案，按照这种格式：答案：xxx。\n<image>\n圆弧EF是一个半圆。AB=55。你知道图形DCEF的总面积吗？"
},
{
"from": "gpt",
"value": "由于AB是55，并且ABCD是矩形，所以对边相等。因此，DC也是55。由公式得知，矩形DCEF的面积为 DC * DF = 55 * 33*√(3) = 1815*√(3)。以EF为直径的半圆，其面积为 (DC /2)^2 * π /2 = 3025*π/8。因此，总面积为 1815*√(3) + 3025*π/8，结果为 3025*π/8 + 1815*√(3)。答案：3025*π/8 + 1815*√(3)"
}
] | 首先进行推理，然后给出正确的答案，按照这种格式：答案：xxx。
<image>
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"path": "depth1_zh/32/33_text.jpg"
} | 答案： | Chinese |
277 | depth1 | text_lite | open_ended | [
{
"from": "human",
"value": "首先进行推理，然后给出正确的答案，按照这种格式：答案：xxx。\n<image>\nABCD是一个正方形。DCEF是平行四边形。AB=90。在图形DCEF中，FE的具体长度是多少？"
},
{
"from": "gpt",
"value": "AB等于90。由于ABCD为正方形，因此其所有边长相同。所以，DC = AB = 90。因为DCEF是平行四边形，故对边相等。因此，FE也是90。答案：90"
}
] | 首先进行推理，然后给出正确的答案，按照这种格式：答案：xxx。
<image>
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"path": "depth1_zh/33/34_text.jpg"
} | 答案： | Chinese |
278 | depth1 | text_lite | open_ended | [
{
"from": "human",
"value": "首先进行推理，然后给出正确的答案，按照这种格式：答案：xxx。\n<image>\n正方形DCEF含有一个内切圆。AB等于13。请问内切圆的面积是多少？"
},
{
"from": "gpt",
"value": "考虑到AB为13，并且ABCD是矩形，因此对边相等。所以，DC也是13。显然，圆内接于正方形DCEF，其直径为 DC = 13，因此其面积为 (13/2)^2 * π = 169*π/4。答案：169*π/4"
}
] | 首先进行推理，然后给出正确的答案，按照这种格式：答案：xxx。
<image>
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"path": "depth1_zh/34/35_text.jpg"
} | 答案： | Chinese |
279 | depth1 | text_lite | open_ended | [
{
"from": "human",
"value": "首先进行推理，然后给出正确的答案，按照这种格式：答案：xxx。\n<image>\nEFG构成一个等边三角形。AB等于11。请问图形DCEGF的周长有多长？"
},
{
"from": "gpt",
"value": "因为AB是11并且ABCD是矩形，因此对边相等。所以，DC也是11。给定一个矩形DCEF，其对边EF与DC相等，因此EF = 11。EFG是等边三角形，所以EG和GF的长度均为11。于是，周长为 DC + DF + CE + GF + EG，即 11 + 17 + 17 + 11 + 11 = 67。答案：67"
}
] | 首先进行推理，然后给出正确的答案，按照这种格式：答案：xxx。
<image>
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"path": "depth1_zh/35/36_text.jpg"
} | 答案： | Chinese |
280 | depth1 | text_lite | open_ended | [
{
"from": "human",
"value": "首先进行推理，然后给出正确的答案，按照这种格式：答案：xxx。\n<image>\nABC呈扇形。边DE向外延展成一个半圆。AB=2。在图形CBDE中，DE的长度是多少？"
},
{
"from": "gpt",
"value": "AB = 2。由于扇形的半径保持恒定，因此BC = 2。DE作为CB的对边，其长度为2。从D到E的半圆以DE为直径，长度是 2 * π/2 = π。答案：π"
}
] | 首先进行推理，然后给出正确的答案，按照这种格式：答案：xxx。
<image>
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"path": "depth1_zh/36/37_text.jpg"
} | 答案： | Chinese |
281 | depth1 | text_lite | open_ended | [
{
"from": "human",
"value": "首先进行推理，然后给出正确的答案，按照这种格式：答案：xxx。\n<image>\nACD呈扇形。角ACB等于30°，AB=4。你能告诉我图形ACD中DC的长度吗？"
},
{
"from": "gpt",
"value": "由于AB的长度是4时，在C处的角度为30°，AC的长度是AB / sin(30°)，即 4 / (1/2) = 8。因为扇形的半径是恒定的，因此CD = 8。答案：8"
}
] | 首先进行推理，然后给出正确的答案，按照这种格式：答案：xxx。
<image>
| {
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"path": "depth1_zh/37/38_text.jpg"
} | 答案： | Chinese |
282 | depth1 | text_lite | open_ended | [
{
"from": "human",
"value": "首先进行推理，然后给出正确的答案，按照这种格式：答案：xxx。\n<image>\nACD是一个扇形。角DCA=45°，角ACB=30°。请问ACD的周长是多少？"
},
{
"from": "gpt",
"value": "由于AB的长度是13时，在C处的角为30°，所以AC为AB / sin(30°)，即 13 / (1/2) = 26。已知扇形的圆心角为45°，半径AC是26，计算得弧长AD为 26 * π/4 = 13*π/2，因此周长为 26 * 2 + 13*π/2 = 13*π/2 + 52。答案：13*π/2 + 52"
}
] | 首先进行推理，然后给出正确的答案，按照这种格式：答案：xxx。
<image>
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"path": "depth1_zh/38/39_text.jpg"
} | 答案： | Chinese |
283 | depth1 | text_lite | open_ended | [
{
"from": "human",
"value": "首先进行推理，然后给出正确的答案，按照这种格式：答案：xxx。\n<image>\nABC是一个等腰三角形，其中两条边AB和BC的长度相等。圆弧DE构成一个半圆。CE等于5*√(3)。图形CBDE中，DE的弧长是多少？"
},
{
"from": "gpt",
"value": "AB等于10，已知ABC是等腰三角形，可以得出BC长度也是10。因为DE是CB的对边，它的长度也是10。半圆从D到E，以DE为直径，长度可得 10 * π/2 = 5*π。答案：5*π"
}
] | 首先进行推理，然后给出正确的答案，按照这种格式：答案：xxx。
<image>
| {
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"path": "depth1_zh/39/40_text.jpg"
} | 答案： | Chinese |
284 | depth1 | text_lite | open_ended | [
{
"from": "human",
"value": "首先进行推理，然后给出正确的答案，按照这种格式：答案：xxx。\n<image>\nABC呈扇形。边DE向内延伸为矩形内的等边三角形。CE等于25。求CBDFE的周长。"
},
{
"from": "gpt",
"value": "AB的长度是20。因为扇形的半径恒定，所以BC也是20。我们有矩形CBDE，DE是CB的对边，所以DE = 20。DEF是一个等边三角形，因此DF = FE = 20。因此，周长为 CB + CE + BD + FE + DF，即 20 + 25 + 25 + 20 + 20 = 110。答案：110"
}
] | 首先进行推理，然后给出正确的答案，按照这种格式：答案：xxx。
<image>
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"path": "depth1_zh/4/5_text.jpg"
} | 答案： | Chinese |
285 | depth1 | text_lite | open_ended | [
{
"from": "human",
"value": "首先进行推理，然后给出正确的答案，按照这种格式：答案：xxx。\n<image>\nABC构成一个扇形。CBD呈扇形。角DBC=120°。如何求CBD的周长？"
},
{
"from": "gpt",
"value": "AB = 12。由于扇形的半径是恒定的，BC = 12。扇形的圆心角为120°，半径CB为12。已知弧长CD为 12 * 2*π/3 = 8*π，所以周长为 12 * 2 + 8*π = 24 + 8*π。答案：24 + 8*π"
}
] | 首先进行推理，然后给出正确的答案，按照这种格式：答案：xxx。
<image>
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"path": "depth1_zh/40/41_text.jpg"
} | 答案： | Chinese |
286 | depth1 | text_lite | open_ended | [
{
"from": "human",
"value": "首先进行推理，然后给出正确的答案，按照这种格式：答案：xxx。\n<image>\nEC=√(2)。求出图形DCEF的面积。"
},
{
"from": "gpt",
"value": "显然，由于AB为1，并且ABCD是矩形，所以对边相等。因此，DC也是1。显然，矩形DCEF的面积可以由DC和EC的乘积计算得到：1 * √(2) = √(2)。答案：√(2)"
}
] | 首先进行推理，然后给出正确的答案，按照这种格式：答案：xxx。
<image>
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"path": "depth1_zh/41/42_text.jpg"
} | 答案： | Chinese |
287 | depth1 | text_lite | open_ended | [
{
"from": "human",
"value": "首先进行推理，然后给出正确的答案，按照这种格式：答案：xxx。\n<image>\n边EF在矩形内展开，成为等边三角形。AB=26。你能告诉我图形DCEGF的面积是多少吗？"
},
{
"from": "gpt",
"value": "考虑到AB = 26。矩形ABCD具有相等的对边。因此，DC也是26。已知EF是DC的对边，故 EF = DC = 26。由于EFG是等边三角形，三角形的高为 EF * √(3)/2 = 13*√(3)。向内三角形EFG的面积为 EF * 高度/2 = 169*√(3)。矩形DCEF的面积为 26 * 52 = 1352。由此可见，DCEGF的总面积为 1352 - 169*√(3) = 1352 - 169*√(3)。答案：1352 - 169*√(3)"
}
] | 首先进行推理，然后给出正确的答案，按照这种格式：答案：xxx。
<image>
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"path": "depth1_zh/42/43_text.jpg"
} | 答案： | Chinese |
288 | depth1 | text_lite | open_ended | [
{
"from": "human",
"value": "首先进行推理，然后给出正确的答案，按照这种格式：答案：xxx。\n<image>\nABC是一个等腰三角形，其中两条边AB和BC的长度相等。弧DE是180度弧。AB=24。你知道图形CBDE的面积是多少吗？"
},
{
"from": "gpt",
"value": "由于AB长度是24，ABC是等腰三角形，故BC的长度也为24。矩形CBDE的面积是CB乘以CE的结果，即 24 * 20*√(3) = 480*√(3)。半圆以DE为直径，其面积为 (CB /2)^2 * π /2 = 72*π。由此可知，总面积计算为 480*√(3) - 72*π = -72*π + 480*√(3)。答案：-72*π + 480*√(3)"
}
] | 首先进行推理，然后给出正确的答案，按照这种格式：答案：xxx。
<image>
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"path": "depth1_zh/43/44_text.jpg"
} | 答案： | Chinese |
289 | depth1 | text_lite | open_ended | [
{
"from": "human",
"value": "首先进行推理，然后给出正确的答案，按照这种格式：答案：xxx。\n<image>\nABC构成一个扇形。圆弧DE构成一个半圆。CE等于36。请问整个图形CBDE的面积是多少？"
},
{
"from": "gpt",
"value": "AB = 24。因为扇形的半径是恒定的，因此BC = 24。通过已知条件，矩形CBDE的面积是CB乘以CE，即 24 * 36 = 864。半圆以DE为直径，其面积计算公式为 (CB /2)^2 * π /2，得 72*π。因此，总面积为 864 + 72*π，即 72*π + 864。答案：72*π + 864"
}
] | 首先进行推理，然后给出正确的答案，按照这种格式：答案：xxx。
<image>
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"path": "depth1_zh/44/45_text.jpg"
} | 答案： | Chinese |
290 | depth1 | text_lite | open_ended | [
{
"from": "human",
"value": "首先进行推理，然后给出正确的答案，按照这种格式：答案：xxx。\n<image>\n角CDB等于60°，角ACB等于45°。图形CBD中，CD的长度有多长？"
},
{
"from": "gpt",
"value": "由于AB的长度是10时，在C处的角度为45°，BC的长度是AB / tan(45°)，即 10 / 1=10。鉴于角CDB = 60°，则CD的长度为CB / sin(60°)，也就是 10 / (√(3)/2) = 20*√(3)/3。答案：20*√(3)/3"
}
] | 首先进行推理，然后给出正确的答案，按照这种格式：答案：xxx。
<image>
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"path": "depth1_zh/45/46_text.jpg"
} | 答案： | Chinese |
291 | depth1 | text_lite | open_ended | [
{
"from": "human",
"value": "首先进行推理，然后给出正确的答案，按照这种格式：答案：xxx。\n<image>\nABCD是平行四边形。正方形DCEF内部有一个与之内切的圆。AB=4。整个内切圆的面积是多少？"
},
{
"from": "gpt",
"value": "因为AB是4，并且ABCD是平行四边形，所以DC作为对边，也是4。根据条件，圆内接于正方形DCEF，因此其半径 DC/2 = 2，可见其面积为 (4/2)^2 * π = 4*π。答案：4*π"
}
] | 首先进行推理，然后给出正确的答案，按照这种格式：答案：xxx。
<image>
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"path": "depth1_zh/46/47_text.jpg"
} | 答案： | Chinese |
292 | depth1 | text_lite | open_ended | [
{
"from": "human",
"value": "首先进行推理，然后给出正确的答案，按照这种格式：答案：xxx。\n<image>\nABCD是平行四边形。DCEF是平行四边形。AB=78。图形DCEF的周长是多少呢？"
},
{
"from": "gpt",
"value": "根据AB是78，并且ABCD是平行四边形，故可得DC也是78。由DCEF是平行四边形可知，对边相等。因此，DCEF的周长为 (DC + DF) * 2 = (78 + 58) * 2 = 272。答案：272"
}
] | 首先进行推理，然后给出正确的答案，按照这种格式：答案：xxx。
<image>
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"path": "depth1_zh/47/48_text.jpg"
} | 答案： | Chinese |
293 | depth1 | text_lite | open_ended | [
{
"from": "human",
"value": "首先进行推理，然后给出正确的答案，按照这种格式：答案：xxx。\n<image>\n由边EF外延，得到矩形外的等边三角形。DF=25。你知道DCEGF的周长是多少吗？"
},
{
"from": "gpt",
"value": "显然，由于AB为30，并且ABCD是矩形，所以对边相等。因此，DC也是30。DCEF是一个矩形，EF是DC的对边，因此EF = 30。EFG是一个等边三角形，因此EG = GF = 30。因此，周长为 DC + DF + CE + GF + EG = 30 + 25 + 25 + 30 + 30 = 140。答案：140"
}
] | 首先进行推理，然后给出正确的答案，按照这种格式：答案：xxx。
<image>
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"path": "depth1_zh/48/49_text.jpg"
} | 答案： | Chinese |
294 | depth1 | text_lite | open_ended | [
{
"from": "human",
"value": "首先进行推理，然后给出正确的答案，按照这种格式：答案：xxx。\n<image>\nDCEF构成一个正方形。AB等于3。图形DCEF中，FE的长度有多长？"
},
{
"from": "gpt",
"value": "已知AB的长度为3，并且ABCD是矩形，所以对边相等。因此，DC也是3。DCEF是一个正方形，因此其所有边的长度都相等。因此，FE = DC = 3。答案：3"
}
] | 首先进行推理，然后给出正确的答案，按照这种格式：答案：xxx。
<image>
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"path": "depth1_zh/49/50_text.jpg"
} | 答案： | Chinese |
295 | depth1 | text_lite | open_ended | [
{
"from": "human",
"value": "首先进行推理，然后给出正确的答案，按照这种格式：答案：xxx。\n<image>\nABCD是平行四边形。AB=39。如何求DCE的周长？"
},
{
"from": "gpt",
"value": "根据AB是39，并且ABCD是平行四边形，故可得DC也是39。已知角 DEC 为 60°，因此CE的长度为 DC / tan(60°) = 39 / √(3) = 13*√(3)。斜边 DE 等于 DC / sin(60°) = 39 / (√(3)/2) = 26*√(3)，因此周长为 DC +CE + DE = 39 + 39*√(3)。答案：39 + 39*√(3)"
}
] | 首先进行推理，然后给出正确的答案，按照这种格式：答案：xxx。
<image>
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"path": "depth1_zh/5/6_text.jpg"
} | 答案： | Chinese |
296 | depth1 | text_lite | open_ended | [
{
"from": "human",
"value": "首先进行推理，然后给出正确的答案，按照这种格式：答案：xxx。\n<image>\nDCEF构成一个正方形。AB=8。计算图形DCEF的面积是多少？"
},
{
"from": "gpt",
"value": "已知AB的长度为8，并且ABCD是矩形，所以对边相等。因此，DC也是8。正方形DCEF的面积等于边长 8 的平方，计算得 64。答案：64"
}
] | 首先进行推理，然后给出正确的答案，按照这种格式：答案：xxx。
<image>
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"path": "depth1_zh/50/51_text.jpg"
} | 答案： | Chinese |
297 | depth1 | text_lite | open_ended | [
{
"from": "human",
"value": "首先进行推理，然后给出正确的答案，按照这种格式：答案：xxx。\n<image>\nCDE构成一个等边三角形。ECFG是平行四边形。角ECF等于60°，EG等于74。在图形ECFG中，GF的具体长度是多少？"
},
{
"from": "gpt",
"value": "由于AB = 99，矩形的对边相等，所以CD也为99。根据CDE是等边三角形，因此EC = CD = 99。因为ECFG是平行四边形，故对边相等。因此，GF也是99。答案：99"
}
] | 首先进行推理，然后给出正确的答案，按照这种格式：答案：xxx。
<image>
| {
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"path": "depth1_zh/51/52_text.jpg"
} | 答案： | Chinese |
298 | depth1 | text_lite | open_ended | [
{
"from": "human",
"value": "首先进行推理，然后给出正确的答案，按照这种格式：答案：xxx。\n<image>\n边CD向外延伸，构成了矩形外的等边三角形。ECF是一个等腰三角形，其中两条边EC和CF的长度相等。角FCE=45°。你能告诉我等腰三角形ECF中，角CEF和角EFC的角度是多少吗？"
},
{
"from": "gpt",
"value": "因为AB是32，矩形的对边相等，因此CD也是32。鉴于CDE是等边三角形，EC = CD = 32。已知ECF为等腰三角形，顶角C的角度为45°，则底角CEF和EFC为 (180° - 45°) / 2 = 67.5°。答案：67.5"
}
] | 首先进行推理，然后给出正确的答案，按照这种格式：答案：xxx。
<image>
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"path": "depth1_zh/52/53_text.jpg"
} | 答案： | Chinese |
299 | depth1 | text_lite | open_ended | [
{
"from": "human",
"value": "首先进行推理，然后给出正确的答案，按照这种格式：答案：xxx。\n<image>\n圆弧DE是一个半圆。AB等于2，AE等于√(6)。你知道图形ACDE的总面积吗？"
},
{
"from": "gpt",
"value": "由于AB的长度为2且在C处的角度为60°，AC为AB / sin(60°) = 2 / (√(3)/2) = 4*√(3)/3。由公式得知，矩形ACDE的面积为 AC * AE = 4*√(3)/3 * √(6) = 4*√(2)。以DE为直径的半圆，其面积为 (AC /2)^2 * π /2 = 2*π/3。总面积为 4*√(2) - 2*π/3 = -2*π/3 + 4*√(2)。答案：-2*π/3 + 4*√(2)"
}
] | 首先进行推理，然后给出正确的答案，按照这种格式：答案：xxx。
<image>
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"path": "depth1_zh/53/54_text.jpg"
} | 答案： | Chinese |
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