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- 答案:1/4
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- 简单回答:易知,当A、B、C三点都在同一个半圆内时,三角形ABC必是直角或钝角三角形;只有当三点不在同一个半圆内,才可以组成锐角三角形。于是问题等价于“在圆周上任取三个不同的点,求它们不在同一半圆内的概率”,故其概率为 ` 1/2 * 1/2 = 1/4 ` (先固定点 A,B 和 C 分别与之在同一个半圆内的概率为 1/2)
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> [ 在一圆周上任意取三个点构成锐角三角形的概率是多少?] ( https://www.zybang.com/question/7ad30f46d6eebb125b6421479d24bdc3.html ) - 作业帮
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- 使用积分计算该概率
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- [ ![ ] ( ../_assets/公式_20180624211704.png )] ( http://www.codecogs.com/eqnedit.php?latex=\int_{0}^{\pi}\frac{\theta&space;}{2\pi}\cdot&space;\frac{1}{\pi}=\frac{\theta^2}{4\pi^2}\Big|^\pi_0=\frac{1}{4} )
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+ [ ![ ] ( ../_assets/公式_20180624211704.png )] ( http://www.codecogs.com/eqnedit.php?latex=\int_{0}^{\pi}\frac{\theta}{2\pi}\cdot\frac{1}{\pi}{d}{\theta}=\frac{\theta^2}{4\pi^2}\Big|^\pi_0=\frac{1}{4} )
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> [ 在一圆周上任意取三个点构成锐角三角形的概率是多少] ( https://zhidao.baidu.com/question/1884315387170029428.html ) - 百度知道
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> [ 【官方双语】如何优雅地解答最难数学竞赛的压轴题? 1:50-4:25, 5:40-7:50] ( https://www.bilibili.com/video/av17275211 ) - bilibili
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