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战巡
Posted 2024-8-12 15:01
大圆周长$100$，可知直径$\frac{100}{\pi}$，故此
\[BC=\frac{100}{\pi}\sin(60\du)=\frac{50\sqrt{3}}{\pi}\]
令小圆半径$r$，连$A$与小圆圆心$I$，可知其平分$\angle BAC$，即$\angle BAI=30\du$，于是
\[r=(7+r)\sin(30\du)\]
\[r=7\]
$A$到小圆的两个切点距离均为$7\sqrt{3}$，而总周长为$2\cdot 7\sqrt{3}+2BC=14\sqrt{3}+\frac{100\sqrt{3}}{\pi}=79.3816$ |
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