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python/数学课程/【内切圆】外国中考题.md

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已知： 长方形，长为4 , 宽为3。

解法：

  • 因为圆A、圆B的两条红线都是圆B的切线，根据切线的性质，所以红线相等，同理绿线相等。
  • 设圆的半径为r,则绿色的为3-r,红色的为4-r
  • 根据勾股定理，得矩形对角线长度=5
  • 同时，知道5=红线+绿线=7-2r -> r=1

\therefore AB=\sqrt{1^2+2^2}=\sqrt{5}