Question

一道关于圆的几何题

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Answer 1

1. k+d=（D-d）*√3/2

   D=d+（k+d）*2√3/3

2. 利用余弦定理：a²=b²+c²-2bccosA

   （d+d‘)²=(D-d)²+(D-d’)²-(D-d)(D-d’)cos60°

   （d+d‘)²-(D-d’)²+(D-d)(D-d’）/2=（D-d）²

   2（d+D)(d-D+2d’)+(D-d)(D-d’）=2（D-d）²

   2（d+D)(d-D)+2(d+D)*2d’+(D-d)D-(D-d)d’=2（D-d）²

   4d’(d+D)-(D-d)d’=2（D-d）²-2（d+D)(d-D)-(D-d)D

   d’(5d+3D)=3D(D-d)

   d’=3D(D-d)/(5d+3D)

3. d0=(d+k)*2√3/3-d

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