Question

已知圆O的半径为根号3,圆O2的半径为2-根号3,圆O3的半径为1,且圆O1分别与圆O2,圆O3外切

Answer 1

O2O3²=(√3+1)²+(√3+2-√3)²-4(√3+1)cos60°

=(√3+1)²+4-2(√3+1)

=(√3+1)(√3-1)+4

=3-1+4=6

所以 O2O3=√6

用正弦定理：

(√3+2-√3)/sin∠O1O3O2=√6/sin60°

sin∠O1O3O2=√2/2

可解得 ∠O1O3O=45°