Question

半圆o的直径AB=12,半径OC垂直AB,圆O’与半圆O相内切,与OB,OC相切与点D,E.求圆O’的半径?

Answer 1

圆O’与半圆O相内切于E,过E作O'的切线ME,连接O'E,则O'E⊥ME;

圆O’与半圆O相内切于E,连接OE,过E作O的切线亦是ME,所以OE⊥ME;

因此O,O'均在过E点与切线ME垂直的直线上,即O,O',E三点共线;

OC⊥AB,O'D⊥AB,O'F⊥OC,O'F=O'D=O'E,所以FODO'为正方形,O'O=O'D√2,

OO'+O'E=OE=(1/2)AB,

O'D√2+O'D=12/2,

O'D(√2+1)=6,

圆O’的半径O'D=6/(√2+1)=6(√2-1)