Question

G

求解拜託

3.)如圖,兩圓外切,外公切線與兩圓所圍成的區域有一內切圓,若大圓半徑
4公分,小圓半徑1公分,則此內切小圓的半徑爲幾公分?

Answer 1

Mer

橘色線段=√[(4+r)^2 - (4-r)^2]
也等於4-√[(1+r)^2-(1-r)^2]

兩邊平方
(4+r)^2 - (4-r)^2
= 16 - 8√[(1+r)^2-(1-r)^2] + (1+r)^2-(1-r)^2

化簡後r=4/9