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※ 引述《maybe85912 (英雄不流淚)》之銘言:
: http://i.imgur.com/C3TlsOZ.jpg
: 題目如圖
: 灰色面積就是藍色那兩顆(抱歉有點醜)
: 麻煩大家了(>_<)
X Y兩圓切點(0, 0)
圓X圓心(-30, 0)
圓Y圓心(70, 0)
圓Z圓心(40, 0)
左上藍圓(-r, h)
(r + 30)^2 - (30 - r)^2 + (-40 - r)^2 = (100 - r)^2
=> 60 * 2r + 1600 + 80r = -200r + 10000
=> r = 21
右上藍圓(R, H)
(R + 70)^2 - (R - 70)^2 + (R - 40)^2 = (100 - R)^2
=> 2R * 140 - 80R + 1600 = 10000 - 200R
=> R = 21
所以兩藍圓面積 = (21^2 + 21^2) * π
= 882π
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