Re: [中學] 國中數學
: 麻煩了，拜託！
連 AD, BD, 由畢氏定理有
AC^2 + CD^2 = AD^2
CD^2 + BC^2 = BD^2
AD^2 + BD^2 = AB^2 (←注意到弧 ADB 是半圓弧, 故角 ADB 為直角)
三式相加消去 AD^2, BD^2 得
AC^2 + 2CD^2 + BC^2 = AB^2
2CD^2 = AB^2 - AC^2 - BC^2
兩邊同乘π/4, 左邊是 (π CD^2)/2 為 CD 半徑圓面積的一半
右邊是 π(AB/2)^2 - π(AC/2)^2 - π(BC/2)^2 為斜線面積的兩倍
所以比例為 1:4
--
'You've sort of made up for it tonight,' said Harry. 'Getting the
sword. Finishing the Horcrux. Saving my life.'
'That makes me sound a lot cooler then I was,' Ron mumbled.
'Stuff like that always sounds cooler then it really was,' said
Harry. 'I've been trying to tell you that for years.'
-- Harry Potter and the Deathly Hollows, P.308
--
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