1楼一叶轻舟
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发表于 2008-7-21 09:43
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设 AB = a, BC = b, AC = c ( c^2 = a^2 + b^2 )
由于O是△ABC的内心, 容易推出 EO = (a+c-b)/2, OF = (b+c-a)/2
∴S矩形EOFD = (a+c-b)/2 * (b+c-a)/2 = [c^2 - (a-b)^2] /4 = [a^2 + b^2 - (a-b)^2 ] = ab/2 = S矩形ABCD/2.
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