Simone
设巧让AB=c BC=a AC=b由角平分线性质定理有：BE/AE=a/b CD/AD=a/c∴BE/AB=a/(a+b) CD/AC=a/(a+c)∴BE=ac/(a+b) CD=ab/(a+c)又由角平分线性质定理有：AI/CI=BE/BC=c/(a+b) DI/BI=CD/BC=b/(a+c)∴S△BIE/S=AI/CI=c/(a+b) S△CID/S=DI/孝亮局BI=b/(a+c) S△DIE/S△BID=DI/BI=b/(a+c) ∴S△DIE/S=bc/[(a+b)(a+c)]∴S四BCDE=S△BIE+S△CID+S△DIE+S =S{c/(a+b)+b/(a+c)+bc/[(a+b)(a+c)]+1} =S{(ac+c^2+ab+b^2+bc)/[(a+b)(a+c)]+1} =S[(ac+a^2+ab+bc)/(ac+a^2+ab+bc)+1] (∵键敬∠A=90° ∴a^2=b^2+c^2) =2S注：角平分线性质定理可参考http://baike.baidu.com/view/1504084.htm
