HMMT 二月 2008 · TEAM2 赛 · 第 10 题

英文解析

10. [ 15 ] Let a, b, c denote the side lengths of BC, CA, AB . Find the lengths of AE, BF, CD interms of a, b, c .
    Solution: Let x = AE = AF , y = BD = BF , z = CD = CE . Since BC = BD + CD , wehave a = x + y . Similarly with the other sides, we arrive at the following system of equations:
    a = y + z, b = x + z, c = x + y.
    Solving this system gives usb + c − a
    AE = x = ,
    a + c − b 2
    BF = y = ,
    a + b − c 2
    CD = z = . 2