Let ABC be a triangle with \A < 60度. Let X and Y be the points on the sides AB and AC, respectively, such that CA+AX = CB +BX and BA+AY = BC +CY . Let P be the point in the plane such that the lines PX and PY are perpendicular to AB and AC, respectively. Prove that \BPC < 120度.

我在lab上ptt還有msn被教授抓包。老闆看我可憐的份上給我20分鐘算...但我花了1個小時。。有人有興趣挑戰嗎?
10小時後公佈解答。