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Nice geometry problem

Source: IZHO2015.P2

January 13, 2015
geometrysymmetrytrigonometrygeometry proposed

Problem Statement

Inside the triangle ABC ABC a point M M is given. The line BM BM meets the side AC AC at N N . The point K K is symmetrical to M M with respect to AC AC . The line BK BK meets AC AC at P P . If ∠AMP=∠CMN \angle AMP = \angle CMN , prove that ∠ABP=∠CBN \angle ABP=\angle CBN .
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