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Balkan MO 2014 shortlist-G1

Source: Balkan MO 2014 shortlist-G1

June 10, 2015
geometry

Problem Statement

Let ABCABC be an isosceles triangle, in which AB=ACAB=AC , and let MM and NN be two points on the sides BCBC and ACAC, respectively such that ∠BAM=∠MNC\angle BAM = \angle MNC. Suppose that the lines MNMN and ABAB intersects at PP. Prove that the bisectors of the angles ∠BAM\angle BAM and ∠BPM\angle BPM intersects at a point lying on the line BCBC
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