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Angle bisectors and concurrency!

Source: Romania TST 2014 Day 3 Problem 1

January 21, 2015
geometrysimilar trianglesgeometry unsolved

Problem Statement

Let ABCABC be an isosceles triangle, AB=ACAB = AC, and let MM and NN be points on the sides BCBC and CACA, respectively, such that ∠BAM=∠CNM\angle BAM=\angle CNM. The lines ABAB and MNMN meet at PP. Show that the internal angle bisectors of the angles BAMBAM and BPMBPM meet at a point on the line BCBC.
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