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Romania TST 2021 Day 3 P1

Source:

June 14, 2021
geometryconstantromaniaRomanian TSTTST

Problem Statement

Consider a fixed triangle ABCABC such that AB=AC.AB=AC. Let MM be the midpoint of BC.BC. Let PP be a variable point inside △ABC,\triangle ABC, such that ∠PBC=∠PCA.\angle PBC=\angle PCA. Prove that the sum of the measures of ∠BPM\angle BPM and ∠APC\angle APC is constant.
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