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APQM cyclic wanted, circumcircle of ABC, arc midpoint, BP = CQ

Source: Mathematics Regional Olympiad of Mexico Northeast 2017 P4

September 21, 2022
geometryConcyclic

Problem Statement

Let Γ\Gamma be the circumcircle of the triangle ABCABC and let MM be the midpoint of the arc Γ\Gamma containing AA and bounded by BB and CC. Let PP and QQ be points on the segments ABAB and ACAC, respectively, such that BP=CQBP = CQ. Prove that APQMAPQM is a cyclic quadrilateral.
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