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Geo problem

Source: Mexican Math Olympiad 2015 Problem 1

November 23, 2015
circumcirclegeometry proposedgeometry

Problem Statement

Let ABCABC be an acuted-angle triangle and let HH be it's orthocenter. Let PQPQ be a segment through HH such that PP lies on ABAB and QQ lies on ACAC and such that ∠PHB=∠CHQ \angle PHB= \angle CHQ. Finally, in the circumcircle of △ABC\triangle ABC, consider MM such that MM is the mid point of the arc BCBC that doesn't contain AA. Prove that MP=MQMP=MQ
Proposed by Eduardo Velasco/Marco Figueroa
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