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Perpendicular to Median

Source: Swiss TST 2019 P9

May 12, 2020
geometrycomputational geometry

Problem Statement

Let ABCABC be an acute triangle with AB<ACAB<AC. E,FE,F are foots of the altitudes drawn from B,CB,C respectively. Let MM be the midpoint of segment BCBC. The tangent at AA to the circumcircle of ABCABC cuts BCBC in PP and EFEF cuts the parallel to BCBC from AA at QQ. Prove that PQPQ is perpendicular to AMAM.
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