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Isosceles triangle with height $HM$

Source: Moldova TST 2010, day 2, problem 3

March 4, 2010
geometryratioparallelogramperpendicular bisectorgeometry proposed

Problem Statement

Let ABC ABC be an acute triangle. H H is the orthocenter and M M is the middle of the side BC BC. A line passing through H H and perpendicular to HM HM intersect the segment AB AB and AC AC in P P and Q Q. Prove that MP \equal{} MQ
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