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scent of a classic geometry

Source: Rioplatense Olympiad 1999 level 3 P1

September 4, 2018
geometryorthocentercircumcircle

Problem Statement

Let ABCABC be a scalene acute triangle whose orthocenter is HH. MM is the midpoint of segment BCBC. NN is the point where the segment AMAM intersects the circle determined by B,CB, C, and HH. Show that lines HNHN and AMAM are perpendicular.
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