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another austrian midpoint, many perpendiculars

Source: 48th Austrian Mathematical Olympiad National Competition (Final Round, part 2 ) 25th May 2017 p5

May 25, 2019
geometrymidpointperpendicular

Problem Statement

Let ABCABC be an acute triangle. Let HH denote its orthocenter and D,ED, E and FF the feet of its altitudes from A,BA, B and CC, respectively. Let the common point of DFDF and the altitude through BB be PP. The line perpendicular to BCBC through PP intersects ABAB in QQ. Furthermore, EQEQ intersects the altitude through AA in NN. Prove that NN is the midpoint of AHAH.
Proposed by Karl Czakler
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