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orthocenter of the triangle DEH lies on segment CP

Source: 2012 Oral Moscow Geometry Olympiad grades 10-11 p3

September 25, 2019
altitudeorthocenterconcurrencyconcurrentgeometry

Problem Statement

HH is the intersection point of the heights AA′AA' and BB′BB' of the acute-angled triangle ABCABC. A straight line, perpendicular to ABAB, intersects these heights at points DD and EE, and side ABAB at point PP. Prove that the orthocenter of the triangle DEHDEH lies on segment CPCP.
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