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Classical Orthocenter Figure

Source: Swiss TST 2019 P1

May 12, 2020
geometryorthocentersimilarity

Problem Statement

Let ABCABC be a triangle and D,E,FD, E, F be the foots of altitudes drawn from A,B,CA,B,C respectively. Let HH be the orthocenter of ABCABC. Lines EFEF and ADAD intersect at GG. Let KK the point on circumcircle of ABCABC such that AKAK is a diameter of this circle. AKAK cuts BCBC in MM. Prove that GMGM and HKHK are parallel.
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