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prove orthocenter for antipodal point

Source: Sharygin 2023 - P11 (Grade-8-10)

March 4, 2023
geometryothorcenterantipodeSharygin Geometry OlympiadSharygin 2023

Problem Statement

Let HH be the orthocenter of an acute-angled triangle ABCABC; EE, FF be points on AB,ACAB, AC respectively, such that AEHFAEHF is a parallelogram; X,YX, Y be the common points of the line EFEF and the circumcircle ω\omega of triangle ABCABC; ZZ be the point of ω\omega opposite to AA. Prove that HH is the orthocenter of triangle XYZXYZ.
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