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midpoints of AH,DK,EL,FM are concyclic if <BAC = 60^o, midpoints, altitudes

Source: 2015 Baltic Way Shortlist G13 BW https://artofproblemsolving.com/community/c2641329_baltic_way_shortlist__geometry

November 23, 2021
Concyclicmidpointsaltitudesgeometry

Problem Statement

Let ABCABC be a triangle. Let its altitudes ADAD, BEBE and CFCF concur at HH. Let K,LK, L and MM be the midpoints of BCBC, CACA and ABAB, respectively. Prove that, if ∠BAC=60o\angle BAC = 60^o, then the midpoints of the segments AHAH, DKDK, ELEL, FMFM are concyclic.
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