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line MH passes through arc midpoint in a 60-45-75 triangle

Source: 2013 Oral Moscow Geometry Olympiad grades 8-9 p5

August 15, 2019
geometrycircumcircleorthocenter

Problem Statement

In triangle ABC,∠C=60o,∠A=45oABC, \angle C= 60^o, \angle A= 45^o. Let MM be the midpoint of BC,HBC, H be the orthocenter of triangle ABCABC. Prove that line MHMH passes through the midpoint of arc ABAB of the circumcircle of triangle ABCABC.
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