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MH intersects the angle bisector

Source: 2021 Oral Moscow Geometry Olympiad grades 8-9 p6

May 17, 2021
geometryangle bisectororthocenter

Problem Statement

Point MM is a midpoint of side BCBC of a triangle ABCABC and HH is the orthocenter of ABCABC. MHMH intersects the AA-angle bisector at QQ. Points XX and YY are the projections of QQ on sides ABAB and ACAC. Prove that XYXY passes through HH.
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