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altitudes, midpoints, concurrent lines with the medial line

Source: 2015 Sharygin Geometry Olympiad Correspondence Round P13

August 2, 2018
geometryconcurrentconcurrencymidpoints

Problem Statement

Let AH1,BH2AH_1, BH_2 and CH3CH_3 be the altitudes of a triangle ABCABC. Point MM is the midpoint of H2H3H_2H_3. Line AMAM meets H2H1H_2H_1 at point KK. Prove that KK lies on the medial line of ABCABC parallel to ACAC.
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