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concurrent lines with the line passing through 2 midpoints

Source: Sharygin Geometry Olympiad 2015 Final 9.5

August 1, 2018
geometryconcurrencyconcurrentmidpoint

Problem Statement

Let BMBM be a median of nonisosceles right-angled triangle ABCABC (∠B=90o\angle B = 90^o), and Ha,HcHa, Hc be the orthocenters of triangles ABM,CBMABM, CBM respectively. Prove that lines AHcAH_c and CHaCH_a meet on the medial line of triangle ABCABC.
(D. Svhetsov)
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