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Right-angled triangle geometry

Source: Sharygin geometry olympiad 2015, grade 10, Final Round, Problem 5

July 17, 2018
geometry

Problem Statement

Let BMBM be a median of right-angled nonisosceles triangle ABCABC (∠B=90\angle B = 90), and HaH_a, HcH_c be the orthocenters of triangles ABMABM, CBMCBM respectively. Lines AHcAH_c and CHaCH_a meet at point KK. Prove that ∠MBK=90\angle MBK = 90.
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