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Tangent circumcircles

Source: Russian TST 2019, Day 9 P3 (Groups A & B)

March 27, 2023
geometry

Problem Statement

Let HH{} be the orthocenter of the acute-angled triangle ABCABC. In the triangle BHCBHC, the median HMHM and the symedian HLHL are drawn. The point KK{} is marked on the line LHLH so that ∠AKL=90∘\angle AKL=90^\circ. Prove that the circumcircles of the triangles ABCABC and KLMKLM are tangent.
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