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one circle with diameter median tangent to altitude, the other one also

Source: Belarus TST 2015 3.2

June 9, 2020
geometrytangentcirclesMedians

Problem Statement

The medians AMAM and BNBN of a triangle ABCABC are the diameters of the circles ω1\omega_1 and ω2\omega_2. If ω1\omega_1 touches the altitude CHCH, prove that ω2\omega_2 also touches CHCH.
I. Gorodnin
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