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Tangent circles in orthocenter configuration

Source: Latvian TST for Baltic Way 2019, Problem 10

June 4, 2020
geometryorthocentertangent circlescircumcircle

Problem Statement

Let △ABC\triangle ABC be an acute angled triangle with orthocenter HH and let MM be a midpoint of BCBC. Circle with diameter AHAH is ω1\omega_1 and circle with center MM is ω2\omega_2. If ω2\omega_2 is tangent to circumcircle of △ABC\triangle ABC, then prove that circles ω1\omega_1 and ω2\omega_2 are tangent to each other.
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