MathDB

10

Part of 2019 Latvia Baltic Way TST

Problems(1)

Tangent circles in orthocenter configuration

Source: Latvian TST for Baltic Way 2019, Problem 10

6/4/2020
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.
geometryorthocentertangent circlescircumcircle