Problem

Source: All-Russian olympiad 2015, class 9, day 2, problem 7

Tags: geometry proposed, geometry, circumcircle



Given an acute triangle $ABC$ with $AB < AC$.Let $\Omega $ be the circumcircle of $ ABC$ and $M$ be centeriod of triangle $ABC$.$AH$ is altitude of $ABC$.$MH$ intersect with $\Omega $ at $A'$.prove that circumcircle of triangle $A'HB$ is tangent to $AB$. A.I.Golovanov, A. Yakubov