Problem

Source: St. Petersburg MO 2001, 11th grade, P5

Tags: geometry, orthocenter, incenter, circumcircle



Let $I$ and $H$ be the incenter and orthocenter of an acute triangle $ABC$. $M$ is the midpoint of arc $AC$ of circumcircle of triangle $ABC$ which does not contain point $B$. If $MI=MH$, find the measure of angle $\angle ABC$. Proposed by F. Bakharev