Let $O$ and $H$ be the circumcenter and the orthocenter of a triangle $ABC$. The line passing through the midpoint of $OH$ and parallel to $BC$ meets $AB$ and $AC$ at points $D$ and $E$. It is known that $O$ is the incenter of triangle $ADE$. Find the angles of $ABC$.
Problem
Source: 2015 Sharygin Geometry Olympiad Correspondence Round P2
Tags: geometry, Circumcenter, orthocenter, incenter, angles