SHARYGIN 2009 Problem 20

Suppose $H$ and $O$ are the orthocenter and the circumcenter of acute triangle $ABC$ ; $AA_1$ , $BB_1$ and $CC_1$ are the altitudes of the triangle. Point $C_2$ is the reflection of $C$ in $A_1B_1$ . Prove that $H$ , $O$ , $C_1$ and $C_2$ are concyclic.