TR-MO 2008 Problem 1

Given an acute angled triangle $ABC$ , $O$ is the circumcenter and $H$ is the orthocenter.Let $A_1$ , $B_1$ , $C_1$ be the midpoints of the sides $BC$ , $AC$ and $AB$ respectively. Rays $[HA_1$ , $[HB_1$ , $[HC_1$ cut the circumcircle of $ABC$ at $A_0$ , $B_0$ and $C_0$ respectively.Prove that $O$ , $H$ and $H_0$ are collinear if $H_0$ is the orthocenter of $A_0B_0C_0$