Question 103
Let $A_1, B_1, C_1$ be the midpoints of the sides $BC, CA, AB$, respectively, of an acute triangle $ABC$ with orthocenter $H$ and circumcenter $O$. The rays $HA_1, HB_1, HC_1$ cut the circumcircle at the points $A_0, B_0, C_0$, respectively. Show that $O, H,$ and $H_0$ are collinear where $H_0$ is the orthocenter of $A_0B_0C_0$.