Question 107
Given acute-angled triangle $ABC$. $O$ is the circumcenter, $H$ is the orthocenter and $AH_A$, $BH_B$, $CH_C$ are the altitudes of $\triangle ABC$. Denote by $A_1$, $B_1$, $C_1$ the circumcenters of triangles $BOC$, $COA$ and $AOB$ respectively. Prove that the lines $A_1H_A$, $B_1H_B$, $C_1H_C$ meet at a point, which lies on the Euler line of $\triangle ABC$. (Euler line of $\triangle ABC$ is the line passing through the circumcenter and centroid of a triangle).