Question 166
Let $H$ be the orthocenter of an acute triangle $ABC$. The circumcircle of $\triangle BCH$ intersects $AB$ and $AC$ again at points $A_1$ and $A_2$ respectively. Define points $B_1, B_2, C_1$ and $C_2$ analogously. Prove that the circumcenter of the triangle formed by lines $A_1A_2, B_1B_2$, and $C_1C_2$ is on the Euler line with respect to $\triangle ABC$.