Question 74
Let $ABC$ be a triangle, $O$ its circumcenter and $AD$ the bisector of the angle $A$ where $D \in BC$. Let $\ell$ be the line passing through $O$ and parallel to the bisector $AD$. Prove that $\ell$ passes through the orthocenter $H$ of the triangle $ABC$ if and only if $ABC$ is isosceles or $\angle BAC = 120^{\circ}$.