Let $ABC$ be a triangle, and let $\ell$ be the line passing through the circumcenter of $ABC$ and parallel to the bisector of the angle $\angle A$. Prove that the line $\ell$ passes through the orthocenter of $ABC$ if and only if $AB = AC$ or $\angle BAC = 120^o$
Problem
Source: 2012 Italy TST 2.1 - also 2012 Balkan Shortlist G2 BMO
Tags: geometry, orthocenter, Circumcenter