Question 82
Let $ABC$ be an acute triangle. Through a point $L$ on $BC$, draw a circle $\omega$ tangent to $AB$ at $B'$ and to $AC$ at $C'$. Suppose also that the circumcenter $O$ of $ABC$ lies on the shorter arc $B'C'$ of $\omega$. Prove that the circumcircle of $ABC$ and $\omega$ intersect at two points.