Question 21
The sides $AB$ and $AC$ of the triangle $ABC$ touch the circle $c$ respectively at points $B'$ and $C'$. The center $L$ of the circle $c$ lies on the side $BC$. The circumcenter $O$ of triangle $ABC$ lies on the shorter arc $B'C'$ of the circle $c$. Prove that the circumcircle of $ABC$ and the circle $c$ meet at two points.