Question 113
Let $O$ be the circumcenter of an acute-angled isosceles triangle $ABC$ with $AB = AC$. The rays $BO$ and $CO$ meet the sides $AC$ and $AB$ at $B'$ and $C'$, respectively. Let $l$ be the line through $C'$ parallel to $AC$. Prove that $l$ is tangent to the circumcircle of the triangle $B'OC$.