Question 5
Let $ABC$ be a non-isosceles triangle with incenter $I$ and let the circumcircle of the triangle $ABC$ has radius $R$. Let $AL$ be the external angle bisector of $\angle BAC$ with $L \in BC$. Let $K$ be the point on the perpendicular bisector of $BC$ such that $IL \perp IK$. Prove that $OK = 3R$.