Question 2
Let $ABC$ be a triangle with circumcenter $O$. The points $P$ and $Q$ are interior points of the sides $CA$ and $AB$ respectively. Let $K$, $L$, $M$ be the midpoints of $\overline{BP}$, $\overline{CQ}$, $\overline{PQ}$. Suppose that $\overline{PQ}$ is tangent to the circumcircle of $\triangle KLM$. Prove that $OP = OQ$.