CMOQR 2021 Problem 4

Let $O$ be the centre of the circumcircle of triangle $ABC$ and let $I$ be the centre of the incircle of triangle $ABC$ . A line passing through the point $I$ is perpendicular to the line $IO$ and passes through the incircle at points $P$ and $Q$ . Prove that the diameter of the circumcircle is equal to the perimeter of triangle $OPQ$ .