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 $OPQ$.
Problem
Source: Canada Repêchage 2021/4 CMOQR
Tags: Canada, repechage, geometry, incircle, circumcircle