JMO 2025 Problem 2

Let $ABC$ be an acute-angled triangle with circumcenter $O$ . Let $O_1$ and $O_2$ be the circumcenters of triangles $ABO$ and $ACO$ , respectively. The circumcircle of $\triangle AO_1O_2$ intersects segment $BC$ at two distinct points $P$ and $Q$ , with the four points $B, P, Q, C$ appearing in this order along $BC$ . Let $O_3$ be the circumcenter of $\triangle OPQ$ . Prove that points $A, O, O_3$ are collinear.