SHARYGIN 2020 Problem 6

Circles $\omega_1$ and $\omega_2$ meet at point $P,Q$ . Let $O$ be the common point of external tangents of $\omega_1$ and $\omega_2$ . A line passing through $O$ meets $\omega_1$ and $\omega_2$ at points $A,B$ located on the same side with respect to line segment $PQ$ .The line $PA$ meets $\omega_2$ for the second time at $C$ and the line $QB$ meets $\omega_1$ for the second time at $D$ . Prove that $O-C-D$ are collinear.