UA-UMO 2021 Problem 96

Circles $w_1$ and $w_2$ intersect at points $P$ and $Q$ and touch a circle $w$ with center at point $O$ internally at points $A$ and $B$ , respectively. It is known that the points $A,B$ and $Q$ lie on one line. Prove that the point $O$ lies on the external bisector $\angle APB$ .

(Nazar Serdyuk)