SHARYGIN 2022 Problem 94

Let $ABC$ be an isosceles triangle with $AB = AC$ , $P$ be the midpoint of the minor arc $AB$ of its circumcircle, and $Q$ be the midpoint of $AC$ . A circumcircle of triangle $APQ$ centered at $O$ meets $AB$ for the second time at point $K$ . Prove that lines $PO$ and $KQ$ meet on the bisector of angle $ABC$ .