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 $ABC$.