Školjka

%V0 Given three fixed pairwisely distinct points $A$, $B$, $C$ lying on one straight line in this order. Let $G$ be a circle passing through $A$ and $C$ whose center does not lie on the line $AC$. The tangents to $G$ at $A$ and $C$ intersect each other at a point $P$. The segment $PB$ meets the circle $G$ at $Q$. Show that the point of intersection of the angle bisector of the angle $AQC$ with the line $AC$ does not depend on the choice of the circle $G$.