$\begin{aligned} & {\left[\begin{array}{l}\text { Intersecting Circles } \\ \text { [Inscribed Quadrilaterals (Miscellaneous)] }\end{array}\right]}\end{aligned}$

Two circles intersect at points $A$ and $B$. A line passing through point $A$ intersects the circles at points $M$ and $N$, different from $A$, and a line parallel to it, passing through $B$, intersects the circles at points $P$ and $Q$, different from $B$. Prove that $M N = P Q$.