Question 191
Two circles intersect at $A$ and $B$. A common tangent to the circles touches the circles at $P$ and $Q$. A circle is drawn through $P$, $Q$ and $A$ and the line $AB$ meets this circle again at $C$. Join $CP$ and $CQ$ and extend both to meet the given circles at $F$ and $E$ respectively. Prove $P$, $Q$, $F$ and $E$ lie on the circumference of a circle.