Question 86
The circles $C_1$ and $C_2$ intersect at $A$ and $B$. The points $P$ and $Q$ are on $C_2$, $P$ in the interior and $Q$ in the exterior of $C_1$. The lines $AP$ and $BP$ meet $C_1$ also at $X$ and $Y$, respectively, while the lines $QA$ and $QB$ meet $C_1$ also at $Z$ and $T$. Show that $XY = ZT$.