Question 65
Let $AB$ be a diameter of a circle $S$, and let $L$ be the tangent at $A$. Furthermore, let $c$ be a fixed, positive real, and consider all pairs of points $X$ and $Y$ lying on $L$, on opposite sides of $A$, such that $|AX| \cdot |AY| = c$. The lines $BX$ and $BY$ intersect $S$ at points $P$ and $Q$, respectively. Show that all the lines $PQ$ pass through a common point.