Question 24
Four points in the order $A,B,C,D$ lie on a circle with the extension of $AB$ meeting the extension of $DC$ at $E$, and the extension of $AD$ meeting the extension of $BC$ at $F$. Let $EP$ and $FQ$ be tangents to this circle with points of tangency $P$ and $Q$ respectively. Suppose $EP=60$ and $FQ=63$. Determine the length of $EF$.