Question 174
Let $ABCD$ be a cyclic quadrilateral with circumcentre $O$. Diagonals $AC$ and $BD$ meet at $E$. $F$ and $G$ are points on segments $AB$ and $CD$ respectively. Suppose $AF = 15$, $FB = 13$, $BE = 30$, $ED = 13$, $DG = 7.5$ and $GC = 6.5$. Let $P$ be a point such that $PF \perp AB$ and $PG \perp CD$. Find $\frac{PE}{PO}$.