Question 171
Let $ABCD$ be a cyclic quadrilateral and $E$ be the intersection of $AC$ and $BD$. $P$ and $Q$ are two points on $AC$ such that the points $A$, $E$, $Q$, $P$, $C$ lie on the same straight line in this order, and that $BP$ bisects $\angle ABC$ whereas $DQ$ bisects $\angle ADC$. If $AE = 4$, $EQ = 2$ and $QP = 3$, find the length of $PC$.