Consider a circle of radius 6 as given in the diagram below. Let $B$, $C , D$ and $E$ be points on the circle such that $B D$ and $C E$, when extended, intersect at $A$. If $A D$ and $A E$ have length 5 and 4 respectively, and $D B C$ is a right angle, then show that the length of $B C$ is $\frac { 12 + 9 \sqrt { 15 } } { 5 }$.