1. $A,B,D$ and $E$ are points on a circle.

$ABC$and $EDC$ are straight lines.

$\begin{matrix}BC & = & (2+\sqrt{5})cm\\ED & = & (4+\sqrt{5})cm\\DC & = & 2\sqrt{5}cm\end{matrix}$

Show that the length of $AB$ is $(p\sqrt{5}+q)cm,$ where $p$ and $q$ are integers whose values are to be found.
Show your working clearly.