OBM 2013 Problem 1

Let $\Gamma$ be a circle and $A$ a point outside $\Gamma$ . The tangent lines to $\Gamma$ through $A$ touch $\Gamma$ at $B$ and $C$ . Let $M$ be the midpoint of $AB$ . The segment $MC$ meets $\Gamma$ again at $D$ and the line $AD$ meets $\Gamma$ again at $E$ . Given that $AB=a$ , $BC=b$ , compute $CE$ in terms of $a$ and $b$ .