Tangent Circles and Radii

In the diagram above, circle $B$ is tangent to circle $A$ at $C$ , circle $E$ is tangent to circle $A$ and $D$ , and circles $B$ and $E$ are tangent to one another. If $\overline{AB} = 5$ , $\overline{AE} = 6$ , and $\overline{BE} = 9$ , what is the measure of $\overline{AD}$ ?