Can you generalise this?

Suppose that $A$ , $B$ and $M$ are points on a circle such that $M$ is the midpoint of arc $AB$ . Let $C$ be an arbitrary point on the arc $AMB$ such that $AC$ is longer than $BC$ . Let $D$ be the foot of the perpendicular from $M$ to $AC$ .

If the length of $DC$ is 5 and the length of $BC$ is 2, find the length of $AD$ .