$14$ has two identical right triangles that are circumscribed around the two semicircles created by the line $\overline { AB }$ cutting the circle in half.

A circle of diameterIf the short legs of the right triangles are $11$ as shown, the length of $\overline { AB }$ can be written as $\frac { a }{ b }$, where $a$ and $b$ are co-prime integers. Find $ab$.