A Parallelogram and 2 Circles

Geometry Level 4

In Parallelogram ABCD, $AB=13$ , $BC=11$ , and $AC=20$ . Two congruent circles are inscribed in $\triangle ACD$ and $\triangle ACB$ as shown in the figure.

The shortest distance between the centers of the two inscribed circles can be expressed in the form $a\sqrt{b}$ . Where $b$ is a square-free integer. Find the value of $a+b$ .

Found this somewhere.