Blazing interpretation

Geometry Level 2

In triangle $ABC$ , $\angle B = 90 ^ \circ, BE = 3,$ and $BD = 4$ .

If $AE = ED = DC$ , then the value of $AC$ can be expressed as $a \sqrt{b}$ , where $a$ and $b$ are positive integers and $b$ is square-free.

Find $a+b$ .