# Blazing interpretation

Geometry Level 3

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 $$a, b$$ are positive integers and $$b$$ is square free.

Find $$a+b$$.

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