Blazing interpretation

Geometry Level 2

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

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

Find a+b a+b .

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