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 \( a+b \).

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