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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