Perpendicular Lines in Triangle

Geometry Level 4

\(ABC\) is a triangle with \(AC = 139\) and \(BC = 178\). Points \(D\) and \(E\) are the midpoints of \(BC\) and \(AC\) respectively. Given that \(AD\) and \(BE\) are perpendicular to each other, what is the length of \(AB\)?

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