Quadrilateral Side Lengths

Geometry Level 3

\(ABCD\) is a quadrilateral with \(\angle ABC = 90^\circ\), \(\angle ACD = 90^\circ\), \(AC = 30\), \(BC = 18\) and \(AD = 50\). If \(BD = a\sqrt{b}\), what is the value of \(a + b\)?

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