AB is lost! Help find him!!

Geometry Level 3

A trapezium AB exists such that \(AB//CD\) and \(CD = 4AB\). If \(AD = 1\) and \(BC = 2\) and AC and BD meet perpendicularly, then \(AB = \sqrt{\frac{m}{n}}\) where \(gcd(m, n) = 1\). Find \(m+n???\)

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