# 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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