Don't get trapped

Geometry Level 3

Suppose \(ABCD\) is an isosceles trapezoid with bases \(AB\) and \(CD\) and sides \(AD\) and \(BC\) such that \(|CD| \gt |AB|.\) Also suppose that \(|CD| = |AC|\) and that the altitude of the trapezoid is equal to \(|AB|.\)

If \(\dfrac{|AB|}{|CD|} = \dfrac{a}{b},\) where \(a\) and \(b\) are positive coprime integers, then find \(\large a^{b}.\)

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