Don't get trapped

Geometry Level 2

Suppose ABCDABCD is an isosceles trapezoid with bases ABAB and CDCD and sides ADAD and BCBC such that CD>AB.|CD| \gt |AB|. Also suppose that CD=AC|CD| = |AC| and that the altitude of the trapezoid is equal to AB.|AB|.

If ABCD=ab,\dfrac{|AB|}{|CD|} = \dfrac{a}{b}, where aa and bb are positive coprime integers, then find ab.\large a^{b}.

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