Another Cyclic Trapezoid

Geometry Level 4

A trapezoid \(ABCD\) is circumscribed around a circle with radius \(r\) and inscribed in a circle with radius \(R\), with bases \(AB\) and \(CD\), such that \(AB>CD\) and \(BC=AD=R\). If \(R=k\cdot AB\), find \(k\) to the nearest 3 decimal places.

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