Hit for the cycle

Geometry Level 3

Suppose \(ABCD\) is a cyclic quadrilateral with side \(AD\) being a diameter of length \(d\), sides \(AB\) and \(BC\) both having length \(a\) and side \(CD\) having length \(b\) such that \(a,b,d\) are all positive integers with \(a \ne b.\)

Determine the minimum possible perimeter of \(ABCD.\)

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