Work those Quadriceps

Geometry Level 5

Suppose \(ABCD\) is a cyclic quadrilateral with all integral sidelengths and \(AD\) being the circumdiameter. Sides \(\overline{AB}\) and \(\overline{BC}\) both having length \(a\) and side \(CD\) having length \(b\) such that \(a \ne b.\)

Determine the sum of the 4 smallest possible perimeters of quadrilateral \(ABCD.\)


Inspired by this beautiful problem

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