Nicolae Anghel, A maximal parallelogram characterization of ovals having circles as orthoptic curves,
Forum Geometricorum, 10 (2010) 21--25.

Abstract:  It is shown that ovals admitting circles as orthoptic curves are  precisely characterized by the property that every one of their  points is the vertex of exactly one maximal-perimeter inscribed parallelogram.  This generalizes an old property of ellipses, most recently revived by  Connes and Zagier in the paper A Property of Parallelograms Inscribed in Ellipses.

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