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