A maximal parallelogram characterization of ovals having circles as orthoptic curves - Nicolae Anghel

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    A maximal parallelogram characterization of ovals having circles as orthoptic curves - Nicolae Anghel

    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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