Abstract
It is shown that a pair of nested concentric ovals has the property that each point on either one of the ovals is a vertex of exactly one inscribed parallelogram of maximal perimeter if and only if the joint Monge orthoptic curve of the ovals is a circle. This gives an answer to a question posed by Connes and Zagier in the note A property of parallelograms inscribed in ellipses, which appeared in the American Mathematical Monthly in 2007.
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