Michel Bataille, Cyclic quadrilaterals with prescribed Varignon parallelogram,
Forum Geometricorum, 7 (2007) 199--206.

Abstract: We prove that the vertices of a given parallelogram P are the midpoints of the sides of infinitely many cyclic quadrilaterals and show how to construct such quadrilaterals. Then we discuss some of their properties and identify related loci. Lastly, the cases when P is a rectangle or a rhombus are examined.

[ps file][pdf]