CZ-SK-MO 1997 Problem 6

In a parallelogram $ABCD$ , triangle $ABD$ is acute-angled and $\angle BAD = \pi /4$ . Consider all possible choices of points $K,L,M,N$ on sides $AB,BC, CD,DA$ respectively, such that $KLMN$ is a cyclic quadrilateral whose circumradius equals those of triangles $ANK$ and $CLM$ . Find the locus of the intersection of the diagonals of $KLMN$