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locus of intersections of diagonals, cyclic quadrilateral and parallelogram

Source: Czech And Slovak Mathematical Olympiad, Round III, Category A 1997 p6

February 20, 2020
CyclicparallelogramdiagonalsLocusgeometry

Problem Statement

In a parallelogram ABCDABCD, triangle ABDABD is acute-angled and ∠BAD=π/4\angle BAD = \pi /4. Consider all possible choices of points K,L,M,NK,L,M,N on sides AB,BC,CD,DAAB,BC, CD,DA respectively, such that KLMNKLMN is a cyclic quadrilateral whose circumradius equals those of triangles ANKANK and CLMCLM. Find the locus of the intersection of the diagonals of KLMNKLMN
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