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Find locus of the midpoints of the sides $KL$ of KLM

Source: Czech and Slovak MO, 2002, P2

September 15, 2012
geometrycircumcircleperpendicular bisectorgeometry unsolved

Problem Statement

Consider an arbitrary equilateral triangle KLMKLM, whose vertices K,LK, L and MM lie on the sides AB,BCAB, BC and CDCD, respectively, of a given square ABCDABCD. Find the locus of the midpoints of the sides KLKL of all such triangles KLMKLM.
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