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2 equal circumcircles wanted, midpoints of cyclic ABCD related

Source: 2013 All-Ukrainian Correspondence MO of magazine ''In the World of Mathematics'', grades 5-12 p9

April 27, 2021
geometrycyclic quadrilateralequal circlesUkraine Correspondence

Problem Statement

Let EE be the point of intersection of the diagonals of the cyclic quadrilateral ABCDABCD, and let K,L,MK, L, M and NN be the midpoints of the sides AB,BC,CDAB, BC, CD and DADA, respectively. Prove that the radii of the circles circumscribed around the triangles KLEKLE and MNEMNE are equal.
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