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2013.9

Part of Ukraine Correspondence MO - geometry

Problems(1)

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

4/27/2021
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.
geometrycyclic quadrilateralequal circlesUkraine Correspondence