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Similar cyclic quadrilateral

Source: Greek TST 2011-pr4

May 23, 2016
geometrycyclic quadrilateralcircumcirclegeometry solvedgeometry proposedNine point centerPoncelet point

Problem Statement

Let ABCDABCD be a cyclic quadrilateral and let K,L,M,N,S,TK,L,M,N,S,T the midpoints of AB,BC,CD,AD,AC,BDAB, BC, CD, AD, AC, BD respectively. Prove that the circumcenters of KLS,LMT,MNS,NKTKLS, LMT, MNS, NKT form a cyclic quadrilateral which is similar to ABCDABCD.
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