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Equidistant circumcenters

Source: Indian IMOTC 2013, Practice Test 1, Problem 2

May 6, 2013
geometrycircumcircletrigonometrycyclic quadrilateralperpendicular bisectorgeometry proposed

Problem Statement

Let ABCDABCD by a cyclic quadrilateral with circumcenter OO. Let PP be the point of intersection of the diagonals ACAC and BDBD, and K,L,M,NK, L, M, N the circumcenters of triangles AOP,BOPAOP, BOP, COP,DOPCOP, DOP, respectively. Prove that KL=MNKL = MN.
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