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Concyclic circumcenters

Source: Problem 2 of Russian Regional Olympiad 2011, grade 10

September 1, 2011
geometrycircumcirclegeometric transformationrotationgeometry proposed

Problem Statement

ABCABC is an acute triangle. Points MM and KK on side ACAC are such that ∠ABM=∠CBK\angle ABM = \angle CBK. Prove that the circumcenters of triangles ABMABM, ABKABK, CBMCBM and CBKCBK are concyclic. (Author: T. Emelyanova)
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