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Estonian Math Competitions 2005/2006

Source: Seniors Problem 3

July 30, 2008
geometry unsolvedgeometry

Problem Statement

Let ABC ABC be an acute triangle and choose points A1,B1 A_1, B_1 and C1 C_1 on sides BC,CA BC, CA and AB AB, respectively. Prove that if the quadrilaterals ABA1B1,BCB1C1 ABA_1B_1, BCB_1C_1 and CAC1A1 CAC_1A_1 are cyclic then their circumcentres lie on the sides of ABC ABC.
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