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1988 USAMO Problem 4

Source:

July 27, 2011
AMCUSA(J)MOUSAMOgeometryincentercircumcircle

Problem Statement

Let II be the incenter of triangle ABCABC, and let A′A', B′B', and C′C' be the circumcenters of triangles IBCIBC, ICAICA, and IABIAB, respectively. Prove that the circumcircles of triangles ABCABC and A′B′C′A'B'C' are concentric.
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