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The incenter lies on circumcircle [Iran Second Round 95]

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November 25, 2010
geometryincentercircumcirclegeometric transformationreflectiongeometry proposed

Problem Statement

Let ABCABC be an acute triangle and let ℓ\ell be a line in the plane of triangle ABC.ABC. We've drawn the reflection of the line ℓ\ell over the sides AB,BCAB, BC and ACAC and they intersect in the points A′,B′A', B' and C′.C'. Prove that the incenter of the triangle A′B′C′A'B'C' lies on the circumcircle of the triangle ABC.ABC.
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