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MN passes through incentre of ABC

Source: Baltic Way 1997

January 28, 2011
geometryincentercircumcirclegeometry proposed

Problem Statement

In the acute triangle ABCABC, the bisectors of A,BA,B and CC intersect the circumcircle again at A1,B1A_1,B_1 and C1C_1, respectively. Let MM be the point of intersection of ABAB and B1C1B_1C_1, and let NN be the point of intersection of BCBC and A1B1A_1B_1. Prove that MNMN passes through the incentre of △ABC\triangle ABC.
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