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Points O,N, I lie on a line [Russia 2003]

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November 4, 2010
geometrycircumcirclegeometry unsolved

Problem Statement

In a triangle ABC,OABC, O is the circumcenter and II the incenter. The excircle ωa\omega_a touches rays AB,ACAB,AC and side BCBC at K,M,NK,M,N, respectively. Prove that if the midpoint PP of KMKM lies on the circumcircle of △ABC\triangle ABC, then points O,N,IO,N, I lie on a line.
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