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Excircle tangency points lie on the circumcircle

Source: Indonesian National Science Olympiad 2018, Mathematics P8

July 6, 2018
geometry

Problem Statement

Let I,OI, O be the incenter and circumcenter of the triangle ABCABC respectively. Let the excircle ωA\omega_A of ABCABC be tangent to the side BCBC on NN, and tangent to the extensions of the sides AB,ACAB, AC on K,MK, M respectively. If the midpoint of KMKM lies on the circumcircle of ABCABC, prove that O,I,NO, I, N are collinear.
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