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Collinearity on bisectors

Source: Sharygin geometry olympiad 2016, grade 10, Final Round, Problem 6.

August 5, 2016
geometrycollinearitycircumcircle

Problem Statement

A triangle ABCABC is given. The point KK is the base of the external bisector of angle AA. The point MM is the midpoint of the arc ACAC of the circumcircle. The point NN on the bisector of angle CC is such that AN∥BMAN \parallel BM. Prove that the points M,N,KM,N,K are collinear.
(Proposed by Ilya Bogdanov)
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