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concyclic wanted, incenter, excenter (2017 Kyiv City MO 9.5)

Source:

September 8, 2020
geometryincenterexcenterConcycliccircumcircle

Problem Statement

Let II be the center of the inscribed circle of ABCABC and let IAI_A be the center of the exscribed circle touching the side BCBC. Let MM be the midpoint of the side BCBC, and NN be the midpoint of the arc BACBAC of the circumscribed circle of ABCABC . The point TT is symmetric to the point NN wrt point AA. Prove that the points IA,M,I,TI_A,M,I,T lie on the same circle.
(Danilo Hilko)
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