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concyclic wanted, incircle of an obtuse triangle related

Source: Thailand Mathematical Olympiad 2015 p4

August 16, 2020
geometryObtuse triangleConcyclicincircle

Problem Statement

Let △ABC\vartriangle ABC be a triangle with an obtuse angle ∠ACB\angle ACB. The incircle of △ABC\vartriangle ABC centered at II is tangent to the sides AB,BC,CAAB, BC, CA at D,E,FD, E, F respectively. Lines AIAI and BIBI intersect EFEF at MM and NN respectively. Let GG be the midpoint of ABAB. Show that M,N,G,DM, N, G, D lie on a circle.
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