Cool Geometry Problem

Geometry Level 3

Let ABC be a triangle with an obtuse angle at \(\angle \)ACB . The incircle of triangle ABC tangent to AB, Bc and CA at D, E and F , respectively. Let G be the midpoint of the side AB and let I be the incenter of triangle ABC. The line EF intersects the line AI and BI at M and N , respectively. Determine \(\angle \) DNM = 78 degree Find \(\angle \) DGM

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