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AK,BC, t are parallel or concurrent , incircle related

Source: Mathley 2014.3 p3

August 18, 2020
geometryparallelconcurrentincircle

Problem Statement

Let the incircle γ\gamma of triangle ABCABC be tangent to BA,BCBA, BC at D,ED, E, respectively. A tangent tt to γ\gamma , distinct from the sidelines, intersects the line ABAB at MM. If lines CM,DECM, DE meet atK K, prove that lines AK,BCAK,BC and tt are parallel or concurrent.
Michel Bataille , France
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