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CN-SMO 2012 Problem 2

    The incircle II of △ABC\triangle ABC is tangent to sides AB,BC,CAAB,BC,CA at D,E,FD,E,F respectively. Line EFEF intersects lines AI,BI,DIAI,BI,DI at M,N,KM,N,K respectively. Prove that DM⋅KE=DN⋅KFDM\cdot KE=DN\cdot KF .

    Dataset text AI-MO AoPS. Quoted with source.

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