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inscribed circle

Source: China south east mathematical Olympiad 2012 day1 problem 2

July 17, 2013
geometrycircumcircletrigonometrygeometry unsolved

Problem Statement

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.
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