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BMO 2015 #2: Collinearity

Source: BMO 2015 problem 2

May 5, 2015
geometrygeometry proposedBMO 2015conic

Problem Statement

Let △ABC\triangle{ABC} be a scalene triangle with incentre II and circumcircle ω\omega. Lines AI,BI,CIAI, BI, CI intersect ω\omega for the second time at points D,E,FD, E, F, respectively. The parallel lines from II to the sides BC,AC,ABBC, AC, AB intersect EF,DF,DEEF, DF, DE at points K,L,MK, L, M, respectively. Prove that the points K,L,MK, L, M are collinear. (Cyprus)
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