Question 50
Let $\triangle ABC$ be a triangle with incenter $I$ and circumcircle $(\omega)$. The lines $AI, BI, CI$ intersect $(\omega)$ for second time at the points $D, E, F$ respectively. The parallel lines through $I$ to the sides $BC, AC, AB$ intersect the lines $EF, DF, DE$ at the points $K, L, M$ respectively. Prove that the points $K, L, M$ are collinear.