Problem

Source: China south east mathematical Olympiad 2008 day2 problem 6

Tags: geometry, trigonometry, geometry unsolved



Circle $I$ is the incircle of $\triangle ABC$. Circle $I$ is tangent to sides $BC$ and $AC$ at $M,N$ respectively. $E,F$ are midpoints of sides $AB$ and $AC$ respectively. Lines $EF, BI$ intersect at $D$. Show that $M,N,D$ are collinear.