Question 2
A circle with center $I$ is inscribed in a hexagon $ABCDEF$. Let $A', B', C', D', E', F'$ be the midpoints of the diagonals $BF, AC, BD, CE, DF, EA$, respectively. Suppose that the lines $AA', CC', EE'$ intersect at $X$, the lines $BB', DD', FF'$ intersect at $Y$. If the triangle residing between the lines $AB, CD, EF$ is not similar to the triangle residing between the lines $BC, DE, FA$, then prove that the points $X, I, Y$ are collinear.
(Batzaya G.)
(Batzaya G.)