TH-TMO 2016 Problem 8

Let $\vartriangle ABC$ be an acute triangle with incenter $I$ . The line passing through $I$ parallel to $AC$ intersects $AB$ at $M$ , and the line passing through $I$ parallel to $AB$ intersects $AC$ at $N$ . Let the line $MN$ intersect the circumcircle of $\vartriangle ABC$ at $X$ and $Y$ . Let $Z$ be the midpoint of arc $BC$ (not containing $A$ ). Prove that $I$ is the orthocenter of $\vartriangle XY Z$