Question 152
In an equilateral triangle $ABC$, the point $X$ on the segment $[BC]$ and the points $Y$, $Z$ on the rays $[BA$ and $[CA$, respectively, are given such that $AX$, $BZ$, $CY$ are parallel. Let $XY$ intersect $AC$ at $M$, and let $XZ$ intersect $AB$ at $N$. Show that $MN$ is tangent to the incircle of $ABC$.