Question 22
Let $ABC$ an equilateral triangle. Let $X$ A point from the line $(BC)$ different from $B$ and $C$. be $Y$ and $Z$ Two dots on the lines $(AB)$ and $(AC)$ so that the two lines $(BZ)$ and $(CY)$ are parallel to the line $(AX)$. The right $(XY)$ intersect the line $(AC)$ in $M$ and the line $(XZ)$ intersect the line $(AB)$ in $N$. Show that the line $(MN)$ is tangent to the inscribed circle of $ABC$.