Question 1
Let $ABC$ be an acute triangle inscribed in circle $(O)$, with orthocenter $H$. Median $AM$ of triangle $ABC$ intersects circle $(O)$ at $A$ and $N$. $AH$ intersects $(O)$ at $A$ and $K$. Three lines $KN$, $BC$ and the line through $H$ and perpendicular to $AN$ intersect each other and form triangle $XYZ$. Prove that the circumcircle of triangle $XYZ$ is tangent to $(O)$.