Question 2
Consider an acute scalene triangle $ABC$ with circumcircle $\Gamma$. The external angle bisector of $\angle BAC$ meets $BC$ at $X$. Lines $\ell_b$ and $\ell_c$ are tangent lines from $B$ and $C$ to $\Gamma$. A line passes through $X$ and intersects $\ell_b$ and $\ell_c$ at points $Y$ and $Z$, such that $X, Y$ and $Z$ lie on this order. Suppose that the circumcircle of triangles $AYB$ and $AZC$ intersect at $N$, for the second time. If $D$ is the intersection point of $\ell_b$ and $\ell_c$, show that $ND$ is the angle bisector of $\angle YNZ$.