Triangle $XYZ$ has side lengths $XY=10$, $YZ=12$, and $ZX=8$. The bisector of $\angle YXZ$ intersects $\overline{YZ}$ in point $W$, and intersects the circumcircle of $△XYZ$ in point $V\ne X$. The circumcircle of $△ZWV$ intersects the line $XZ$ in points $Z$ and $U\ne Z$. What is $YU$?