Distance Between Intersection Points

Geometry Level 4

On a semicircle with diameter $AB$ and centre $O$ points $X$ and $Y$ are chosen such that $\angle XOY = 120^{\circ}$ . Let $AX$ and $BY$ meet at $Z$ and $AY$ and $BX$ meet at $W$ . If $AB = 5\sqrt{3}$ , find $WZ$ .