Let $\mathrm{A}, \mathrm{B}$ be points on the two half-lines $x-\sqrt{3}|y|=\alpha, \alpha>0$ at a distance of $\alpha$ from their point of intersection $P$. The line segment AB meets the angle bisector of the given half-lines at the point Q . If $\mathrm{PQ}=\frac{9}{2}$ and R is the radius of the circumcircle of VPAB , then $\frac{\alpha^2}{\mathrm{R}}$ is equal to