Let A, B be points on the two half-lines x-√ 3 |y|=α, α>0 at a distance of α from their point of intersection P. The line segment AB meets the angle…

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