Consider a triangle having vertices $\mathrm{A}(-2,3), \mathrm{B}(1,9)$ and $\mathrm{C}(3,8)$. If a line L passing through the circum-centre of triangle $A B C$, bisects line $B C$, and intersects $y$-axis at point $\left(0, \frac{\alpha}{2}\right)$, then the value of real number $\alpha$ is
