Consider two circles C_1: x^2+y^2=25 and C_2:(x-α)^2+y^2=16, where α ∈(5,9). Let the angle between the two radii (one to each circle) drawn from one…

Consider two circles $\displaystyle C_1: x^2+y^2=25$ and $\displaystyle C_2:(x-\alpha)^2+y^2=16$, where $\displaystyle \alpha \in(5,9)$. Let the angle between the two radii (one to each circle) drawn from one of the intersection points of $\displaystyle C_1$ and $\displaystyle C_2$ be $\displaystyle \sin ^{-1}\left(\frac{\sqrt{63}}{8}\right)$. If the length of common chord of $\displaystyle C_1$ and $\displaystyle C_2$ is $\displaystyle \beta$, then the value of $\displaystyle (\alpha \beta)^2$ equals $\displaystyle \_\_\_\_$.