Consider a circle (x-α)^2+(y-β)^2=50, where α, β>0. If the circle touches the line y+x=0 at the point P, whose distance from the origin is 4 √ 2,…

Consider a circle $\displaystyle (x-\alpha)^2+(y-\beta)^2=50$, where $\displaystyle \alpha, \beta>0$. If the circle touches the line $\displaystyle y+x=0$ at the point P, whose distance from the origin is $\displaystyle 4 \sqrt{2}$, then $\displaystyle (\alpha+\beta)^2$ is equal to $\displaystyle \_\_\_\_$.