Three Dimensional Geometry: JEE Main 2022 Mathematics question

Consider a triangle ABC whose vertices are A(0, $\alpha$, $\alpha$), B($\alpha$, 0, $\alpha$) and C($\alpha$, $\alpha$, 0), $\alpha$ > 0. Let D be a point moving on the line x + z $-$ 3 = 0 = y and G be the centroid of $\Delta$ABC. If the minimum length of GD is $\sqrt {{{57} \over 2}}$, then $\alpha$ is equal to ____________.