JEE Main 2022 · 30 Jun · Shift 1, Mathematics question 28

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 $\sqrt{\dfrac{57}2}$, then $\alpha$ is equal to ______.