Let a be the side of the cube.
Diagonal = √3*a
since DF= AG = CE
the triangle will be an equilateral triangle with side=√3 *a
According to the property of equilateral triangle, altitude is √3/2 times hypotenuse of the triangle (hypotenuse is side of equilateral triangle in this case)
Median itself is the altitude in equilateral trinagle. Centroid divides the median in the ratio 2:1.
now, the radius of the circle is the distance between a vertex to centroid of the equilateral triangle
so radius is 2/3 time altitude or median of the triangle
Radius = 2/3 * √3/2 *√3 * a = a which is side of triangle. option A is the answer