let a and b be opposite vertices of a unit cube (i.e. , the distance between a and b is the square root of 3). find the radius of a sphere, whose center is in the interior of the cube, that is tangent to the three faces that at a and also tangent to the three edges that meet at b.

Question

let a and b be opposite vertices of a unit cube (i.e. , the distance between a and b is  the square root of 3). find the radius of a sphere, whose center is in the interior of the cube, that is tangent to the three faces that at a and also tangent to the three edges that meet at b.