Calculate Radius of a sphere

[Halsafar]

Okay...I got a node in a quad tree.

I have 4 points which make up its bounding box..

I can get the center of the 4 points easily. That center can be used as the center of the sphere.

I am wondering how I can get the radius which would indeed cover those four points, or at least just past those 4 points. The sphere in most case's should be a bit bigger I think.

Any help at all though?

So far what I am doing is taking the magnitude of the a vector and dividing it by 2.
That works in most cases's...see
P1 (4,0) P3 (8,0)
P2 (4,4) P4 (8,4)
Center = ((P4 - P1) / 2) + P1 = (4,4 / 2) + 4,0 = (2,2) + (4,0) = 6,2
Center = 6,2 is indeed correct if you wish to picture the grid.

r^2 = x^2 + z^2 (the points I shall use will be from P4)
r^2 = 8^2 + 4^2
r^2 = 64 + 4
SqrRt(r) = SqrRt(68)
r = 8.2462112512353210996428197119482 / 2
r = 4.1231056256176605498214098559741

Indeed r as 4.1 is JUST outside the bounding box...is this correct????