Like walkingcarcass said, there''s only recursive solutions to this problem. In 2D a sphere is defined by a maximum of 3 points (if they don''t lie on the same line), but in 3D you have a maximum of 4 points. Finding these 4 points is not as easy as some suggest.

What Zipster suggests won''t work, because you not only have to determine the radius of the sphere, but also the location of its center

If you look at Mr.Freeze''s link, you''ll understand the problem and find some code implementing it.