Sphere through four Points

Four non-coplanar points define exactly one sphere. Given the coordinates of four points the program determines the equation of the sphere, its center and radius.

Example:

Sphere through the points: 
A(1|0|0), B(0|2|0), C(0|0|3), D(1|0|1)

Normal form:
¯¯¯¯¯¯¯¯¯¯¯¯
     ⎧ ->    ⎧-2,5 ⎫ ⎫2 
 K : ⎪ x   - ⎪-0,5 ⎪ ⎪   = 12,75
     ⎩       ⎩ 0,5 ⎭ ⎭

Center and radius:
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
 M(-2,5|-0,5|0,5),  r = 3,5707142