Show that there exist one point equidistant from four non complainer distinct points (maybe it can be solved using axis of a circle )
1. Four non-complanar points are located on a sphere. Thus you are looking for it's center.
2. If the center of the sphere is then the equation of the sphere is:
Plug in the coordinates of the four points. You'll get a system of 4 equations which can be easily reduced to a system of 3 linear equations. Solve for .