how to find center/radius of a sphere Say you have an irregular tetrahedron, but you know the (x,y,z) coordinates of the four vertices; is there a simple formula for finding a sphere whose center exists within the tetrahedron formed by the four points and on whose surface the four points lie?

Hint:
Step 1:  Find circumcircle $A$ for any three of the four points.
Step 2:  Find a circumcircle for the fourth point $P$ together with two points connected by a diameter $l$ of circle $A$ where a plane containing $l$ meets $A$ at a perpendicular angle and also contains $P$.
Then your circumsphere has radius and center equivalent to the radius and center of the circle found in step 2.
