As you pointed out at the beginning this easy enough in principle.
But the details of the calculation are fairly gruesome.
If you want another approach, consider the circle determined by the three points.
The center of this circle is equidistant from them.
Here's a description of the solution: circle from three points.
Oops, just realized that is for 2d, i.e. no z.
That's what I get for trying to help without making any real effort.
Still, it's handy to know about Paul Bourke's site. Lots of neat stuff there.
But the details of the calculation are fairly gruesome.
If you want another approach, consider the circle determined by the three points.
The center of this circle is equidistant from them.
Here's a description of the solution: circle from three points.
Oops, just realized that is for 2d, i.e. no z.
That's what I get for trying to help without making any real effort.
Still, it's handy to know about Paul Bourke's site. Lots of neat stuff there.