# What is the average center of six points in space

I have three pairs of points in 3D space. These may or may not be coplanar. I want to find a point such that it is equidistant from each pair of points. I know that may or may not be possible depending on the positions of the points. What I want is the best average point, which I can take safely as the centre and draw a sphere from there whose radius is the maximum distance of this point from any of the six points, then I want all the points to remain inside the sphere.

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Your question would probably be more appropriate at MO's sister site math.stackexchange.com. This site is for research-level questions, in mathematics itself. 'Research-level' means, roughly, questions that might be discussed between two professors, or between graduate students working on PhD's. – HJRW Oct 29 '10 at 14:20
If you mean that research-level means questions can be asked only by research students or professors then please note that I do have a Masters in Mathematics. Right now I am involved in computer graphics, and this question relates to that. Thanks for the reference to the site, I appeciate. – Alok Gandhi Oct 29 '10 at 14:36
Alok - no, I mean that there are plenty of very interesting questions with some mathematical content that are not suitable for MO. I think this is one of them. – HJRW Oct 29 '10 at 19:05
@Henry : I agree absolutely, I went to the site and it is quite interesting as well as engaging. Thanks again. – Alok Gandhi Oct 29 '10 at 19:23

@Alok I'm still not clear on the pairs of points. Is one pair $(x_{min},y,z) \text{and} (x_{max},y,z)$ with the same $y$ and $z$? The sense would be that you really want the whole segment to be in the sphere. That is OK as the sphere is convex. Could you give an example of three pairs? – Ross Millikan Oct 29 '10 at 17:01