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Sphere formula

1. The center of a sphere through 4 points has a very nice determinant 
form. ( What I want is a nice 
formula for the center of a sphere through 3 points, where the center is 
in the plane of the three points. I have a formula but it's a horrible 
mess of hundreds of lines, even after FullSimplify.

2. (Unlikely) Is there a way to get Mathematica to put a long formula into a 
matrix/determinant form if there is a nice one?

Any tips will be appreciated.

Steve Gray

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