Given four non-coplanar points, how many different planes exist that are equidistant from all four points?

Three of the given points determine a plane P.  The fourth point x is not in this plane.  There is exactly one plane Q parallel to P which passes half way between x and P.  Hence Q is the unique plane which is equidistant from all four points.  So the answer is ONE plane.

Posted by McWorter on 2005-02-26 00:31:03