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

I have trouble with this from the start. A point can be equidistant from a set of points, a circle or a sphere. A set of points equidistant from a given point will lie on a circle or the surface of a sphere. All points on a circumference or on the surface of the sphere can be equidistant from a point. The point will be the center of the circle or sphere.

Planes can be parallel and there can be a point halfway between but the point is not equidistant from the planes, only from specific points on the planes. If the planes are viewed as an infinity of circles whose centers are opposite one another at right angles to the plane, then a point can be equidistant from two circles having equal radii on two parallel planes, or from two circles with different radii on non-parallel planes provided the planes also intersect the surface of a sphere on which the circles lie.

Posted by CeeAnne on 2004-12-17 19:20:33