Until someone brings a link from MIT's website, I'm calling bullshit on this one. This sounds like what pops up every other day in Egyptian newspapers about genius Egyptian kids who invent this or that. The theorem stated in the article is not a theorem at all. It's a direct consequence of the definition of a circle and is perfectly obvious to anyone who spends two minutes pondering the implications of that definitio…
A circle is defined as all the points in the same distance from a certain center point. But a point thats distanced from the circle circumference by R isn't necessarily the circles center. But if you can draw 3 (and hence more) lines from a point to the circles circumference that are all the same lenght, that is the circles center, and the distance is the radius.
I think they also need to be on the same plane, otherwise it's a hollow sphere.
Also, by that definition, there's an infinity of centers. There can be a line that passes through the center and perpendicular to the plane on which the circle lies. Every point of that line is equally distant from the points of the circle.
And for an infinity of planes parallel to our plane of interest, the intersection of the line and that plane gives the center of the projection of our first circle onto that new plane.