Choose any four points in a plane, such that no three are collinear and the four do not lie on a circle.

Show that one of the points must lie within the circle formed by the other three.

If "within the circle" is assumed to include being on the circle itself, there's no need to exclude the possibility of the four points lying on a circle.

Posted by e.g. on 2004-02-19 14:31:20