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.

(In reply to re: 'Within' includes 'on'? by Federico Kereki)

But, for these more "inclusive" definitions of "within," the proof involves showing that these are trivial special cases and then proving the case where the conditions are as stated. So what is gained?

Posted by TomM on 2004-02-20 22:21:43