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.

I am not sure whether I understand your question correctly, but it seems that it can be disproved easily. Since there are always some points outside a circle, hence one of the points does not have to lie within the circle formed by the other three.

Posted by tan on 2004-02-20 00:51:12