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 believe this problem is related to deep mathematical analysis involving the "nine point circle", which is the circle that can be constructed from any triangle in the plane. Of course I don't understand this well enough to copy/paste it without embarrassment, but greater minds than mine can read all about it at:

http://en.wikipedia.org/wiki/Nine_point_circle

:-)

Posted by Penny on 2004-02-19 18:59:18