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 'Within' includes 'on'? by e.g.)

If you also accept straight lines as zero curvature circles (i.e., of infinite radius, with the center at infinity) then you can also do without the condition about the points not being collinear...

Posted by Federico Kereki on 2004-02-19 15:09:40