Given a rectangle with diagonal length d. On each side pick an arbitrary point that is not a corner.
Let u, x, y, and z be the side lengths of the convex quadrilateral determined by these four points.

Prove that

   d2 ≤ u2 + x2 + y2 + z2 < 2d2.

(In reply to re(3): Solution - your reason to edit by Charlie)

On the other hand, I could check "view source" and put int the html code for a capital sigma: Ó

 

and, well, it still didn't work.

Edited on July 19, 2009, 1:08 pm

Posted by Charlie on 2009-07-19 13:08:13