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
d^{2} ≤ u^{2} + x^{2} + y^{2} + z^{2} < 2d^{2}.
(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 20090719 13:08:13 