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(2): Solution  your reason to edit by Harry)
Yes, I've found that the special characters from the specialcharacter button on the comment editor give bad results, as in Ó for a capital sigma. It looks good here in the comment box, but I'm confident that once this is posted, that won't look like a capital sigma.

Posted by Charlie
on 20090719 13:07:02 