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: Solution - your reason to edit by brianjn)

No, I typed it in on-line. It's always worked before.

One of life's many mysteries..

Thanks for your concern anyway.

Posted by Harry on 2009-07-18 16:53:08