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 Solution by Harry)

"Edited, sadly, because all the indices and inequalty signs obtained from the extra font facility appeared as gobbledegook in the posted version. Why was that?"

Without seeing your original text I cannot tell, did you copy and paste into here from another application?  The text box provided does not like formats that may come from Word for instance.

The 3 tiered dropdown window may allow for some, I never use them but some other users may be able to advise more.

Posted by brianjn on 2009-07-17 22:59:13