Construct a large square ABCD with AB at the top.

Next construct a smaller square (A'B'C'D') inside ABCD, with any orientation and centre and join the corresponding corners.

This divides the region between the squares into four.

We will name these divisions (and their areas):

(N)orth = ABB'A'
(E)ast = BCC'B'
(S)outh = CDD'C'
(W)est = DAA'D'.

Show that the areas of these regions satisfy the equality
N+S = E+W.

Gofish - this was a HORRIBLE problem - horrible in that it took hold of me and would nto let go.  I started it yesterday, worked it all evening - I can do it IF AB is parrell to A'B' - will work the rest later.  Enjoyed it, lookign forward to seeing your answwer.

Posted by ceb on 2006-01-06 15:09:43