A rectangle ABCD is circumscribed around a
rhombus AECF. The long sides of the rectangle coincide with two sides of the rhombus. Also, the rhombus and the rectangle share a common diagonal AC.
B E A
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C F D
What are the smallest dimensions when all the lengths AB, BC, AE, AC and EF are integers?
Find a parameterization of all such integral rectangle/rhombus pairs.
I've just come online and caught it. I've something lengthy to consider here.
I would observe however that BC is quite important if ΔBCE, ΔABC and ΔEFX, er, X? CX=FD, are to be Pythagorean triangles.
Let me see some other thoughts before I make my post.

Posted by brianjn
on 20080414 11:53:24 