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
+-------+---------------+
|      /               /|
|     /               / |
|    /               /  |
|   /               /   |
|  /               /    |
| /               /     |
|/               /      |
+---------------+-------+
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 on-line 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 2008-04-14 11:53:24