The cyclic octagon ABCDEFGH has the sides a√2, a√2, a√2, a√2, b, b, b and b respectively in that order. Each of a, b and r are positive integers, where r is the radius of the circumcircle.

Analytically determine:

(i) The minimum value of a with a < b

(ii) The minimum value of b with a > b

(In reply to re: Solution by Bractals)

Let (x,y,z) be a PT with z > y > x.  From the right triangle r > a+(b/2) > b/2.  Then z=r, y=a+(b/2) and x=b/2.  If y>3x then the PT will generate a solution with a>b, similarily, if 3x>y then the solution will have b>a.

Posted by Brian Smith on 2007-04-24 01:00:13