The cyclic octagon ABCDEFGH has sides a, a, a, a, b, b, b, b respectively. Find the radius
of the circle that circumscribes ABCDEFGH in terms of a and b.
Let O be the circumcenter. As noted by
Steve and Broll  DOF = DOE + EOF = 90.
DEF = DEO + OEF
= (90  DOE/2) + (90  EOF/2)
= 180  (DOE + EOF)/2
= 180  45
= 135
2R^2 = DF^2
= DE^2 + EF^2  2DEEFcos(135)
= a^2 + b^2  2ab[1/sqrt(2)]
R = sqrt([a^2 + b^2 + ab*sqrt(2)]/2)

Posted by Bractals
on 20130718 10:55:00 