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
2R^2 = |DF|^2
= |DE|^2 + |EF|^2 - 2|DE||EF|cos(135)
= a^2 + b^2 - 2ab[-1/sqrt(2)]
R = sqrt([a^2 + b^2 + ab*sqrt(2)]/2)
Posted by Bractals
on 2013-07-18 10:55:00