perplexus.info :: Geometry : Framing

Framing (Posted on 2013-07-16)

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.

No Solution Yet Submitted by Danish Ahmed Khan

Rating: 4.0000 (1 votes)

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Solution

| Comment 3 of 5 |

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 - 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

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