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        riddles >> medium >> Cyclic hexagon
        
(Message started by: NickH on May 18^th, 2003, 12:19pm)

Title: Cyclic hexagon
Post by NickH on May 18^th, 2003, 12:19pm

A hexagon with sides of length 2, 7, 2, 11, 7, 11 is inscribed in a circle. Find the radius of the circle.

Title: Re: Cyclic hexagon
Post by towr on May 18^th, 2003, 1:46pm

I'm getting imaginary numbers..
guess I'd better sleep on it..

Title: Re: Cyclic hexagon
Post by SWF on May 18^th, 2003, 9:05pm

[hide]Noting that the two sides of length 7 are parallel means that
sin^-1(1/R)+sin^-1(11/2/R)=cos^-1(7/2/R)
which simplfies to 0=(R-7)*(2*R²+14*R+11)
The only positive root is R=7[/hide]

Title: Re: Cyclic hexagon
Post by NickH on May 20^th, 2003, 2:38pm

Very concise solution!

How much harder would the puzzle have been if I'd specified the order of the sides as 2,2,7,7,11,11? Not much... I guess??