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Topic: Cyclic hexagon (Read 432 times) |
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NickH
Senior Riddler
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Cyclic hexagon
« on: May 18th, 2003, 12:19pm » |
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A hexagon with sides of length 2, 7, 2, 11, 7, 11 is inscribed in a circle. Find the radius of the circle.
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towr
wu::riddles Moderator
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Some people are average, some are just mean.
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Re: Cyclic hexagon
« Reply #1 on: May 18th, 2003, 1:46pm » |
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I'm getting imaginary numbers..
guess I'd better sleep on it..
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Wikipedia, Google, Mathworld, Integer sequence DB
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SWF
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Re: Cyclic hexagon
« Reply #2 on: May 18th, 2003, 9:05pm » |
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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
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NickH
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Re: Cyclic hexagon
« Reply #3 on: May 20th, 2003, 2:38pm » |
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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??
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