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Hexagonal Dilemma (Posted on 2004-06-02) Difficulty: 4 of 5
A hexagon with sides of length 2, 7, 2, 11, 7, 11 is inscribed in a circle. Find the radius of the circle.

As suggested, *if* it matters, you may assume that the sides listed are given in order

No Solution Yet Submitted by SilverKnight    
Rating: 4.0000 (5 votes)

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No Subject | Comment 6 of 18 |

I don't fully understand Charlie's solution. Mine uses the law of cosines:

Divide the circle into "wedges" such that each are isosceles.

All the C angles (the ones between the two congruent sides) in the different triangles add up to pi radians or 180 degrees (since there are duplicates) This means x is a and b in these cases:

inverse cos(1-(2/x)/2)+ inverse cos(1-(7/x)/2)+ inverse cos(1-(11/x)/2) = pi radians or 180 degrees

7 works in the above equation to solve this.

  Posted by Gamer on 2004-06-02 22:27:10
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