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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)

Comments: ( Back to comment list | You must be logged in to post comments.)
A first step | Comment 3 of 18 |
Any two consecutive sides can be swapped with each other and the hexagon will still be inscribed within the circle.

To see this, connect the diagonal formed by their endpoints. This triangle can be flipped over.

This means the sides can be reordered 2, 7, 11, 2, 7, 11.
Opposite diagonals are then diameters.
There are also rectangles in the picture, too.

Beyond that: I'm stuck.

-Jer
  Posted by Jer on 2004-06-02 14:29:04
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