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

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