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

(In reply to No Subject by Gamer)

My Excel solution is related to Gamer's law of cosines solution, in that I divided each of Gamer's isosceles triangles into two right triangles.  In each of these, the "opposite" side is half the length of the particular side of the hexagon, and the hypotenuse is the radius of the circle.  When you take the arcsine you then have half the vertex angle of one of Gamer's isosceles triangles, so to get the full vertex angle you need twice the arcsine of half the hex-side divided by the radius.

Then, I used all the (duplicated) sides given, rather than half, and made them add up to 360 degrees rather than 180.

Posted by Charlie on 2004-06-03 08:04:28