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
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)²/2)+ inverse cos(1-(7/x)²/2)+ inverse cos(1-(11/x)²/2) = pi radians or 180 degrees
7 works in the above equation to solve this.
Posted by Gamer
on 2004-06-02 22:27:10