Here is another good problem from Five Hundred Mathematical Challenges:

“Problem 100.  A hexagon inscribed in a circle has three consecutive sides of length a and three consecutive sides of length b. Determine the radius of the circle.”

This problem made me think of the Putnam Octagon Problem.  Again my approach might be considered a bit pedestrian.  500 Math Challenges had a slightly slicker solution.

Answer.

See the Lop-sided Hexagon Problem for solutions.