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.

See the Lop-sided Hexagon Problem