Hi praveensahni,
When posting GMAT questions, you should be sure to post the answer choices along with the prompt (in some cases, the answer choices provide a huge hint as to how to answer the question or how to avoid a long, calculation-heavy approach).
I'm going to provide you with some 'hints' as to how to approach this question, so that you can re-attempt it:
1) A "regular" hexagon is a 6-sided shape that has 6 equal sides and 6 equal angles.
2) The total number of degrees in a hexagon is 720. Each of the 6 angles in THIS hexagon is a 120 degree angle.
3) Since this question involves a circle, the RADIUS of the circle will likely play a big role in the solution.
4) Draw the picture as described and draw in a radius from "A" to the center of the circle and from "C" to the center of the circle. Think about what you know about this triangle...
GMAT assassins aren't born, they're made,
Rich