Hi sucheta.lahiri,
If this is a GMAT question, then you should include the 5 answer choices. In many cases, the answers provide a clue as to how you might go about solving the problem (and potentially avoid most/all of the 'math').
This prompt can be approached in a couple of different ways. I'm going to walk you through how to add some lines to this picture so that you can use the implied angles to get to the correct answer. You can use a variation on TESTing VALUES to get to the solution.
1) To start, the prompt does NOT state if AB and AC are equal, so they clearly don't have to be. By extension, BC could be the diameter. Draw a new picture with that idea in mind.
2) Next, you can create triangle ABC. Since BC is the diameter, angle A must be 90 degrees. What does that make angle C?
3) Draw two radii out from the center to point A and point C. You now have an ISOSCELES triangle. Since you have angle C, you can fill in the other two angles.
4) With the central angle AOC [spoiler] = 80 degrees[/spoiler], you now know what Arc ABC is: 280 degrees. You can now calculate the arc length.
Final Answer: [spoiler](280/360)(36pi) = 28pi[/spoiler]
GMAT assassins aren't born, they're made,
Rich
