AB is a Line Segment of Length 2a, with M as Mid-Point:

AB is a line segment of length 2a, with M as mid-point. Semicircles are drawn on one side with AM, MB and AB as diameter as shown in the above figure. A circle with centre O and radius r is drawn such that this circle touches all the three semicircles. The value of r is

1. 2a/ 3
2. a²/2
3. a/3
4. a/4