I saw an example from math book that I don't really realize. If you look at attachment, then you see a drawing related to this example. There are two circle which are in the same size. Both radius are 12 cm. The points O and O1 are centers of the circles. If you look at attachment then you see that there are formed two equilateral triangle OO1B and OO1A. My task is to find a general area (the area which is between the points BOA and BO1A)

My math book says that better is at first to find half of the area. We get this when we disjoint an area of a sector OAB by(from?) an area of a triangular AOB. Because sector's angle is 120 degrees, then sector's area is: 1/3*pi*12^2=48*pi(cm^2)

Area(OAB)=[12^2*sqrt(3)]/4=36sqrt(3)(cm^2)

And according to this the required area = 2* [48*pi -36sqrt(3)]

Answer: The general area (the area which is between the points AOBO1) is 2* [48*pi -36sqrt(3)]

The following things need an explanation:

1) How to show that sector's angle is 120 degrees.

2) Don't understand that one: [48*pi -36sqrt(3)]

This approach seems to me confusing.

Please explain me. Thanks in advance.