center of gravity of an arc



The shape given below:
From a sector of a cicle an arc is cut out. The angle of the sector is
theta. The radii are r1 and r2.
What is required is to find the center of gravity of the shape (shaded
with *), enclosed by thetha, r1 and (r1+r2).
An derivation along with the formula would be highly appreciated.


- - -
- - - * * *-
- - - * * * * * -
- - - * * * * * * * * -
- - - - * * * * * * * * -
- - - -* * * * * * * * * -
- <---- r1 ---> - <---- r2 ------> -
- - - -* * * * * * * * * -
- - - -* * * * * * * * * * -
- - -* * * * * * * * * * * -
- - -* * * * * * * * -
- - - ******* -
- - - * * -
- - -
Regds,
Raj.

.