Question
Find the area of the region enclosed between the two circles x2 + y2 = 4 and (x - 2)2 + y2 = 4.
Solution
The equations of the given circles are
and
...(2)
Equation (1) is a circle with centre O at the origin and radius 2. Equation (2) is a circle with centre C(2, 0) and radius 2.
Solving equations (1) and (2), we have
or
or
or x = 1
from (1), 
the points of intersection of the given circles are 
Required area of the enclosed region OACA'O between the circles
= 2 [area of region ODCAO]
=2 [area of region ODAO + area of the region DCAD]
and
...(2)Equation (1) is a circle with centre O at the origin and radius 2. Equation (2) is a circle with centre C(2, 0) and radius 2.
Solving equations (1) and (2), we have
or
or
or x = 1
from (1), the points of intersection of the given circles are Required area of the enclosed region OACA'O between the circles
= 2 [area of region ODCAO]
=2 [area of region ODAO + area of the region DCAD]
