Equations of the given circles are
x2 + y2 = 4 ……….. (1)
(x - 2)2 + y2 = 4 ………….(2)
Equation (1) is a circle with centre O at the origin and radius 2.
Eqn. (2) is a circle with centre C (2, 0) and radius 2. Solving Eqn.
(1) and (2), we have.
(x - 2 )2 + y2 = x2 + y2
x2 – 4x + 4 + y2 = x2 + y2 + 4x = -4
⇒ x = 1 x = 1 which given y = ± √3
Thus the points of intersection of the given circles are A(1,√3) and A1(1,-√3) as shown in the fig.
Required area of the enclosed region OACA1O between circles
= 2 [area of the region ODCAO]
= 2 [area of the region ODAO + area of the region on DCAD]
