Given circles are x2+y2=1 ...(i) and (x−1)2+y2=1 ...(ii) Centre of (i) is O(0,0) and radius =1
Both these circle are symmetrical about x-axis solving (i) and (ii), we get, −2x+1=0 ⇒ x=
1
2
then y2=1−(
1
2
)2=34 ⇒y=
√3
2
∴ The points of intersection are P(
1
2
,
√3
2
) and Q(
1
2
,−
√3
2
) It is clear from the figure that the shaded portion in region whose area is required. ∴ Required area = area OQAPO =2× area of the region OLAP = 2 ×( area of the region OLPO + area of LAPL )