Circle 1: centre (0,0), r=2. Circle 2: centre (0,2), r=2. Distance between centres d=2.
Intersection: y2=(y−2)2⇒y=1, giving x=±3.
Angle subtended at centre of circle 1 by the chord: θ=2π/3.
Segment area =21(4)(32π)−21(4)sin32π=34π−3.
By symmetry, total intersection area =2(34π−3)=38π−63=32(4π−33).