Let the radius of the big circle be r and the radius of the small circle be r.

R+r=a......( 1)

R-r=b.......(2)

( 1)+(2):2R=a+b

R=(a+b)/2

( 1)-(2):2r=a-b

r=(a-b)/2

S yin =πR? -πr？

=π[(a+b)？ /4-(a-b)？ /4]

=π/4[(a+b+(a-b)][a+b-(a-b)]

=π/4(2a*2b)

=πab