Let the radius of the big circle be R and the radius of the small circle be R to connect OB, so that the vertical foot of OE⊥AB is E.
The shaded area is (R*R-r*r) pie =9 pie.
So R*R-r*r=9.
In the right triangle OEB
OB=R OE=r
So BE*BE=R*R-r*r=9.
So BE=3
So AB=6