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