The area of the shaded part is equal to the area of the circle minus the area of the sector ABCO plus the area of the triangle AOC.

First, find the radius r of the circle, connect BO and AC at D, and extend BO with E. BEcause Be passes through the center of the circle and is the diameter, then ABE is a right triangle, AB is perpendicular to AE, ABC = 120, so ABE=60, so ARB=30, and according to the central angle, it is equal to twice the circumferential angle, so the angle AOB = 2aeb =.

The area of a circle is S=π*r*r, the area of a sector is S 1= the area of the third circle (angle AOC = 120) = π * r * r/3, and the area of a triangle AOC is S2=OD*AC/2.

So the shadow area S3=2π/3-(2π/3)/3+ (root number 2)* (the square root of 6) /2.

=4π/9+ (radical number 3)/6