Notes
semi-circles in a quarter circle solution

Semi-Circles in a Quarter Circle

Solution by Similarity

The radius of the quarter circle is twice that of the semi-circles, so the area of the segment of the quarter circle outside chord $A C$ is four times the area of the segment of one of the semi-circles outside chord $O B$, so has area $8$. Then the area of the segment of the semi-circle outside chord $A B$ is the same as that outside chord $O B$, so shaded region has area $8 - 2 - 2 = 4$.