smc

The requested area is the area of $C$ minus the area shared between circles $A$, $B$ and $C$. Let $M$ be the midpoint of $\overline{AB}$ and $D$ be the other intersection of circles $C$ and $B$. The area shared between $C$, $A$ and $B$ is $4$ of the regions between arc $\widehat{MD}$ and line $\overline{MD}$, which is (considering the arc on circle $B$) a quarter of the circle $B$ minus $△MDB$: $\frac{\pi r^2}{4}-\frac{bh}{2}$ $b=h=r=1$ (We can assume this because $\angle DBM$ is 90 degrees, since $CDBM$ is a square, due to the application of the tangent chord theorem at point $M$) So the area of the small region is $\frac{\pi }{4}-\frac{1}{2}$ The requested area is area of circle $C$ minus 4 of this area: $\pi 1^2-4\left(\frac{\pi }{4}-\frac{1}{2}\right)=\pi -\pi +2=2$ $\boxed{2}$.