Functions of perimeter and area of parts from two circles

Question

We have a circle with radius $1$. Next we draw a circle with radius $r$, whose center lay on the first circle, so $0\leqslant r\leqslant2$. When $r=0$ there is only $1$ part with $$C(0)=2\pi, S(0)=\pi$$ When $r=2$ there are $2$ parts with $$C_{1}(2)=2\pi, S_{1}(2)=\pi$$ $$C_{2}(2)=6\pi, S_{2}(2)=3\pi$$ For all other cases there are $3$ parts. There is only $1$ case when $2$ of them are the same ($r=1$) $$C_{1}(1)=\frac{4\pi}{3}, S_{1}(1)=\frac{2\pi}{3}-\frac{\sqrt{3}}{2}$$ $$C_{2}(1)=C_{3}(1)=2\pi, S_{2}(1)=S_{3}(1)=\frac{\pi}{3}+\frac{\sqrt{3}}{2}$$ Are there functions for perimeter and area for each of $3$ parts when $0<r<2$?