This is the problem.
A circular corral of unit radius is enclosed by a fence. A goat inside the corral is tied to the fence with a rope of length $0 \le a \le 2$ (see figure). What is the area of the region (inside the corral) that the goat can graze? Check your answer with the special cases $a=0$ and $a=2$.
This is what I have so far.
I figured that I can't do filling with
PolarPlot and I wonder what are the alternative ways of showing the problem in Mathematica.
I think ultimately I will need something that look like this: (Blue is the shaded part)