**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 $a=2$.
> 
> 
> 

See figure:

![figure](https://i.stack.imgur.com/K99jc.jpg)

**This is what I have so far.**

[![attempt](https://i.stack.imgur.com/za4oN.png)](https://i.stack.imgur.com/za4oN.png)

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)** 

[![result](https://i.stack.imgur.com/K5Otv.png)](https://i.stack.imgur.com/K5Otv.png)