Calculate AB, Find the length, Find the area of the shaded region (A long one)

So to start off, I already graphed the system of inequalities on the set of axes, I as well found the coordinates of the points of intersection algebraically. But I am now at a loss, I do not understand how to do the following problems, I'm a little rusty on Chords(I believe thats what this is called) so any help is appreciated. In any case, here is the problem:

Graph the following system of inequalities on the same set of axes:

http://i.imgur.com/Ket2iKe.jpg

Now I just need to do the following:

Calculate AB

Calculate the length of arc AB

Calculate the area of the shaded region

However I do not know how, and as I stated earlier any help is appreciated, please and thank you!

Re: Calculate AB, Find the length, Find the area of the shaded region (A long one)

Circular Segment -- from Wolfram MathWorld tells you all you should need to know to finish the problem.

The circle radius here is 3. You can find the length of AB by finding the distance between it's endpoints which you've calculated.