Calc 3 Problem

[ijnek]

So, a friend of mine and myself were working on this one problem.

The outer circle has radius 1 and the centers of the interior circles arcs lie on the outer circle. Find the area of the shaded region.

http://www.wolframalpha.com/input/?...2=2;+x^2+(y-1)^2=2;++(x-1)^2+y^2=2;+x^2+y^2=1
(The shaded region would be the center-most one)

Since then, we've been under the impression that you should take the area of one of the area's under the arc and subtract the other three in order to find the shaded region. The problem is in finding a way to do this properly, also we're rather rusty at calc at this point...mostly my fault, but this seems like a good place to ask as any for help.

 

[stapel]

The outer circle has radius 1 and the centers of the interior circles arcs lie on the outer circle. Find the area of the shaded region.

http://www.wolframalpha.com/input/?...2=2;+x^2+(y-1)^2=2;++(x-1)^2+y^2=2;+x^2+y^2=1
(The shaded region would be the center-most one)

Start with the algebra. (And maybe consider just the first quadrant, since the entire area will be four times of that.) What are the equations of the "lines" forming the edges of the figure? Where do those lines intersect? What then are the coordinates of the corner points?

Then we can move on to the calculus.