I found this problem on a thread on Stack overflow where it was posted as "job interview question". Unfortunately I cannot find the question. But I saved the picture and just cannot figure it out.
The problem is to calculate the area of the crescent.
Best Answer
Assuming AD is the diameter of the smaller circle and C is the center of the larger circle.
If $CD = x$ then, $CE = 4+x$.
Note that angle DEA is a right triangle.
We have by the similarity of triangles EDC and ACE that
$\frac{x}{4+x} = \frac{4+x}{9+x}$
Solving gives $x = 16$. Thus the radius of larger circle is $25$. The radius of the smaller circle is $\frac{x + 9+x}{2} = 20.5$
Area of the crescent = $\pi ((25)^2 - (20.5)^2) = 204.75 \times \pi$