A friend of mine sent me this picture some time ago, telling me to solve this. I thought this problem pretty interesting so I thought that I should try to solve it. After some time, I finally did it.
In this problem, you are supposed to find out the area of the square containing the circles with the given information you have on the picture. Got any idea how to solve it? Read more to find out! š
At first, glimpse I didn’t see it but after a little thinking, I realized that I have enough of information to solve this problem. All I needed to do was sit down and get drawing lines and triangles.
When I drew a sketch 
I was sure, this problem is possible to be solved by a mere Pythagoras theorem and that a hard problem like this had turned into quite an easy one.
As you can see on the picture, triangles ABC and DEC are similar to each other. There is much information we can get from this sketch.
At first, I found out the size of BC, then sides AB and AC with help of two right triangles (ABS and ACS). The rest was quite easy, I used another right triangle and created an equation with one unknown variable and I was good to go!
See? Not that hard!
EDIT:
My friend showed me recently that there is another very simple solution, in which he used sine ans cosine and their deffinition in right triangles.
Welcome to the madhouse! 
Neat : ) . Another solution which I see is that you can use the fact that the vertical in the smaller circle which you called b-4 is the geometric mean (square root of the product of) the two parts that line splits the diameter into. So if x and y were the two segments left and right of the center on the x-axis one equation would be
and $6 + x = y$ which could be combined and solved for one in turn. Maybe the picture in http://en.wikipedia.org/wiki/Semicircle clears up the 
-thing and formally I think it is Prop 25 Book 5 in the Elements.
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