The logo opposite is constituted by two semicircles and by a quarter circle. Compare the area of domains A and B
I tried to compare the area of one of the semicircles to the area of a quarter of circles, to be able to express this relation according to areas A, B and C but with no luck
- Is there any way to solve that problem ?
Hint
If the diameter of semicircles is $d$, and C, A, B are the areas of the regions indicated by these letters, we have:
$ 2C+A+B=\frac{\pi}{4}d^2 $ because this is the area of a quarter of a circle of radius $r=d$
$ C+A=\frac{\pi}{8}d^2 $ because this is the area of a semicircle of radius $\frac{1}{2}d$
so $$ 2C+2A=2C+A+B $$