Question

* BRAINLY TEASER *

Hello everybody! What do you think about this problem?

// Look at the given graph and calculate the area of the big square //

Answer 1

Hey guys, look at this :: 

Firstly, we need to take care of the bigger circle's radius :: 
$x + 6 = (x + 2) + 4$

The next step is calculating the diameter of the smaller one ::
$x + (x+6) = 2x + 6$

Ok, knowing that, we can say that the Radius of the small circle is
$x + 3$

Now, we can see, that there's a right triangle created with centres of the two circles and top intersection point, to which we can apply the Pythagoras law. 
$3^2 + (x+2)^2 = (x+3)^2$
 $x=2$

We know that the two lines in the picture cutting the whole square in it's very middle. knowing our $x$ we can now calculate a half of its side, being
$6+x = 8$ so the side of the square is $2*8=16$. 

Therefore, the whole are is 
$16^{2}=256units^{2}$

I hope this is clear enough :) 

Answer 2

 see the diagram.

We use Pythagoras theorem to solve the problem. Let the Radii of bigger and smaller circles be :  R and r respectively.

AB = AC + CB
=> 2 R = 6 + 2 r
=> R = r + 3        --- (1)

In ΔCOE,  OC = R - 6    and   OE = R - 4
=> CE² = (R-6)² + (R - 4)² = 2 [R² - 10 R +26 ]      --- (2)

In ΔOEB,   OB = R and  OE = R-4
=> EB² = (R-4)² + R² = 2 [R² - 4 R + 8]          --- (3)

Adding (1) and(2)
CB² = CE² + EB²
=>   (2 R - 6)² = 2 [ 2 R² - 14 R + 34 ]
=>  4 [R² + 9 - 6 R]  = 4 [R² - 7 R + 17]

=>  R = 8
=>  r = 5
=> B = 2 R = 16
=> Area of big square = 16² = 256