SOLUTION: Two circles each with radius of 1 are inscribed so that their centers lie along the diagonal of the square . Each circle is tangent to two sides of the square and they are tangent

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> SOLUTION: Two circles each with radius of 1 are inscribed so that their centers lie along the diagonal of the square . Each circle is tangent to two sides of the square and they are tangent       Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 319088: Two circles each with radius of 1 are inscribed so that their centers lie along the diagonal of the square . Each circle is tangent to two sides of the square and they are tangent to each other. Find the area between the circles and the square.
Found 2 solutions by Fombitz, edjones:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!

.
.
.
I think this is what you mean.
You can find the length of the side of the square by using the radii of the circle.
The length of the green line can be calculated using the hypotenuse 2R since that triangle is a right isoceles triangle.
The green line length, L is,
L%5E2%2BL%5E2=%282R%29%5E2
2L%5E2=4R%5E2
L=2R%5E2
L=sqrt%282%29%2AR
The side of the square is then,
S=R%2BL%2BR
S=2R%2Bsqrt%282%29R
S=R%282%2Bsqrt%282%29%29
So then the area of the square is,
As=R%5E2%282%2Bsqrt%282%29%29%5E2
and the area of the two circles is,
Ac=2%2Api%2AR%5E2
So then the area between the two would be the difference,
highlight%28A=R%5E2%28%282%2Bsqrt%282%29%29%5E2-2%2Api%29%5E2%29%29+or approximately,
A=5.37R%5E2
For R=1,
A=5.37

Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
The diagonal of the square is 4.
2a^2=c^2 Pythagoras
2a^2=16
a^2=8
a=sqrt(4*2)
=2sqrt(2) side of square
a^2=8 area of square
.
A=pi*r^2
=pi area of one of the circles
2pi area of both circles
.
8-2pi= area between the circles and the square.
.
Ed