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Two circles inside a square are externally tangent to each other and are tangent to certain sides of the square as shown. The perimeter of the square is  What is the sum of the circumferences of the two circles?

 Feb 19, 2021
edited by Guest  Feb 19, 2021
 #1
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Two circles inside a square are externally tangent to each other and are tangent to certain sides of the square as shown.

The perimeter of the square is ????

 Feb 19, 2021
 #3
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2+sqrt(2)

Guest Feb 19, 2021
 #2
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Sorry the perimeter of the square is 2 + sqrt(2)

 Feb 19, 2021
 #4
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Since the perimeter of the square is 2*sqrt(2), the side length of one side of the square is sqrt(2)/2. The diagonal of that square is then equal to sqrt(2)/2*sqrt(2) = 1.

Let x be the radius of one circle, and let y be the radius of the other circle. 

Notice that the diagonal is equal to x*sqrt(2) + x + y*sqrt(2) + y.

. Therefore,  x + y = sqrt(2) - 1.

Since the sum of the circumference of the circle is 2 times the radius times pi, just multiply 2pi to get the final answer: 2*sqrt(2)*pi - 2*pi.

 Feb 20, 2021

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