SOLUTION: If a square is inscribed in a circle with center O and a radius of 2, what is the perimeter of the square?

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Question 197702: If a square is inscribed in a circle with center O and a radius of 2, what is the perimeter of the square?
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
If a square is inscribed in a circle with center O and a radius of 2, what is the perimeter of the square?

Let s repreent a side of the square:



Draw another radius:



That is a right triangle. So we use the Pythagorean
theorem to find s:

c%5E2=a%5E2%2Bb%5E2
s%5E2=2%5E2%2B2%5E2
s%5E2=4%2B4
s%5E2=8
s=sqrt%288%29
s=sqrt%284%2A2%29
s=sqrt%284%29sqrt%282%29
s=2sqrt%282%29

So that's the length of a side of the square.
Since there are 4 sides, we multiply by 4 and
the perimeter is

4%2A2sqrt%282%29
8sqrt%282%29

Edwin