SOLUTION: a circle is inscribed in a square and there's another small circle at the down part of the circle in the right side, how to get the area of the small square and circumference?

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Question 463746: a circle is inscribed in a square and there's another small circle at the down part of the circle in the right side, how to get the area of the small square and circumference?
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
Let s = the length of the edge of the square, and let r = radius of the smaller circle. ==> the radius of the circle inscribed in the square is s/2.
Then
by the Pythagorean theorem.
<==> %281%2Bsqrt%282%29%29%5E2r%5E2++%2B+s%281%2Bsqrt%282%29%29r+-+s%5E2%2F4+=+0, after simplification.
Applying the quadratic formula, we get
.
r = %28s%2F2%29%28%28sqrt%282%29+-+1%29%2F%28sqrt%282%29+%2B+1%29%29, or -s%2F2.
Eliminate the second value for r. (Why?)
From here just apply the formulas A+=+pi%2Ar%5E2 and C+=+2%2Api%2Ar to get the area and circumference of the small circle, respectively.