SOLUTION: Find the perimeter of square which is inscribed in a circle which is also inscribed in another square whose diagonal is 20cm.

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Question 1014341: Find the perimeter of square which is inscribed in a circle which is also inscribed in another square whose diagonal is 20cm.
Answer by ikleyn(52788) About Me  (Show Source):
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Find the perimeter of square which is inscribed in a circle which is also inscribed in another square whose diagonal is 20cm.
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Let us start with the square whose diagonal is 20 cm.

Its side measure is 20%2Fsqrt%282%29.

I will not explain it. It is clear without explanations, isn't it?


Then the diameter of the circle inscribed into this square is 20%2Fsqrt%282%29 cm. Correct ?


Now consider the square inscribed to the circle whose diameter is 20%2Fsqrt%282%29 cm.

The diagonal of this square is equal to the diameter 20%2Fsqrt%282%29 cm.

Hence, the side of this square is %2820%2Fsqrt%282%29%29%2A%28sqrt%282%29%2F2%29 cm = 10 cm.