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A square is inscribed in a big circle and a small circle is inscribed in the square as shown in the figure above. (All of them are concentric and their center is the point O). If the radius of the big circle is √2 cm, what is the semi perimeter of the small circle?
  • a)
    1
  • b)
    2
  • c)
    3
  • d)
    π
  • e)
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
A square is inscribed in a big circle and a small circle is inscribed ...
Let us assume that
the radius of big circle = R
side of the square = S
radius of the small circle = r
Observe that the diameter of the big circle = diagonal of the square.
  • 2R = √2 * S
  • S = √2 * R
Also the diameter of the small circle = side of the square
  • 2r = S
  • 2r = √2 * R
​   
Semi perimeter of the small circle = πr = π(R/√2)
Putting R = √2 in the above equation, we get:
Semi perimeter of the small circle = π
Correct Answer: D
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