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A square ABCD is inscribed in a circle of radius R. Another circle is inscribed in ABCD and a square EFGH is inscribed in this circle. The side EF is equal to
  • a)
    R
  • b)
    R/√2
  • c)
    R/2
  • d)
    R/√2
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
A square ABCD is inscribed in a circle of radius R. Another circle is ...
The diameter of the circle becomes the diagonal of the first square. So the side of the first square is R(2)1/2. This side becomes the diameter of the second circle as well as the diagonal of the second square. So the side of the second square will be R.
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Most Upvoted Answer
A square ABCD is inscribed in a circle of radius R. Another circle is ...
The diagonal of the smaller square EFGH is equal to the diameter of the larger circle. Since the larger circle has a radius R, its diameter is 2R.

Let x be the side length of the smaller square EFGH. The diagonal of a square is equal to √2 times the side length, so we have:

√2 * x = 2R

Dividing both sides by √2, we get:

x = 2R/√2 = R√2

Therefore, the side length EF is equal to R√2.

So the correct answer is b) R√2.
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A square ABCD is inscribed in a circle of radius R. Another circle is inscribed in ABCD and a square EFGH is inscribed in this circle. The side EF is equal toa)Rb)R/√2c)R/2d)R/√2Correct answer is option 'A'. Can you explain this answer?
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