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17 Sep 2021, 01:30
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Difficulty:
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61% (01:14) correct
39%
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In the figure above, FGHI is inscribed in the circle with center J. What is the ratio of the area of FGHI to the area of the circle?
(1) FGHI is a square.
(2) The area of the circle is 8π.
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1.jpg [ 10.33 KiB | Viewed 2578 times ]
17 Sep 2021, 02:00
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Statement 1-
Suppose the radius of the circle is R, then the diagonal of square(diameter of circle) is 2R.
We can find the sides of the square, hence the area too in terms of R and the area of circle in terms of R too.
Statement 1 is sufficient.
Statement 2
We don't know if the figure inscribed in the circle is a square or a rectangle, if it's a rectangle then we can visualise many rectangles of different lengths and breaths. We will basically get multiple ratios and hence the statement is insufficient.
Answer - A
Posted from my mobile device
Suppose the radius of the circle is R, then the diagonal of square(diameter of circle) is 2R.
We can find the sides of the square, hence the area too in terms of R and the area of circle in terms of R too.
Statement 1 is sufficient.
Statement 2
We don't know if the figure inscribed in the circle is a square or a rectangle, if it's a rectangle then we can visualise many rectangles of different lengths and breaths. We will basically get multiple ratios and hence the statement is insufficient.
Answer - A
Posted from my mobile device
20 Sep 2021, 00:12
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(1) FGHI is a square.
the radius of the circle is R
=> side length of square = \(R\sqrt{2}\)
=> Can calculate the area of the square and the area of the circle in term of R and then calculate the ratio
=> sufficient
(2) The area of the circle is 8π.
Don't know if the figure inscribed in the circle is which kind of quadrilateral
Can not calculate the area of FGHI
=> insufficient
=> Choice A
the radius of the circle is R
=> side length of square = \(R\sqrt{2}\)
=> Can calculate the area of the square and the area of the circle in term of R and then calculate the ratio
=> sufficient
(2) The area of the circle is 8π.
Don't know if the figure inscribed in the circle is which kind of quadrilateral
Can not calculate the area of FGHI
=> insufficient
=> Choice A
