Bunuel wrote:
What is the area of circle O ?
(1) The ratio of the area of the square circumscribed about circle O to the square inscribed in it is 2 to 1.
(2) The ratio of the length of a side of the square circumscribed about circle O to the diameter of O is 1 to 1.
DS21214
STATEMENT 1: Let the radius of circle = r units
Let the side of the inscribed square be a units.
Let's focus on the inscribed square first.
The diagonal of this square will be the diameter of the circle. Using pythagoras algorithm, we have -
\((2r)^2 = a^2 + a^2 \)
Upon solving, we get : a = \sqrt{2r}
For the circumbscribed square, the diameter of the circle = the side of the square.
Therefore, side of sqaure = 2r
The area of the square circumscribed about circle O ^ The area of the square inscribed in circle O
= 2r^2 ^ sqrt(2)
= 2 : 1
This is already stated in STATEMENT 1. The radius of the circle can be of any measurement.
Insufficient (BCE)
STATEMENT 2:As discussed in statement 1, the ratio of the length of the square circumscribed = 2r = diameter of the circle.
Thus, their ratio is 1:1.
Again, we already knew this. The value of radius can be anything for this rule to hold true.
Insufficient (CE)
Even upon combiing the two statements, we don't have a fixed value of the radius, thus,
(E). _________________
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