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09 Dec 2019, 01:18
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Difficulty:
45%
(medium)
Question Stats:
66% (02:06) correct
34%
(02:24)
wrong
based on 80
sessions
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A circle C is drawn around a square S such that the sides of the square become the four chords of the circle. What is the area of square S?
(1) Had a circle been drawn such that the four sides of square S were tangents to the circle, the area of the circle would be 30 square centimetres less than the area of circle C
(2) Had a circle been drawn with the diagonal of square S as its radius, the area of the circle have been 180 square centimetres more than the area of circle C
Are You Up For the Challenge: 700 Level Questions
(1) Had a circle been drawn such that the four sides of square S were tangents to the circle, the area of the circle would be 30 square centimetres less than the area of circle C
(2) Had a circle been drawn with the diagonal of square S as its radius, the area of the circle have been 180 square centimetres more than the area of circle C
Are You Up For the Challenge: 700 Level Questions
09 Dec 2019, 12:19
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Let side of the square =a
Radius of the circle C= 1/2* diagonal of square= \(\frac{1}{2}*\sqrt{2}a\)
Area of circle C= \(pi*\frac{a^2}{2}\)
Statement 1-
Had a circle been drawn such that the four sides of square S were tangents to the circle, it's radius would have half of the side of the square.
(\(pi*\frac{a^2}{2}\)) - (\(pi*\frac{a^2}{4}\)) = 30
We can find a^2.
Sufficient
Statement 2-
(\(pi*2*a^2\)) - (\(pi*\frac{a^2}{2}\))= 180
We can find a^2.
Sufficient
Radius of the circle C= 1/2* diagonal of square= \(\frac{1}{2}*\sqrt{2}a\)
Area of circle C= \(pi*\frac{a^2}{2}\)
Statement 1-
Had a circle been drawn such that the four sides of square S were tangents to the circle, it's radius would have half of the side of the square.
(\(pi*\frac{a^2}{2}\)) - (\(pi*\frac{a^2}{4}\)) = 30
We can find a^2.
Sufficient
Statement 2-
(\(pi*2*a^2\)) - (\(pi*\frac{a^2}{2}\))= 180
We can find a^2.
Sufficient
Bunuel
28 Jun 2021, 07:45
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