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14 Oct 2019, 07:20
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C
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Difficulty:
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85% (01:59) correct
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The diameter of circle S is equal in length to a side of a certain square. The diameter of circle T is equal in length to a diagonal of the same square. The area of circle T is how many times the area of circle S ?
A. \(√2\)
B. \(√2 + 1\)
C. 2
D. \(\pi\)
E. \(\sqrt{2\pi}\)
A. \(√2\)
B. \(√2 + 1\)
C. 2
D. \(\pi\)
E. \(\sqrt{2\pi}\)
14 Oct 2019, 07:26
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Bunuel
Let the side of square = a & the radius of circle S & T are s & t respectively
The diameter of circle S is equal in length to a side of a certain square
--> 2s = a
--> s = a/2
The diameter of circle T is equal in length to a diagonal of the same square
--> 2t = √2a
--> t = a/√2
The area of circle T is how many times the area of circle S
--> \(\pi\)*t^2 = x*\(\pi\)*s^2
--> a^2/2 = x*a^2/4
--> x = 2
IMO Option C
22 Oct 2019, 15:20
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Bunuel
Since any two circles are similar, the ratio of their areas must be equal to the square of the ratio of their diameters.
\(A_T/A_S=(d_T/d_S)^2=(\sqrt{2}/1)^2=2\)
Answer: C
