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03 May 2020, 10:14
Kudos
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B
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Difficulty:
55%
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Question Stats:
57% (02:07) correct
43%
(02:59)
wrong
based on 35
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A square is inscribed in a circle, which is inscribed in a square, which is inscribed in a circle as shown above. What is the ratio of the circumference of the largest circle to the perimeter of the smallest square?
A. π : 1
B. π : 2
C. π : √2
D. 2 : √2
E. π : 4
Are You Up For the Challenge: 700 Level Questions
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03 May 2020, 10:40
Kudos
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Bunuel
Given: A square is inscribed in a circle, which is inscribed in a square, which is inscribed in a circle as shown above.
Asked: What is the ratio of the circumference of the largest circle to the perimeter of the smallest square?
Attachment:
Screenshot 2020-05-03 at 11.08.14 PM.png [ 28.37 KiB | Viewed 3275 times ]
Let us assume side of smallest square be 2.
Radius of inner circle = √2
Side of bigger square = 2√2
Radius of largest circle = 2
Circumference of largest circle = 4π
Perimeter of smallest square = 8
Ratio = 4π:8 = π:2
IMO B
Archit3110
Major Poster
03 May 2020, 10:47
Kudos
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let inner square diagonal be 4 which would be same as dia of inner circle
so side of inner square be 2√2 and perimeter ; 8√2
the dia of inner circle will be side of outer square whose digonal would then be 4√2 which would give the dia of the outer circle
so circumference of outer circle ; 2√2*2*pi and perimeter of inner square = 8√2
ratio ;
2√2*2*pi/ 8√2 = pi/2
OPTION B
so side of inner square be 2√2 and perimeter ; 8√2
the dia of inner circle will be side of outer square whose digonal would then be 4√2 which would give the dia of the outer circle
so circumference of outer circle ; 2√2*2*pi and perimeter of inner square = 8√2
ratio ;
2√2*2*pi/ 8√2 = pi/2
OPTION B
Bunuel
