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# The Quadrilateral shown above is a square. Four circles are

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Intern
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26 Apr 2013, 12:12
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Difficulty:

75% (hard)

Question Stats:

61% (02:56) correct 39% (02:36) wrong based on 85 sessions

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The Quadrilateral shown above is a square. Four circles are tangent to the sides of the square and the small circle in the centre is tangent to each of the four circles. What is the ratio of the small circle to the side of the square?
a 1/2
b 1/4(\sqrt{2} -1)
c 1/2(\sqrt{2}-1)
d \sqrt{2} -1
e 2 (\sqrt{2}-2)
[Reveal] Spoiler: OA

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Re: The Quadrilateral shown above is a square. Four circles are [#permalink]

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26 Apr 2013, 12:39
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alex90 wrote:
The Quadrilateral shown above is a square. Four circles are tangent to the sides of the square and the small circle in the centre is tangent to each of the four circles. What is the ratio of the small circle to the side of the square?
a 1/2
b 1/4(\sqrt{2} -1)
c 1/2(\sqrt{2}-1)
d \sqrt{2} -1
e 2 (\sqrt{2}-2)

Lets assume that the radius of the big circle is 1.
Create a square connecting all the centers (look picture). Its side is 2, it diagonal is $$2\sqrt{2}$$, this if formed by 2 radius and the diameter of the smaller circle
$$2\sqrt{2}-2(=2*radiusBig)=diameterSmall$$ $$2(\sqrt{2}-1)=diamSmall$$
so radius small = $$\sqrt{2}-1$$

The ratio radius to side square (= 4) is $$(\sqrt{2}-1)/4$$
B
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Re: The Quadrilateral shown above is a square. Four circles are [#permalink]

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26 Apr 2013, 15:45
alex90 wrote:
The Quadrilateral shown above is a square. Four circles are tangent to the sides of the square and the small circle in the centre is tangent to each of the four circles. What is the ratio of the small circle to the side of the square?
a 1/2
b 1/4(\sqrt{2} -1)
c 1/2(\sqrt{2}-1)
d \sqrt{2} -1
e 2 (\sqrt{2}-2)

Is this question copied from the OG verbatim?

The section I highlighted in red seems to fail to aknowledge what ratio they asking (diameter of small circle vs side of square? Circumference of circle vs side of square? etc)
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Re: The Quadrilateral shown above is a square. Four circles are [#permalink]

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29 Apr 2013, 02:45
I considered it as ratio of radius of small circle to the side of the square (yes, the question lacks clarity as to what ratio asked for)

Considering 2 as side of the square

(sqrt2 - 1)/2 = Radius of small circle
2 = Side of Square;Solving it further, we get ans = 1/(4.sqrt2-1)
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Re: The Quadrilateral shown above is a square. Four circles are [#permalink]

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01 May 2015, 03:11
the wording of this problem is bad. it is not from og.

ok, the concept tested is simple.
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Re: The Quadrilateral shown above is a square. Four circles are [#permalink]

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14 Nov 2016, 12:32
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Re: The Quadrilateral shown above is a square. Four circles are   [#permalink] 14 Nov 2016, 12:32
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