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Updated on: 09 Sep 2019, 08:08
Originally posted by alex90 on 26 Apr 2013, 12:12.
Last edited by Gladiator59 on 09 Sep 2019, 08:08, edited 1 time in total.
Last edited by Gladiator59 on 09 Sep 2019, 08:08, edited 1 time in total.
Question stem and options fixed.
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
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58% (02:58) correct
42%
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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 radius of the small circle to the side of the square?
a \(\frac{1}{2}\)
b \(\frac{1}{4}(\sqrt{2} -1)\)
c \(\frac{1}{2}(\sqrt{2}-1)\)
d \(\sqrt{2} -1\)
e \(2 (\sqrt{2}-2)\)
a \(\frac{1}{2}\)
b \(\frac{1}{4}(\sqrt{2} -1)\)
c \(\frac{1}{2}(\sqrt{2}-1)\)
d \(\sqrt{2} -1\)
e \(2 (\sqrt{2}-2)\)
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Untitled.png [ 10.2 KiB | Viewed 10694 times ]
26 Apr 2013, 12:39
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alex90
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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General Discussion
26 Apr 2013, 15:45
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alex90
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)
