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Updated on: 21 Sep 2015, 17:33
Originally posted by se7en14 on 12 Jan 2014, 20:19.
Last edited by ENGRTOMBA2018 on 21 Sep 2015, 17:33, edited 1 time in total.
Last edited by ENGRTOMBA2018 on 21 Sep 2015, 17:33, edited 1 time in total.
Formatted the question
Kudos
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
61% (02:04) correct
39%
(02:09)
wrong
based on 192
sessions
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If circle O is inscribed inside of equilateral triangle T, which of the following expresses the ratio of the radius of circle O to one of the sides of triangle T?
A) 1 to 2
B) 1 to \(\sqrt{2}\)
C) 1 to \(\sqrt{3}\)
D) 1 to 2\(\sqrt{2}\)
E) 1 to 2\(\sqrt{3}\)
No diagram is provided.
A) 1 to 2
B) 1 to \(\sqrt{2}\)
C) 1 to \(\sqrt{3}\)
D) 1 to 2\(\sqrt{2}\)
E) 1 to 2\(\sqrt{3}\)
No diagram is provided.
13 Jan 2014, 10:54
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se7en14
Dear se7en14,
I'm happy to help.
Here's a diagram:
Attachment:
equilateral with inscribed circle.JPG [ 15.35 KiB | Viewed 5728 times ]
https://magoosh.com/gmat/2012/the-gmats- ... triangles/
The sides have ratios of 1-2-sqrt(3). Here:
DE = 1
CE = 2
DC = \(\sqrt{3}\)
Now, notice that DC is half the side, because D is a midpoint of the side. This means
AC = 2*(DC) = \(2*\sqrt{3}\)
That's the length of the side. Therefore,
radius:side = 1: \(2*\sqrt{3}\)
Answer = (D)
Does all this make sense?
Mike
General Discussion
