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m14 question 2

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Intern
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Joined: 15 Feb 2010
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m14 question 2 [#permalink] New post 17 May 2010, 15:30
if three circles having radii 1,2, and 3 respectively lie on a plane, do any two of these circles intersect?

1. centers of the circles form an equilateral triangle with height 2\sqrt{3}
2. centers of the circles do not lie on the same line.

i am unable to draw a picture with this
can anyone show me! :cry:
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Re: m14 question 2 [#permalink] New post 17 May 2010, 18:44
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I am unable to draw on the comment section as I don't have the technical skills. But visualizing this may not be necessary. The important thing is to look at statement one and rank the order of the circle radii with the sides of the equilateral triangle whose vertices are made from the circle centers. This ranking would be 1, 1.154.., 2,3. Therefore statement 1 is sufficient to answer the question of intersection. Statement 2 does not seem helpful.

Kudos if I helped please.
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Re: m14 question 2 [#permalink] New post 18 May 2010, 02:52
I didn't get :(

How you found these values = 1, 1.154.., 2,3 ?? Marked +1 kudos already :)

Please explain.
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Re: m14 question 2 [#permalink] New post 18 May 2010, 07:01
I've drawn a sketch that might help you. Height AG is equal to 2\sqrt{3}.
Image
[Reveal] Spoiler: Image
Attachment:
m14-02.png
m14-02.png [ 13.87 KiB | Viewed 631 times ]

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Re: m14 question 2   [#permalink] 18 May 2010, 07:01
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