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Re: There are three circles, with radii 2, 4 and 5, respectively [#permalink]
15 Jun 2013, 12:43

1

This post received KUDOS

There are three circles, with radii 2, 4 and 5, respectively, that lie on a plane. Do any two of these circles intersect with each other?

(1) The centres of the three circles lie on a straight line Not sufficient. Consider the case in which, even on the same line they are 1 away from each other ( hence they intersect) or the case in which they are 100 away from each other (hence they do not intersect)

(2) The greatest distance between the centres of any two of these circles is 7 Since even the distance between the 4 and 5 radius circle is 7, they will intersect. Those two circles intersect because the distance between their centers is less than 4+5=9. Sufficient
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It is beyond a doubt that all our knowledge that begins with experience.

What if centers of circles are 5 radius : (0,0) 4 radius : (0.5,0) 2 radius : (1,0)

Here, Centers are on straight line but circles are not intersecting. Hence it should be E right?

Thank you

(2) says that the greatest distance between the centres of any two of these circles is 7. In your examples this condition is not met.
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What if centers of circles are 5 radius : (0,0) 4 radius : (0.5,0) 2 radius : (1,0)

Here, Centers are on straight line but circles are not intersecting. Hence it should be E right?

Thank you

(2) says that the greatest distance between the centres of any two of these circles is 7. In your examples this condition is not met.

[/quote]

Dear Bunuel,

Sorry but I really didn't understand. It said GREATEST, that means distance can be zero to seven. I suppose in my example it's met. If it just said that the distance between any two circles is 7 then I guess your point is correct. Can you pls explain why GREATEST is not playing significant role here?

Re: There are three circles, with radii 2, 4 and 5, respectively [#permalink]
05 Nov 2013, 10:07

1

This post received KUDOS

Expert's post

Shashank1149 wrote:

Dear Bunuel,

Sorry but I really didn't understand. It said GREATEST, that means distance can be zero to seven. I suppose in my example it's met. If it just said that the distance between any two circles is 7 then I guess your point is correct. Can you pls explain why GREATEST is not playing significant role here?

Thank you

You misinterpreted the statement. It means that the distance IS 7 between the centers of 2 particular circles of the 3 but the distance between any other two of these circles is not more than that.
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