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# Maximum number of points that 10 circles of different radii intersect

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Intern
Joined: 25 Oct 2016
Posts: 5
Maximum number of points that 10 circles of different radii intersect [#permalink]

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25 Oct 2016, 12:22
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Question Stats:

60% (01:03) correct 40% (01:22) wrong based on 98 sessions

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What is the maximum number of points that 10 circles of different radii intersect?

A: 24
B: 26
C: 33
D: 90
E: 100
[Reveal] Spoiler: OA
Intern
Joined: 18 Sep 2016
Posts: 49
Re: Maximum number of points that 10 circles of different radii intersect [#permalink]

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25 Oct 2016, 12:39
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sitagupta385 wrote:
What is the maximum number of points that 10 circles of different radii intersect?

A: 24
B: 26
C: 33
D: 90
E: 100

the maximum number of points that two circles intersect is two.

therefore, each of these 10 circles intersect two point with each of the other 9 circles.

as a consequence, the number of these points is equal to two times the number of combination of the 10 circles.

$$2*\frac{(10!)}{(2!*10!)}= 90$$

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Intern
Joined: 22 Jan 2015
Posts: 15
Re: Maximum number of points that 10 circles of different radii intersect [#permalink]

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01 Feb 2017, 00:22
sitagupta385 wrote:
What is the maximum number of points that 10 circles of different radii intersect?

A: 24
B: 26
C: 33
D: 90
E: 100

=n(n-1)
=10*9
=90 (D)
Intern
Joined: 29 Dec 2015
Posts: 4
Re: Maximum number of points that 10 circles of different radii intersect [#permalink]

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26 Feb 2017, 15:25
Every circle intersects with another circle at max 2 points. Every circle interacts with a total of 9 circles. So, every circle has a max of 18 intersections (2*9). There are 10 circles, so 2*9*10 intersections. However, every intersection in counted twice. therefore we must divide by 2. this gets us to 9*10=90.
Re: Maximum number of points that 10 circles of different radii intersect   [#permalink] 26 Feb 2017, 15:25
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# Maximum number of points that 10 circles of different radii intersect

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