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# Three identical circles are arranged such that their diameters overlap

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Math Expert
Joined: 02 Sep 2009
Posts: 60467
Three identical circles are arranged such that their diameters overlap  [#permalink]

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11 Sep 2016, 05:20
00:00

Difficulty:

45% (medium)

Question Stats:

68% (01:05) correct 32% (00:52) wrong based on 69 sessions

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Three identical circles are arranged such that their diameters overlap the diameter of a larger circle, as shown above. What is the ratio of the radius of the larger circle to the diameter of a smaller circle?

A. 4/3
B. 1.5
C. 3
D. 6
E. 9

Attachment:

T6044.png [ 7.66 KiB | Viewed 1003 times ]

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Re: Three identical circles are arranged such that their diameters overlap  [#permalink]

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11 Sep 2016, 09:52
Bunuel wrote:

Three identical circles are arranged such that their diameters overlap the diameter of a larger circle, as shown above. What is the ratio of the radius of the larger circle to the diameter of a smaller circle?

A. 4/3
B. 1.5
C. 3
D. 6
E. 9

Attachment:
T6044.png

Diameter of larger is divided into 3 equal parts each being the diameter of a smaller circle.

Let diameter of larger be 3D, so diameter of one smaller = D.

Ratio of Radius of larger to Diameter of Smaller = 3D/(2 *D) = 3/2 =1.5 Answer B.
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Re: Three identical circles are arranged such that their diameters overlap  [#permalink]

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11 Sep 2016, 23:37
IMO B

Just plug in numbers:

I chose number 30 to be diameter of the larger circle since it has to be divided by three to get the diameters of the smaller circles. Hence 30/2 = 15 is the radius of the larger circle and 30/3 = 10 is the diameter of a smaller circle.

15/10 = 1.5
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Re: Three identical circles are arranged such that their diameters overlap  [#permalink]

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12 Sep 2016, 05:14
consider radius of smaller circle to be x
so diameter of smaller circle is 2x
there are 3 identical smaller circles
diameter of larger circle consists of diameter of 3 smaller circles in a straight line
diameter of larger circle is 6x
radius of smaller circle is 3x
radius of larger circle : diameter of smaller circle = 3x : 2x = 1.5
correct answer - B

+1 kudos if you like the solution
Re: Three identical circles are arranged such that their diameters overlap   [#permalink] 12 Sep 2016, 05:14
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# Three identical circles are arranged such that their diameters overlap

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