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# A circle passes through the center of a larger circle, as shown above.

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Math Expert
Joined: 02 Sep 2009
Posts: 58453
A circle passes through the center of a larger circle, as shown above.  [#permalink]

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02 Sep 2016, 05:54
00:00

Difficulty:

5% (low)

Question Stats:

85% (00:58) correct 15% (01:14) wrong based on 169 sessions

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A circle passes through the center of a larger circle, as shown above. The circumference of the larger circle is how many times the circumference of the smaller circle?

A. √2
B. 2
C. 3
D. 4
E. 9

Attachment:

T6105.png [ 6.82 KiB | Viewed 2957 times ]

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Joined: 03 Jul 2016
Posts: 68
Re: A circle passes through the center of a larger circle, as shown above.  [#permalink]

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02 Sep 2016, 06:15
Say R1 and r2 are the radii of the larger circle and smaller circle respectively.

R1 = 2r2

ratio of circumference of the larger to smaller circle is = 2*pie*R1/ 2*pie*r2 => 2

B
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Joined: 12 Sep 2015
Posts: 4009
Re: A circle passes through the center of a larger circle, as shown above.  [#permalink]

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02 Sep 2016, 08:23
1
Top Contributor
Bunuel wrote:

A circle passes through the center of a larger circle, as shown above. The circumference of the larger circle is how many times the circumference of the smaller circle?

A. √2
B. 2
C. 3
D. 4
E. 9

Attachment:
T6105.png

As we can see, (the diameter of the smaller circle) = (radius of larger circle)
If we let the diameter of the smaller circle = 1, then the radius of larger circle = 1
This means the DIAMETER of the larger circle = 2

Now let's find the CIRCUMFERENCE of each circle

Formula: circumference = (diameter)(pi)
Circumference of small circle = (1)(pi)
Circumference of larger circle = (2)(pi)

So, the circumference of the larger circle is 2 TIMES the circumference of small circle.

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Joined: 01 May 2016
Posts: 72
Location: United States
GPA: 3.8
A circle passes through the center and edge of a larger circle, as  [#permalink]

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11 Mar 2018, 09:42
Attachment:

12.png [ 6.75 KiB | Viewed 1332 times ]

A circle passes through the center and edge of a larger circle, as shown above. The diameter of the smaller circle is how many times the radius of the larger circle?

a. 1/4

b. 1/2

c. 1

d. 2

e. 4
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Math Expert
Joined: 02 Aug 2009
Posts: 7978
Re: A circle passes through the center and edge of a larger circle, as  [#permalink]

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11 Mar 2018, 10:06
Tridhipal wrote:
Attachment:
12.png

A circle passes through the center and edge of a larger circle, as shown above. The diameter of the smaller circle is how many times the radius of the larger circle?

a. 1/4

b. 1/2

c. 1

d. 2

e. 4

Not a 700+ level question in any way..

You have to be just careful about which circle's dia and which circle's radius..
Clearly the Dia of SMALLER circle=radius of BIGGER circle..
So RATIO =1

C
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Math Expert
Joined: 02 Sep 2009
Posts: 58453
Re: A circle passes through the center of a larger circle, as shown above.  [#permalink]

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11 Mar 2018, 11:10
Tridhipal wrote:
Attachment:
12.png

A circle passes through the center and edge of a larger circle, as shown above. The diameter of the smaller circle is how many times the radius of the larger circle?

a. 1/4

b. 1/2

c. 1

d. 2

e. 4

Merging topics. Please search before posting. Thank you.
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Re: A circle passes through the center of a larger circle, as shown above.   [#permalink] 11 Mar 2018, 11:10
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