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A and B are centers of two circles that touch each other externally

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A and B are centers of two circles that touch each other externally  [#permalink]

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New post Updated on: 22 Jul 2019, 05:35
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A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

95% (00:56) correct 5% (00:36) wrong based on 19 sessions

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Image
A and B are centers of two circles that touch each other externally, as shown in the figure. What is the area of the circle whose diameter is AB ?

(A) \(4\pi\)

(B) \(\frac{25\pi}{4}\)

(C) \(9\pi\)

(D) \(16\pi\)

(E) \(25\pi\)

Source: Nova GMAT
Difficulty Level: 550

Attachment:
circles.jpg
circles.jpg [ 26.87 KiB | Viewed 474 times ]

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Originally posted by Bunuel on 09 Oct 2018, 23:33.
Last edited by SajjadAhmad on 22 Jul 2019, 05:35, edited 1 time in total.
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Re: A and B are centers of two circles that touch each other externally  [#permalink]

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New post 10 Oct 2018, 01:24
Bunuel wrote:
Image
A and B are centers of two circles that touch each other externally, as shown in the figure. What is the area of the circle whose diameter is AB ?

(A) \(4\pi\)

(B) \(\frac{25\pi}{4}\)

(C) \(9\pi\)

(D) \(16\pi\)

(E) \(25\pi\)


Attachment:
circles.jpg


From the figure it may be inferred that AB = 5

i.e. Diameter of Circle = 5

i.e. Radius = 5/2

\(Area = πr^2 = π(5/2)^2 = (25/4)π\)

Answer: Option B
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Re: A and B are centers of two circles that touch each other externally  [#permalink]

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New post 10 Oct 2018, 01:41
As shown in the attachment:
Diameter of red circle is \(D=2+3=5\)
so radius is \(r=\frac{5}{2}\)
Area of circle is \(A=πr^2\)
\(A=π*(\frac{5}{2})^2\)
\(A= \frac{25π}{4}\)
Attachments

Capture.PNG
Capture.PNG [ 29.18 KiB | Viewed 367 times ]


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Re: A and B are centers of two circles that touch each other externally  [#permalink]

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New post 13 Oct 2018, 18:33
Bunuel wrote:
Image
A and B are centers of two circles that touch each other externally, as shown in the figure. What is the area of the circle whose diameter is AB ?

(A) \(4\pi\)

(B) \(\frac{25\pi}{4}\)

(C) \(9\pi\)

(D) \(16\pi\)

(E) \(25\pi\)


Attachment:
circles.jpg


Since the diameter of circle AB is 5, the radius is 5/2, and thus the area is (5/2)^2 x ? = 25?/4.

Answer: B
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Re: A and B are centers of two circles that touch each other externally   [#permalink] 13 Oct 2018, 18:33
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