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

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Math Expert
Joined: 02 Sep 2009
Posts: 58458
A and B are centers of two circles that touch each other externally  [#permalink]

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Updated on: 22 Jul 2019, 05:35
00:00

Difficulty:

15% (low)

Question Stats:

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

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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 [ 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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10 Oct 2018, 01:24
Bunuel wrote:

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

$$Area = πr^2 = π(5/2)^2 = (25/4)π$$

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

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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 [ 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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13 Oct 2018, 18:33
Bunuel wrote:

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.

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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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