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# In the above figure, the two circles touch at C, and line AB is tangen

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Math Expert
Joined: 02 Sep 2009
Posts: 44656
In the above figure, the two circles touch at C, and line AB is tangen [#permalink]

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29 Nov 2017, 23:06
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Difficulty:

25% (medium)

Question Stats:

82% (00:36) correct 18% (00:41) wrong based on 38 sessions

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In the above figure, the two circles touch at C, and line AB is tangent to the smaller circle at O, which is also the center of the larger circle. If the length of AB = 8, what is the circumference of the smaller circle?

(A) 2π
(B) 4π
(C) 6π
(D) 8π
(E) 12π

[Reveal] Spoiler:
Attachment:

2017-11-30_1001_001.png [ 6.68 KiB | Viewed 542 times ]
[Reveal] Spoiler: OA

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Joined: 16 Oct 2017
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Re: In the above figure, the two circles touch at C, and line AB is tangen [#permalink]

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29 Nov 2017, 23:23
Bunuel wrote:

In the above figure, the two circles touch at C, and line AB is tangent to the smaller circle at O, which is also the center of the larger circle. If the length of AB = 8, what is the circumference of the smaller circle?

(A) 2π
(B) 4π
(C) 6π
(D) 8π
(E) 12π

[Reveal] Spoiler:
Attachment:
2017-11-30_1001_001.png

If AB = 8 => AO = 4
AO = OC = 4 = Diameter of small circle => r = 2
circumference of the smaller circle = $$2\pi * r = 4\pi$$
B
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Joined: 04 Jan 2015
Posts: 1029
Re: In the above figure, the two circles touch at C, and line AB is tangen [#permalink]

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30 Nov 2017, 11:49
1
KUDOS
Expert's post
Bunuel wrote:

In the above figure, the two circles touch at C, and line AB is tangent to the smaller circle at O, which is also the center of the larger circle. If the length of AB = 8, what is the circumference of the smaller circle?

(A) 2π
(B) 4π
(C) 6π
(D) 8π
(E) 12π

[Reveal] Spoiler:
Attachment:
2017-11-30_1001_001.png

If O, which is the centre of the larger circle, is the point at which AB is tangent to the smaller circle, then we can easily conclude that the radius of the larger circle = diameter of the smaller circle.

If r is the radius of the smaller circle and R the radius of the larger circle, then we can write :

$$2r = R$$
$$2r = \frac{AB}{2}$$
$$r = \frac{8}{4} = 2$$

Thus, the circumference of the smaller circle $$= 2πr = 2 *π* 2 = 4π$$

The correct answer is Option B.
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Re: In the above figure, the two circles touch at C, and line AB is tangen [#permalink]

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03 Dec 2017, 18:58
Bunuel wrote:

In the above figure, the two circles touch at C, and line AB is tangent to the smaller circle at O, which is also the center of the larger circle. If the length of AB = 8, what is the circumference of the smaller circle?

(A) 2π
(B) 4π
(C) 6π
(D) 8π
(E) 12π

[Reveal] Spoiler:
Attachment:
2017-11-30_1001_001.png

Since AB = 8, AO = BO = CO = 4.

We see that CO is the diameter of the smaller circle; thus the circumference of the smaller circle is 4 x π = 4π.

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Re: In the above figure, the two circles touch at C, and line AB is tangen   [#permalink] 03 Dec 2017, 18:58
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