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

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Joined: 02 Sep 2009
Posts: 47077
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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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

Attachment:

2017-11-30_1001_001.png [ 6.68 KiB | Viewed 576 times ]

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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

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 = $$2\pi * r = 4\pi$$
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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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30 Nov 2017, 11:49
1
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

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

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

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