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

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

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New post 29 Nov 2017, 23:06
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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
2017-11-30_1001_001.png [ 6.68 KiB | Viewed 626 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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New post 29 Nov 2017, 23:23
Bunuel wrote:
Image
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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New post 30 Nov 2017, 11:49
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Bunuel wrote:
Image
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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New post 03 Dec 2017, 18:58
Bunuel wrote:
Image
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.

Answer: B
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Re: In the above figure, the two circles touch at C, and line AB is tangen &nbs [#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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