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29 Nov 2017, 23:06
Kudos
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
(low)
Question Stats:
89% (00:48) correct
11%
(01:12)
wrong
based on 49
sessions
History
Date
Time
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Not Attempted Yet
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 1947 times ]
29 Nov 2017, 23:23
Kudos
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Bunuel
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
30 Nov 2017, 11:49
Kudos
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Bunuel
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.
