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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