Bunuel wrote:

The two circles above have centers at A and B, and their circumferences are x and y respectively. If the two circles touch at one point, what is the distance between A and B?

A. \(2\pi x + 2\pi y\)

B. \(\frac{x+y}{2\pi}\)

C. \(\frac{\pi}{x+y}\)

D. \(\pi x + \pi y\)

E. \(\frac{x+y}{\pi}\)

Attachment:

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The distance from A to B is the sum of the radii of Circles A and B.

We use the circumference formula C = 2πr. For circle A, we are given that the circumference is x, so we have:

x = 2πr

r =x/2π

Similarly, for Circle B, we solve for its radius:

y = 2πr

r = y/2π

The radius of circle A is x/2π, and the radius of circle B is y/2π, so the distance between A and B is:

x/2π + y/2π = (x + y)/2π

Answer: B

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