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Sub 505 (Easy)|   Geometry|      
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Bunuel
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The two circles above have centers at A and B, and their circumference 18 Jan 2018, 03:17
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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. \(\frac{x+y}{\pi}\)

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B
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The two circles above have centers at A and B, and their circumference 18 Jan 2018, 06:47
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2*pi*R = x
2*pi*r = y

Distance between the 2 centers = R + r = (x + y)/2*pi

Answer: B
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The two circles above have centers at A and B, and their circumference 18 Jan 2018, 07:13
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Bunuel

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

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\(2πR = x\)
\(2πr = y\)

So,\(R = \frac{x}{2π}\) & \(r = \frac{y}{2π}\)

Distance between A and B = Radius of A + Radius of B

So, Distance between A and B = \(\frac{x}{2π} + \frac{y}{2π}\)

Or, Distance between A and B = \(\frac{x+y}{2\pi}\), answer will be (B)
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The two circles above have centers at A and B, and their circumference 20 Jan 2018, 07:31
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Bunuel

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

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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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The two circles above have centers at A and B, and their circumference 12 Jul 2019, 19:02
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Bunuel

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

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The radius of circle A is x/2π, and the radius of circle B is y/2π, so the distance from A to B is x/2π + y/2π = (x + y)/2π.

Answer: B
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