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# The two circles above have centers at A and B, and their circumference

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Math Expert
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The two circles above have centers at A and B, and their circumference  [#permalink]

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18 Jan 2018, 03:17
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5% (low)

Question Stats:

89% (01:07) correct 11% (01:05) wrong based on 62 sessions

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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. $$\frac{x+y}{\pi}$$

Attachment:

2018-01-18_1414.png [ 12.06 KiB | Viewed 998 times ]

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Marshall & McDonough Moderator
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Re: The two circles above have centers at A and B, and their circumference  [#permalink]

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18 Jan 2018, 06:47
2*pi*R = x
2*pi*r = y

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

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Re: The two circles above have centers at A and B, and their circumference  [#permalink]

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18 Jan 2018, 07:13
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:
2018-01-18_1414.png

$$2πR = x$$
$$2πr = y$$

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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Re: The two circles above have centers at A and B, and their circumference  [#permalink]

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20 Jan 2018, 07:31
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:
2018-01-18_1414.png

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

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# Scott Woodbury-Stewart

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Target Test Prep Representative
Status: Founder & CEO
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Re: The two circles above have centers at A and B, and their circumference  [#permalink]

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12 Jul 2019, 19:02
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:
2018-01-18_1414.png

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.

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Re: The two circles above have centers at A and B, and their circumference   [#permalink] 12 Jul 2019, 19:02
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