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The figure above represents two tangential wheels touching one another

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Bunuel
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The figure above represents two tangential wheels touching one another [#permalink] New post   29 Dec 2014, 09:04
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Tough and Tricky questions: Geometry.



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2014-12-29_2003.png
2014-12-29_2003.png [ 4.72 KiB | Viewed 2989 times ]
The figure above represents two tangential wheels touching one another at exactly one point. The larger wheel has a circumference of 6π and the smaller wheel has a circumference of 4π. If x and y are the centers of the wheels, what is the distance from point x to point y?

A. 5
B. 6
C. 10
D. 12
E. 15

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A
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Re: The figure above represents two tangential wheels touching one another [#permalink] New post   29 Dec 2014, 09:58
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The relation between circumference and radius of a circle is \(C=2\pi*r\). From that we can calculate the radii of the two circles:
\(r_x=2\)
\(r_y=3\)

As the two circles are tangent, the distance between the center points x and y is the sum of the radii, 5.

Answer A.
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Re: The figure above represents two tangential wheels touching one another [#permalink] New post   29 Dec 2014, 12:59
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Radius of bigger circle, r1 = 2πr = 6π, so r1= 3
Radius of smaller circle, r2 = 2πr = 4π, so r1= 2

It is said that the circle touches only at 1 point. so the line xy must be a straight line. Hence this will be the sum of radius of 2 circles = 5.

Answer is A
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Re: The figure above represents two tangential wheels touching one another [#permalink] New post   04 Jan 2015, 11:10
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radius of small circle => 2* pi *r =4*pi
=> r = 2

radius of big circle => 2*pi*R = 6*pi
=> R =3


distance = r+R = 5 (A)
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Re: The figure above represents two tangential wheels touching one another [#permalink] New post   02 Jan 2015, 01:17
Answer = A. 5

Distance between X & Y is sum of radius of Circle X & Circle Y

\(= \frac{6\pi}{2\pi} + \frac{4\pi}{2\pi}= 3\pi + 2\pi = 5\)
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Re: The figure above represents two tangential wheels touching one another [#permalink] New post   04 Jan 2015, 12:55
Bunuel wrote:

Tough and Tricky questions: Geometry.



Attachment:
2014-12-29_2003.png
The figure above represents two tangential wheels touching one another at exactly one point. The larger wheel has a circumference of 6π and the smaller wheel has a circumference of 4π. If x and y are the centers of the wheels, what is the distance from point x to point y?

A. 5
B. 6
C. 10
D. 12
E. 15

Kudos for a correct solution.



Circumference of larger wheel = 6π = 2πr => r=3
Circumference of smaller wheel = 4π = 2πr => r = 2

Distance between points x and y is equal to sum r of both wheels = 3+2 = 5

Ans A
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Re: The figure above represents two tangential wheels touching one another [#permalink] New post   04 Jan 2015, 12:56
Bunuel wrote:

Tough and Tricky questions: Geometry.



Attachment:
2014-12-29_2003.png
The figure above represents two tangential wheels touching one another at exactly one point. The larger wheel has a circumference of 6π and the smaller wheel has a circumference of 4π. If x and y are the centers of the wheels, what is the distance from point x to point y?

A. 5
B. 6
C. 10
D. 12
E. 15

Kudos for a correct solution.



Circumference of larger wheel = 6π = 2πr => r=3
Circumference of smaller wheel = 4π = 2πr => r = 2

Distance between points x and y is equal to sum r of both wheels = 3+2 = 5

Ans A
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Re: The figure above represents two tangential wheels touching one another [#permalink] New post   08 Jan 2015, 09:45
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Bunuel wrote:

Tough and Tricky questions: Geometry.



Attachment:
2014-12-29_2003.png
The figure above represents two tangential wheels touching one another at exactly one point. The larger wheel has a circumference of 6π and the smaller wheel has a circumference of 4π. If x and y are the centers of the wheels, what is the distance from point x to point y?

A. 5
B. 6
C. 10
D. 12
E. 15

Kudos for a correct solution.


OFFICIAL SOLUTION:

(A) This question is essentially just asking for the sum of the two radii, since the wheels are touching.

Since circumference = 2πr, radius = circumference/2π.

Thus, the smaller wheel has a radius of 4π/2π = 2 and the larger wheel has a radius of 6π/2π = 3.

The distance between x and y is 2 + 3 = 5.

The correct answer is choice (A).
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Re: The figure above represents two tangential wheels touching one another [#permalink] New post   05 Jan 2021, 04:23
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Re: The figure above represents two tangential wheels touching one another [#permalink]
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