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2 circles have the same center and the smaller circle’s radius r is 5.

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MathRevolution
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2 circles have the same center and the smaller circle’s radius r is 5. [#permalink] New post   29 May 2016, 20:54
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A
B
C
D
E

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15% (low)

Question Stats:

81% (01:21) correct 19% (01:23) wrong based on 101 sessions
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2 circles have the same center and the smaller circle’s radius r is 5. If line segment AB is tangent to a smaller circle shown as above figure and the larger circle’s radius is R, what is the length of AB?
1) R=10
2) The circumference of the lager circle is 20π

*An answer will be posted in 2 days.
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D

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adiagr
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Re: 2 circles have the same center and the smaller circle’s radius r is 5. [#permalink] New post   29 May 2016, 21:18
MathRevolution wrote:
2 circles have the same center and the smaller circle’s radius r is 5. If line segment AB is tangent to a smaller circle shown as above figure and the larger circle’s radius is R, what is the length of AB?
1) R=10
2) The circumference of the lager circle is 20π

*An answer will be posted in 2 days.


The tangent makes a 90 degree with the radius. We know small radius = 5. If we get the hypotenuse, which is nothing but the radius of bigger circle, we get half of the length of tangent.

so Statement (1) is sufficient.

Statement (2) is also sufficient.

We know the circumference of bigger circle. 2\(/pi\)R = 20\(/pi\). So R is known.

Answer will be D
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Re: 2 circles have the same center and the smaller circle’s radius r is 5. [#permalink] New post   30 May 2016, 06:49
If we name the center of both circles as O and draw a perpendicular line from O to AB (called OD) then OAD and OBD are two right triangles.

Given:
DO=r=5 (radius of the smaller circle)
AO=R
\(DA^2=OA^2 -DO^2 = R^2 - 5^2 = R^2 - 25\)

Find:
2 x DA - ?

Need:
To find DA we need the value of R

Answer: D
1) R = 10 (we have the value of R) SUFFICIENT
2) C = 20π = 2Rπ, thus R = 10 (we have the value of R) SUFFICIENT
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Re: 2 circles have the same center and the smaller circle’s rad [#permalink] New post   01 Jun 2016, 06:38
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There is 1 variable in the original condition. In order to match the number of equations to the number of variables, we need 1 equation. Hence, there is high chance that D is the correct answer. In fact, the condition 1) and the condition 2) equals. So, the correct answer is D.

- Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.
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Re: 2 circles have the same center and the smaller circle’s rad [#permalink]
01 Jun 2016, 06:38
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