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29 May 2016, 20:54
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
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.
1) R=10
2) The circumference of the lager circle is 20π
*An answer will be posted in 2 days.
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29 May 2016, 21:18
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MathRevolution
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
30 May 2016, 06:49
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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
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
