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If in the figure above, AB is the diameter of a circle of radius 6

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If in the figure above, AB is the diameter of a circle of radius 6 [#permalink]

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New post Updated on: 09 May 2015, 04:26
2
6
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

59% (01:54) correct 41% (01:58) wrong based on 135 sessions

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If in the figure above, AB is the diameter of a circle of radius 6, what is the perimeter of the shaded region?

A. π+6+6√3
B. π+12+6√3
C. 2π+9+6√3
D. 2π+12+6√3
E. 2π+12+12√3

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Originally posted by reto on 09 May 2015, 04:22.
Last edited by Bunuel on 09 May 2015, 04:26, edited 1 time in total.
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Re: If in the figure above, AB is the diameter of a circle of radius 6 [#permalink]

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New post 09 May 2015, 07:34
1
ABC is a 30-60-90 triangle since the AB is the diameter.

Since AB = 12, AC = 6√3

Now if ARC BC makes an angle of 30°, it would make 60° at the center.
Length of arc \(BC = 60/360*2π*6 = 2π\)

Thus, perimeter of the highlighted region = AB+AC+arcBC = 12+6√3+2π

Answer D.
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Re: If in the figure above, AB is the diameter of a circle of radius 6 [#permalink]

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New post 08 Mar 2017, 13:33
What I don't understand about this problem- why wouldn't it work if we tried to use 30 degrees to calculate the arc length? Using that I arrived at answer B- how do you know its a 30 60 90 triangle?
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If in the figure above, AB is the diameter of a circle of radius 6 [#permalink]

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New post 03 Apr 2017, 18:10
Nunuboy1994 wrote:
What I don't understand about this problem- why wouldn't it work if we tried to use 30 degrees to calculate the arc length? Using that I arrived at answer B- how do you know its a 30 60 90 triangle?


We know it's a 30-60-90 triangle because any inscribed triangle that has the diameter of the circle as one of its sides is a right triangle. If it's a right triangle, one of the angles is 90. We are given that the other angle is 30. Therefore it must be 30 + 90 + X = 180. X = 60.

(Converse is also true. IF a right triangle is inscribed in a circle, its hypotenuse will be the diameter.)

(Take a look at GMAT Club Math Book, Triangles - Right Triangle Inscribed in a Circle, \(https://gmatclub.com/forum/math-triangles-87197.html\))

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If in the figure above, AB is the diameter of a circle of radius 6   [#permalink] 03 Apr 2017, 18:10
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