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sector AOB consists

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by sanju09 » Wed May 02, 2012 2:52 am
A and B are two distinct points on circle O, such that the central angle AOB measures 72 degrees. The radius of the circle is r. The perimeter of sector AOB consists of line segments AO and BO and arc AB. Which of the following expression gives the perimeter of sector AOB in terms of r?
(A) (π + 10) · r / 5
(B) (π + 8) · r / 4
(C) (π + 6) · r / 3
(D) (π + 2) · r / 5
(E) (2π + 10) · r / 5



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rephrased to avoid giving figure
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Source: — Problem Solving |

by Anurag@Gurome » Wed May 02, 2012 8:46 pm
sanju09 wrote:A and B are two distinct points on circle O, such that the central angle AOB measures 72 degrees. The radius of the circle is r. The perimeter of sector AOB consists of line segments AO and BO and arc AB. Which of the following expression gives the perimeter of sector AOB in terms of r?
(A) (π + 10) · r / 5
(B) (π + 8) · r / 4
(C) (π + 6) · r / 3
(D) (π + 2) · r / 5
(E) (2π + 10) · r / 5



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rephrased to avoid giving figure

Image

Length of the arc = central angle AOB * (Ï€/180) * r
So, here length of arc = 72 * (Ï€/180) * r

Therefore, perimeter of sector AOB in terms of r = r + r + [72 * π/180 * r]
= 2r + 2Ï€r/5
= (2π + 10) · r / 5

The correct answer is E.
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