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# The area of circle with center O is 36π and the distance from A to B

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Math Expert
Joined: 02 Sep 2009
Posts: 52294
The area of circle with center O is 36π and the distance from A to B  [#permalink]

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17 Sep 2018, 20:58
00:00

Difficulty:

55% (hard)

Question Stats:

64% (02:48) correct 36% (02:54) wrong based on 25 sessions

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The area of circle with center O is 36π and the distance from A to B is 6. If point P lies on the circumference of circle O and is the center of the smaller circle then the perimeter of the figure is approximately

A. 51
B. 43
C. 29
D. 24
E. 13

Attachment:

image041.jpg [ 3.96 KiB | Viewed 326 times ]

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Joined: 22 Jan 2014
Posts: 174
WE: Project Management (Computer Hardware)
Re: The area of circle with center O is 36π and the distance from A to B  [#permalink]

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18 Sep 2018, 04:01
Bunuel wrote:

The area of circle with center O is 36π and the distance from A to B is 6. If point P lies on the circumference of circle O and is the center of the smaller circle then the perimeter of the figure is approximately

A. 51
B. 43
C. 29
D. 24
E. 13

Attachment:
The attachment image041.jpg is no longer available

As per attached image, to find perimeter of the image we need to find circumference of both circles and then subtract length of the 2 arcs inside (dotted lines)

circumference of bigger circle = 12*pi -- (1)

circumference of smaller circle = 6rt(2)*pi --- (2)

angle AOB is 60 degree as triangle AOB is equilateral
=> length of arc APB = 2*pi*6*60/30 = 2*pi -- (3)

angle APB is 90 degree:
cos x = [(3rt(2))^2 + (3rt(2))^2 - 6^2] / 2*(3rt(2))^2
=> cos x = 0
=> x = 90
=> length of arc AXB = 2*pi*(3rt(2)*90/360 = 3*pi/rt(2) -- (4)

now, perimeter becomes: (1) + (2) - [(3) + (4)]
which comes out to be ~ 51.

Option A.
Attachments

Geo.JPG [ 29.39 KiB | Viewed 278 times ]

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Re: The area of circle with center O is 36π and the distance from A to B &nbs [#permalink] 18 Sep 2018, 04:01
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