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If the area of each of the three semicircles shown above is 72, and Q

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If the area of each of the three semicircles shown above is 72, and Q [#permalink]

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New post 28 Nov 2017, 20:13
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If the area of each of the three semicircles shown above is 72, and Q is the midpoint of segment PR, what is the area of the shaded region?

(A) 4
(B) 8
(C) 9
(D) 12
(E) 20

[Reveal] Spoiler:
Attachment:
2017-11-29_0806.png
2017-11-29_0806.png [ 49.45 KiB | Viewed 253 times ]
[Reveal] Spoiler: OA

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Kudos [?]: 135880 [0], given: 12715

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If the area of each of the three semicircles shown above is 72, and Q [#permalink]

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New post 28 Nov 2017, 23:06
imo B- 8
explaining gets difficult here. Will post a proper solution if the answer is correct.
Awaiting OA
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Hit Kudus if this has helped you get closer to your goal, and also to assist others save time. Tq :)

Kudos [?]: 93 [0], given: 468

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Re: If the area of each of the three semicircles shown above is 72, and Q [#permalink]

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New post 29 Nov 2017, 18:26
Considering that the Area of each semicircle is 72, the radius = 12/(pi)^1/2.

The key here is noticing that the sector QRS (S being the point of intersection between the Semicircle at an angle and the first semicircle) is the same as the shaded region.

Area (qrs) = (20/360) *pi* r^2

Area = 8

For clarity, if another semicircle is drawn to mimic the semicircle at an angle, it is easy to notice that the area made by the two domes (the result of two semicircles intersecting) will be the same. From this, we can conclude that the shaded area is equal to the area of the sector QRS

Kudos [?]: 1 [0], given: 182

Re: If the area of each of the three semicircles shown above is 72, and Q   [#permalink] 29 Nov 2017, 18:26
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If the area of each of the three semicircles shown above is 72, and Q

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