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# In the figure above, LMN and NPQ are semicircles of the same size. If

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Joined: 02 Sep 2009
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In the figure above, LMN and NPQ are semicircles of the same size. If [#permalink]

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28 Nov 2017, 21:15
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25% (medium)

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90% (00:41) correct 10% (00:25) wrong based on 30 sessions

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In the figure above, LMN and NPQ are semicircles of the same size. If arc LRQ is also a semicircleand the length of line segment NQ is 5, what is the area of the semicircular region LRQ?

(A) 25π/8
(B) 25π/4
(C) 10π
(D) 25π/2
(E) 25π

[Reveal] Spoiler:
Attachment:

2017-11-29_0806_001.png [ 36.85 KiB | Viewed 496 times ]
[Reveal] Spoiler: OA

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In the figure above, LMN and NPQ are semicircles of the same size. If [#permalink]

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29 Nov 2017, 12:10
Bunuel wrote:

In the figure above, LMN and NPQ are semicircles of the same size. If arc LRQ is also a semicircleand the length of line segment NQ is 5, what is the area of the semicircular region LRQ?

(A) 25π/8
(B) 25π/4
(C) 10π
(D) 25π/2
(E) 25π

[Reveal] Spoiler:
Attachment:
2017-11-29_0806_001.png

Two small semicircles of the same size have equal diameters.

Semicircle NPQ has diameter NQ = 5
The other small semicircle has diameter (LN)=5

Large semicircle LRQ intercepts both equally-sized small semicircles. Thus, one small semicircle's diameter =

Area of large semicircle LRQ:
$$\frac{\pi r^2}{2} = \frac{\pi 5^2}{2}=\frac{25\pi}{2}$$

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Re: In the figure above, LMN and NPQ are semicircles of the same size. If [#permalink]

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04 Dec 2017, 11:52
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Expert's post
Bunuel wrote:

In the figure above, LMN and NPQ are semicircles of the same size. If arc LRQ is also a semicircleand the length of line segment NQ is 5, what is the area of the semicircular region LRQ?

(A) 25π/8
(B) 25π/4
(C) 10π
(D) 25π/2
(E) 25π

[Reveal] Spoiler:
Attachment:
2017-11-29_0806_001.png

LRQ is a semicircle of radius 5. Therefore, the area of LRQ is 1/2 x π x 5^2 = 25π/2.

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Re: In the figure above, LMN and NPQ are semicircles of the same size. If   [#permalink] 04 Dec 2017, 11:52
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