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

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 =

LRQ's radius = 5

Area of large semicircle LRQ:

\(\frac{\pi r^2}{2} = \frac{\pi 5^2}{2}=\frac{25\pi}{2}\)

Answer D

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