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The sides of triangle PQR touch or pass through the center points of

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The sides of triangle PQR touch or pass through the center points of  [#permalink]

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New post 21 May 2019, 22:58
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A
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C
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  15% (low)

Question Stats:

92% (00:56) correct 8% (01:37) wrong based on 25 sessions

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The sides of triangle PQR touch or pass through the center points of each of the six circles. Each of the circles has the same circumference of \(8\pi\). What is the perimeter of triangle \(PQR\)?

A. 16

B. 36

C. 48

D. 56

E. 72

Attachment:
#GREpracticequestion The sides of triangle PQR.jpg
#GREpracticequestion The sides of triangle PQR.jpg [ 19.94 KiB | Viewed 363 times ]

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Re: The sides of triangle PQR touch or pass through the center points of  [#permalink]

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New post 21 May 2019, 23:06
Bunuel wrote:
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The sides of triangle PQR touch or pass through the center points of each of the six circles. Each of the circles has the same circumference of \(8\pi\). What is the perimeter of triangle \(PQR\)?

A. 16

B. 36

C. 48

D. 56

E. 72

Attachment:
#GREpracticequestion The sides of triangle PQR.jpg


For each circle, r=radius

2(pi)r = 8(pi)

r=4.
Now each side of the triangle PQR: 4+4+8= 16
Perimeter= 16*3= 48
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Re: The sides of triangle PQR touch or pass through the center points of  [#permalink]

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New post 22 May 2019, 03:22
Bunuel wrote:
Image
The sides of triangle PQR touch or pass through the center points of each of the six circles. Each of the circles has the same circumference of \(8\pi\). What is the perimeter of triangle \(PQR\)?

A. 16

B. 36

C. 48

D. 56

E. 72

Attachment:
#GREpracticequestion The sides of triangle PQR.jpg


from given info we can find radius = 4
so perimeter will be sum of one side * 3 ; 16*3 ; 48
IMO C
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Re: The sides of triangle PQR touch or pass through the center points of  [#permalink]

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New post 23 May 2019, 05:41
Given

The circumference of the circle = 8*Pi

As we know, the circumference of a Circle, having radius "r" = 2*Pi*r

For the given circles:

2*Pi*r = 8*Pi

r = 4

In the triangle PQR, Each side is composed of ( Diameter of the middle circle) + (Sum of Radius of both the corner circles )

Since the circles are of the same radius, PQ = QR = PR = Radius of the circle + Diameter of the circle + Radius of the circle

PQ = PR = QR = 4 + 8 + 4 = 16

So the perimeter of triangle PQ + QR + PR = 16 + 16 + 16 = 48

The correct answer is C
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Re: The sides of triangle PQR touch or pass through the center points of   [#permalink] 23 May 2019, 05:41
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