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

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Math Expert
Joined: 02 Sep 2009
Posts: 55614
The sides of triangle PQR touch or pass through the center points of  [#permalink]

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21 May 2019, 22:58
00:00

Difficulty:

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 [ 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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21 May 2019, 23:06
Bunuel wrote:

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

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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22 May 2019, 03:22
Bunuel wrote:

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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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

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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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