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# In the figure, O is the center of the circle. Which one of the followi

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Math Expert
Joined: 02 Sep 2009
Posts: 58400
In the figure, O is the center of the circle. Which one of the followi  [#permalink]

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Updated on: 15 Jul 2019, 04:21
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81% (00:57) correct 19% (01:06) wrong based on 16 sessions

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In the figure, O is the center of the circle. Which one of the following must be true about the perimeter of the triangle shown?

(A) Always less than 10
(B) Always greater than 40
(C) Always greater than 30
(D) Always less than 30
(E) Less than 40 and greater than 20

Source: Nova GMAT
Difficulty Level: 600

Attachment:

circle.jpg [ 18.56 KiB | Viewed 440 times ]

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Originally posted by Bunuel on 09 Oct 2018, 21:51.
Last edited by SajjadAhmad on 15 Jul 2019, 04:21, edited 1 time in total.
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Re: In the figure, O is the center of the circle. Which one of the followi  [#permalink]

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09 Oct 2018, 22:04
1
Bunuel wrote:

In the figure, O is the center of the circle. Which one of the following must be true about the perimeter of the triangle shown?

(A) Always less than 10
(B) Always greater than 40
(C) Always greater than 30
(D) Always less than 30
(E) Less than 40 and greater than 20

Attachment:
circle.jpg

+1 for E

$$OA=OB=Radius=10$$

Property of triangle:
a+b>c>a-b

We know a=10, b=10 and
let c(max) = 19 (As c should be less than a+b),
c(min) = 1 (As c should be greater than a-b)

Perimeter(max) = a+b+c = 10+10+19 = 39
Perimeter(min) = a+b+c = 10+10+1 =21

Less than 40 and greater than 20
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Re: In the figure, O is the center of the circle. Which one of the followi   [#permalink] 09 Oct 2018, 22:04
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