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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: 53066
In the figure, O is the center of the circle. Which one of the followi  [#permalink]

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09 Oct 2018, 20:51
00:00

Difficulty:

25% (medium)

Question Stats:

77% (00:54) correct 23% (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

Attachment:

circle.jpg [ 18.56 KiB | Viewed 224 times ]

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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, 21:04
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, 21:04
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