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# Which of the following can be a perimeter of a triangle

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Which of the following can be a perimeter of a triangle [#permalink]

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02 Aug 2008, 20:27
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Which of the following can be a perimeter of a triangle inscribed in a circle of radius 1?

I. 0.001
II. 0.010
III. 0.100

A. I only
B. III only
C. II and III only
D. I, II, and III
E. Not I, II, or III
[Reveal] Spoiler: OA

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02 Aug 2008, 20:30
aaron22197 wrote:
Which of the following can be a perimeter of a triangle inscribed in a circle of radius 1?

I. 0.001

II. 0.010

III. 0.100

# I only
# III only
# II and III only
# I, II, and III
# not I, II, or III

i think its D. we can have very small triangle possbile in one small chord of the circle ...

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02 Aug 2008, 20:39
aaron22197 wrote:
Which of the following can be a perimeter of a triangle inscribed in a circle of radius 1?

I. 0.001

II. 0.010

III. 0.100

# I only
# III only
# II and III only
# I, II, and III
# not I, II, or III

IMO there is no restriction in the size(perimeter) of a triangle inscribed in a circle since there are many sets of triplets of coordinates in triangle.Hence D is IMO Answer
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02 Aug 2008, 20:41
You post so many good questions in quant.whats the source of these questions?is there any Q bank ? or Book?
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02 Aug 2008, 20:55
spriya wrote:
You post so many good questions in quant.whats the source of these questions?is there any Q bank ? or Book?

I am working through the GMAT Club tests right now Priya. Most of the questions I post are questions I find interesting/challenging/conceptual. I think gmatclub has a summer pack for \$29.

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02 Aug 2008, 21:12
E

by definition, an inscribed triangle must have all 3 vertexes as points on the perimeter of the circle.

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02 Aug 2008, 21:18
gmatnub wrote:
E

by definition, an inscribed triangle must have all 3 vertexes as points on the perimeter of the circle.

even with all 3 points on the perimeter of the circle, we can have a very small triangle possible ....

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02 Aug 2008, 21:22
durgesh79 wrote:
gmatnub wrote:
E

by definition, an inscribed triangle must have all 3 vertexes as points on the perimeter of the circle.

even with all 3 points on the perimeter of the circle, we can have a very small triangle possible ....

the question stated that the radius of the circle is 1

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02 Aug 2008, 21:30
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gmatnub wrote:
durgesh79 wrote:
gmatnub wrote:
E

by definition, an inscribed triangle must have all 3 vertexes as points on the perimeter of the circle.

even with all 3 points on the perimeter of the circle, we can have a very small triangle possible ....

the question stated that the radius of the circle is 1

doesnt matter.. please see attached pic.. can make that traingle even smaller as compared to circle
Attachment:

circle.PNG [ 11.33 KiB | Viewed 5747 times ]

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02 Aug 2008, 21:45
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thanks, did not see that coming.

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Re: Which of the following can be a perimeter of a triangle [#permalink]

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03 Feb 2013, 14:00
I have a very specifc doubt

Since we know that perimeter of equilateral triangle is the smallest. Hence, Formula for circul radius is s/Square root (3)
Than the side of the equilateral triangle is Sqr root(3)
Therefore minimum perimeter that a triangle can have is 3*Sqr root of 3

Hence the answer should be E.

i know i am missing sthn

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Re: Which of the following can be a perimeter of a triangle [#permalink]

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30 Apr 2013, 07:05
Hi
While solving question I was stuck that we need to take care of the property that sum of two sides must be greater than the third side. Isn't it required?

Regards,
H
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Re: Which of the following can be a perimeter of a triangle [#permalink]

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30 Apr 2013, 08:00
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imhimanshu wrote:
Hi
While solving question I was stuck that we need to take care of the property that sum of two sides must be greater than the third side. Isn't it required?

Regards,
H

Yes, the length of any side of a triangle must be larger than the positive difference of the other two sides, but smaller than the sum of the other two sides.

But how do you use the above property to solve the question?

The lower limit of the perimeter of an inscribed triangle in a circle of ANY radius is 0: P>0.

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Re: Which of the following can be a perimeter of a triangle [#permalink]

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30 Apr 2013, 08:28
Bunuel wrote:

Yes, the length of any side of a triangle must be larger than the positive difference of the other two sides, but smaller than the sum of the other two sides.

But how do you use the above property to solve the question?

The lower limit of the perimeter of an inscribed triangle in a circle of ANY radius is 0: P>0.

Thanks Bunuel, It makes sense.
Just wondering, , had the question been Must be True, then I believe, Answer would have been None of These. Am I correct?

Regards,
H
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Re: Which of the following can be a perimeter of a triangle [#permalink]

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30 Apr 2013, 08:30
imhimanshu wrote:
Bunuel wrote:

Yes, the length of any side of a triangle must be larger than the positive difference of the other two sides, but smaller than the sum of the other two sides.

But how do you use the above property to solve the question?

The lower limit of the perimeter of an inscribed triangle in a circle of ANY radius is 0: P>0.

Thanks Bunuel, It makes sense.
Just wondering, , had the question been Must be True, then I believe, Answer would have been None of These. Am I correct?

Regards,
H

Sure. We don't know what is the actual perimeter of the triangle.
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Re: Which of the following can be a perimeter of a triangle [#permalink]

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02 Jun 2016, 06:58
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Hi debbiem,

with the given info we can have an upper limit to the perimeter but cannot say the lower limit, it can be easily any minute value.
Here we are given radius as 1..
the max perimeter should be of a triangle which has two sides almost of the length of dia and third a very very minute value, so it will be nearly 4..
so you can easily say any value<4 is a possiblity..

all three are less than 4..
D
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Re: Which of the following can be a perimeter of a triangle [#permalink]

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26 Sep 2017, 01:57
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aaron22197 wrote:
Which of the following can be a perimeter of a triangle inscribed in a circle of radius 1?

I. 0.001
II. 0.010
III. 0.100

A. I only
B. III only
C. II and III only
D. I, II, and III
E. Not I, II, or III

If you start making triangles within the circle, you will realize that any smallest triangle can be formed with its 3 points lying on the circle. So triangle with minimum perimeter ->(tends to) 0.

Also maximum perimeter is possible when the 2 sides of triangle is just on the verge of becoming diameter of the circle. In that case perimeter of the triangle ->(tends to) (2+2) = 4

So, 0< Required perimeter < 4

Hence I , II and III are all possible.
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Re: Which of the following can be a perimeter of a triangle   [#permalink] 26 Sep 2017, 01:57
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