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M17-16

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M17-16  [#permalink]

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New post 16 Sep 2014, 01:01
1
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A
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D
E

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  85% (hard)

Question Stats:

41% (01:18) correct 59% (01:30) wrong based on 343 sessions

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Re M17-16  [#permalink]

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New post 16 Sep 2014, 01:01
Official Solution:


Which of the following can be the perimeter of a triangle inscribed in a circle with a radius of 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

The perimeter of a triangle inscribed in a circle can be infinitely small. We can place all three vertices on a tiny arc of less than 0.001. The circle consists of infinite number of points. The circle isn't a straight line, so the three vertices will make a triangle.

Answer: D
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Re: M17-16  [#permalink]

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New post 16 Dec 2016, 08:19
Inscribed in a circle means that all the vertices of triangle must be on the circumference of the circle or some of them can be just inside?
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Re: M17-16  [#permalink]

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New post 16 Dec 2016, 12:32
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Re: M17-16  [#permalink]

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New post 25 Mar 2017, 16:01
Bunuel wrote:
Official Solution:


Which of the following can be the perimeter of a triangle inscribed in a circle with a radius of 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

The perimeter of a triangle inscribed in a circle can be infinitely small. We can place all three vertices on a tiny arc of less than 0.001. The circle consists of infinite number of points. The circle isn't a straight line, so the three vertices will make a triangle.

Answer: D


Hi,

Why should be place all three vertices on a tiny arc of less than 0.001? I mean how can we find 0.001?
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Re: M17-16  [#permalink]

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New post 26 Mar 2017, 04:55
dyg wrote:
Bunuel wrote:
Official Solution:


Which of the following can be the perimeter of a triangle inscribed in a circle with a radius of 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

The perimeter of a triangle inscribed in a circle can be infinitely small. We can place all three vertices on a tiny arc of less than 0.001. The circle consists of infinite number of points. The circle isn't a straight line, so the three vertices will make a triangle.

Answer: D


Hi,

Why should be place all three vertices on a tiny arc of less than 0.001? I mean how can we find 0.001?


The solution implies that we can choose three points on a circle so that the area of a triangle will be as small as we want it to be. It does not matter how we can find the area then, important thing is that the minimum are of an inscribed triangle is not limited.

Hope it's clear.
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Re: M17-16  [#permalink]

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New post 14 Sep 2017, 09:09
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Damn it. It makes sense after reading the answer. I assumed third point of triangle will be on opposite side (like outward not inward)
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Re: M17-16  [#permalink]

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New post 11 Nov 2017, 06:59
septwibowo wrote:
Bunuel wrote:
Official Solution:


Which of the following can be the perimeter of a triangle inscribed in a circle with a radius of 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

The perimeter of a triangle inscribed in a circle can be infinitely small. We can place all three vertices on a tiny arc of less than 0.001. The circle consists of infinite number of points. The circle isn't a straight line, so the three vertices will make a triangle.

Answer: D


Dear Bunuel, I'm still hard to understand this explanation. Would you mind to share the picture or maybe link related to the inscribed triangle?

Thank you very much.


Check other solutions of this question here: https://gmatclub.com/forum/which-of-the ... 68310.html

Hope it helps.
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Re: M17-16  [#permalink]

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New post 09 Dec 2017, 05:29
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High quality question. I took a pass at drawing.
>> !!!

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Re: M17-16  [#permalink]

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New post 11 Jan 2019, 08:52
Dear Bunuel will the max perimeter of the inscribed triangle comes out to be 3root3??
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New post 12 Jan 2019, 03:44
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Re: M17-16  [#permalink]

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New post 21 May 2019, 18:34
Bunuel wrote:
thewayfareryogi wrote:
Dear Bunuel will the max perimeter of the inscribed triangle comes out to be 3root3??

___________________________________
Yes.


Bunuel - How to find out the max perimeter?
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New post 22 May 2019, 00:00
pikolo2510 wrote:
Bunuel wrote:
thewayfareryogi wrote:
Dear Bunuel will the max perimeter of the inscribed triangle comes out to be 3root3??

___________________________________
Yes.


Bunuel - How to find out the max perimeter?


Among all triangles inscribed in a given circle, the equilateral one has the largest perimeter.

The radius of the circumscribed circle for an equilateral triangle is \(R=side*\frac{\sqrt{3}}{3}\). From this \(side=\frac{3R}{\sqrt{3}}\). Rationalize: \(side=R\sqrt{3}\). Perimeter = \(side=3R\sqrt{3}\).
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Re: M17-16   [#permalink] 22 May 2019, 00:00
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