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# M17-16

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Math Expert
Joined: 02 Sep 2009
Posts: 59632

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16 Sep 2014, 01:01
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Difficulty:

85% (hard)

Question Stats:

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

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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

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Math Expert
Joined: 02 Sep 2009
Posts: 59632

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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.

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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?
Math Expert
Joined: 02 Sep 2009
Posts: 59632

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16 Dec 2016, 12:32
Klenex wrote:
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?

The vertices must be on the circumference.
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Joined: 28 Apr 2016
Posts: 19

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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.

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?
Math Expert
Joined: 02 Sep 2009
Posts: 59632

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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.

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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GMAT 1: 660 Q44 V38
GMAT 2: 690 Q46 V40
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14 Sep 2017, 09:09
1
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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Math Expert
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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.

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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09 Dec 2017, 05:29
2
1
High quality question. I took a pass at drawing.
>> !!!

You do not have the required permissions to view the files attached to this post.

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Joined: 14 Apr 2018
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11 Jan 2019, 08:52
Dear Bunuel will the max perimeter of the inscribed triangle comes out to be 3root3??
Math Expert
Joined: 02 Sep 2009
Posts: 59632

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12 Jan 2019, 03:44
thewayfareryogi wrote:
Dear Bunuel will the max perimeter of the inscribed triangle comes out to be 3root3??

___________________________________
Yes.
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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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Math Expert
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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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# M17-16

Moderators: chetan2u, Bunuel