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Math Expert V
Joined: 02 Sep 2009
Posts: 59632

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13 00:00

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 V
Joined: 02 Sep 2009
Posts: 59632

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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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Current Student B
Joined: 18 Nov 2013
Posts: 25
Location: India
WE: Engineering (Transportation)

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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 V
Joined: 02 Sep 2009
Posts: 59632

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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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Intern  B
Joined: 28 Apr 2016
Posts: 19

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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 V
Joined: 02 Sep 2009
Posts: 59632

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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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Posts: 353
GMAT 1: 660 Q44 V38 GMAT 2: 690 Q46 V40 GPA: 3.9
WE: Information Technology (Consumer Products)

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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 V
Joined: 02 Sep 2009
Posts: 59632

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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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Intern  B
Joined: 11 Jul 2017
Posts: 15

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2
1
High quality question. I took a pass at drawing.
>> !!!

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Intern  B
Joined: 14 Apr 2018
Posts: 3
Location: India

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Dear Bunuel will the max perimeter of the inscribed triangle comes out to be 3root3??
Math Expert V
Joined: 02 Sep 2009
Posts: 59632

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thewayfareryogi wrote:
Dear Bunuel will the max perimeter of the inscribed triangle comes out to be 3root3??

___________________________________
Yes.
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BSchool Forum Moderator P
Joined: 05 Jul 2017
Posts: 507
Location: India
GMAT 1: 700 Q49 V36 GPA: 4

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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 V
Joined: 02 Sep 2009
Posts: 59632

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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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# M17-16

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