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M17-16

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M17-16 [#permalink]

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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
[Reveal] Spoiler: OA

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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.

Answer: D
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: M17-16 [#permalink]

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New post 27 Nov 2014, 20:17
Can someone please explain how we got the value of .001 for the infinitely small arc?

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Re: M17-16 [#permalink]

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New post 28 Nov 2014, 06:58
Hi @kritu
there can be many points in a circle none of which are parallel, hence we can construct as small a traingle as possible. However there will be restrictions when asked about the largest perimeter of the triangle.

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Re M17-16 [#permalink]

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I think this question is poor and not helpful.

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Re: M17-16 [#permalink]

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New post 01 Nov 2015, 03:44
Dear Bunuel,

If it is possible, could you show us the graph/picture? I think the visual graph/picture can help to understand the solution better?

Many thanks!



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

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M17-16 [#permalink]

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New post 06 Oct 2016, 13:38
This question looks quite vague. Bunuel , chetan2u ! Can you help show any one of the case (I, II, III) mathematically!

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New post 11 Nov 2016, 02:08
I think this is a high-quality question and I agree with explanation. Hi,

What would be the maximum perimeter of ther triangle ? Options given are very small in number, so we can mark all of them. But, if any one option had a large value such as 4 or 5 etc, then how would be solve? Pls help.

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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 30 Dec 2016, 11:14
Hi All. How would the maximum perimeter be found?

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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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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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M17-16 [#permalink]

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New post 30 Mar 2017, 00:40
Your definition of inscribed does not match with that at wikipedia https://en.wikipedia.org/wiki/Inscribed_figure

Last edited by rrajk on 30 Mar 2017, 00:41, edited 1 time in total.

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Re: M17-16 [#permalink]

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New post 11 May 2017, 10:56
rrajk wrote:
Your definition of inscribed does not match with that at wikipedia https://en.wikipedia.org/wiki/Inscribed_figure


With all due respect, I hope you are not confusing inscribed with circumscribed.

in the wikipedia link : circle is inscribed and polygons are circumscribed

but in our question the case is reversed. the triangle is inscribed in a circle. In general term a triangle inside a circle where all of the vertices of the triangle touches the circle. in such a case try to put these vertices on circumference very very close and then the options given would seem valid.
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Re: M17-16 [#permalink]

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New post 15 May 2017, 03:17
What would be the largest area of the triangle inscribed in this circle?

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Re: M17-16 [#permalink]

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New post 15 May 2017, 03:22
addisubhashree wrote:
What would be the largest area of the triangle inscribed in this circle?


then I believe it should be equilateral triangle

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Re: M17-16 [#permalink]

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New post 14 Sep 2017, 09:09
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, 06:56
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.
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Re: M17-16   [#permalink] 11 Nov 2017, 06:56

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