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Triangle inscribed in a circle

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by GMATGuruNY » Sun Dec 04, 2011 4:17 am
satishchandra wrote: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 figure below illustrates how the perimeter of the inscribed triangle can be infinitely small:

Image

Thus, any of the perimeters listed are possible.

The correct answer is D.
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by mankey » Sun Dec 04, 2011 8:55 am
Dear Mitch

Doesnt "inscribed" means that all three vertices of the triangle should fall on the circle?

Please clarify.

Thanks.
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by chieftang » Sun Dec 04, 2011 9:07 am
mankey wrote:Dear Mitch

Doesnt "inscribed" means that all three vertices of the triangle should fall on the circle?

Please clarify.

Thanks.
All three vertices do touch the circle in Mitch's drawing.
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by jainpiyushjain » Mon Dec 24, 2012 10:58 pm
GMATGuruNY wrote:
satishchandra wrote: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 figure below illustrates how the perimeter of the inscribed triangle can be infinitely small:

Image

Thus, any of the perimeters listed are possible.

The correct answer is D.
Is there a way to find out the perimeter of the largest triangle inscribed in the same circle with the given information ?
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Posts: 15539
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by GMATGuruNY » Tue Dec 25, 2012 4:54 am
jainpiyushjain wrote:
GMATGuruNY wrote:
satishchandra wrote: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 figure below illustrates how the perimeter of the inscribed triangle can be infinitely small:

Image

Thus, any of the perimeters listed are possible.

The correct answer is D.
Is there a way to find out the perimeter of the largest triangle inscribed in the same circle with the given information ?
A triangle inscribed in a circle will have the MAXIMUM possible area if the triangle is EQUILATERAL.
Check here for one way to determine the perimeter of an equilateral triangle inscribed in a circle:

https://www.beatthegmat.com/triangle-ins ... 90961.html
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
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