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number of points a circle can intersect a triangle

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by AMat700 » Tue Feb 22, 2011 8:03 pm
Which of the following lists the number of points at which a circle can intersect a triangle?

A)2 and 6 only
B)2, 4, and 6 only
C)1, 2, 3 and 6 only
D)1, 2, 3, 4 and 6 only
E)1, 2, 3, 4, 5, and 6

Answer: E

How do you solve? I don't even understand this question.
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by Anurag@Gurome » Tue Feb 22, 2011 8:12 pm
See the following figures:

Image

Hence, correct answer is E.
Last edited by Anurag@Gurome on Wed Aug 03, 2011 7:54 pm, edited 1 time in total.
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by GMATGuruNY » Wed Feb 23, 2011 6:52 am
AMat700 wrote:Which of the following lists the number of points at which a circle can intersect a triangle?

A)2 and 6 only
B)2, 4, and 6 only
C)1, 2, 3 and 6 only
D)1, 2, 3, 4 and 6 only
E)1, 2, 3, 4, 5, and 6

Answer: E

How do you solve? I don't even understand this question.
The quickest approach is to notice how the answer choices differ. Only answer choice E says that 5 intersections are possible:

Image

Since 5 intersections are possible, eliminate A, B, C and D. No need to try any other options.

The correct answer is E.
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by Kemmy G » Mon May 21, 2012 1:53 pm
@GMATGuruNY,

I beg to differ. For those who don't even understand the question (like me!) Your explanation doesn't help at all. What if the testmakers purposely threw in the 5 to confuse those who don't know what to do? I'll appreciate if you could give a more detailed explanation. Thank you!
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by aircraft » Mon May 20, 2013 2:17 pm
Define the difference between intersecting and to be tangent in cases 1 three and five...I know the OA, but with all due respect, 1, 3 and 5 strictly speaking is not intersecting.
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by Brent@GMATPrepNow » Mon May 20, 2013 2:26 pm
aircraft wrote:Define the difference between intersecting and to be tangent in cases 1 three and five...I know the OA, but with all due respect, 1, 3 and 5 strictly speaking is not intersecting.
"Intersect" does not necessarily mean "pass through."
To intersect is to share a common point.
So, a line that is tangent to a circle (touching the circle but not passing through it) can be said to intersect the circle.

The Official Guide doesn't have a formal definition of "intersect," but we can infer its meaning from the test-maker's definition of a closed plane figure (e.g., a rectangle):

A polygon is a closed plane figure formed by three or more line segments, called the sides of the
polygon. Each side intersects exactly two other sides at their endpoints.

So, the adjacent sides of a rectangle do not pass through each other, but they are said to intersect.

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by ygcrowanhand » Thu Sep 28, 2017 7:05 am
Hi GMATters,

Here's my video solution to this question:

https://youtu.be/pxGsBiEYndo

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Re: number of points a circle can intersect a triangle

by Scott@TargetTestPrep » Sat Jul 11, 2020 12:51 pm
AMat700 wrote: ↑
Tue Feb 22, 2011 8:03 pm
 Which of the following lists the number of points at which a circle can intersect a triangle?

A)2 and 6 only
B)2, 4, and 6 only
C)1, 2, 3 and 6 only
D)1, 2, 3, 4 and 6 only
E)1, 2, 3, 4, 5, and 6

Answer: E

Solution:

A circle can intersect a triangle at 1 to 6 points, inclusively (see diagrams below):
circles triangles.png
(Note: Technically, 0 should be included in choice E since a circle and a triangle don’t need to intersect each other.)

Answer: E
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