Which of the following lists the number of points at which

[Harish Dorai]

Which of the following lists the number of points at which a circle can intersect a triangle?

1) 2 and 6 only
2) 2,4 and 6 only
3) 1,2,3 and 6 only
4) 1,2,3,4 and 6 only
5) 1,2,3,4,5 and 6

[anadi]

E) 1,2,3,4,5,6,

1 - Triangle is out side the circle and tangential
2 - Circle divides one side of triangle in 3 parts. Intersects only one side at 2 points.
3 - Inscribed circle. All sides of triangle tangent to circle.
4 - Circle intersects only 2 sides of triangle, 2 points each side.
5 - Circle intersects 2 sides , at 2 points each, and is tangential to the third side.
6 - Circle intersects all 3 sides, each of them at 2 points.

[Guest]

I do not understand the question! What does the question mean?

[StaceyKoprince]

Take a circle and a triangle and figure out all of the different ways you can place them so that they overlap (or cross) in one place, in two places, in three places, etc.

Best way to approach this one is to draw it out.

[chron]

Correct me if i'm wrong, but i always had the impressions that to 'intersect' means to 'cut through' and not just 'touch' tangentially.
Sorry if this is a stupid question, but i'm not english native and I thought that intersecting does not include touching.

Obviously it does include it though?

[blue_lotus]

intersection means any common points.

when a line is tangent to circle, both the circle and the line has a common point, which is the intersection point.

[RonPurewal]

intersection means any common points.

when a line is tangent to circle, both the circle and the line has a common point, which is the intersection point.

correct: 'intersection' just means 'shared points'.

notice other non-intuitive uses of the term, too. for instance, if line L is contained within plane P, then the intersection of L and P is L itself.

[anoo.anand]

can somebody please explain what the question is asking ?

some diagram please....

Thanks....

[RonPurewal]

can somebody please explain what the question is asking ?

some diagram please....

Thanks....

basically:
imagine that you have a circle and a triangle. if you draw them on the same page, what are the possible numbers of points at which they cross (i.e., intersection points)?

--

incidentally, the way the question is written, there's no reason they couldn't intersect at 0 points. so it should be "0, 1, 2, 3, 4, 5, or 6".

is this seriously a GMAT PREP SOFTWARE question? because overlooking 0 is a pretty serious omission.

[william.braden.young]

Ron: If a triangle and circle intersect at 0 points then they would not intersect. Therefore 0 intersection points is not a viable answer option based on the structure of the question being asked.

[mschwrtz]

Sorry William, that's just not so. The question doesn't ask, "If a triangle and a circle intersect, at how many points might they intersect?" Nothing about the question requires that the triangle and circle intersect. 0 is a perfectly good answer to the question "how many."

How many times has the US elected a woman president?

How many times have the Cowboys beat the 49ers in the Superbowl?

How many times have I been out to dinner with Salma Hayek?

Zero.


So far.

[RonPurewal]

here's a drawing of several different ways to get each number of intersection points:
http://postimage.org/image/3f6p1ttw/

[ouyangjackie]

I am really sorry to say that how werid your american math definition is!!!! the meaning of intersect and tangential is absolutely different.Intersect means the points between the two graphs are greater than 2. tangential means the point is the only one. How sad 。。。。。but for taking the exam, i have to endure these werid regulations。。。。。。

[RonPurewal]

I am really sorry to say that how werid your american math definition is!!!! the meaning of intersect and tangential is absolutely different.Intersect means the points between the two graphs are greater than 2. tangential means the point is the only one. How sad 。。。。。but for taking the exam, i have to endure these werid regulations。。。。。。

fyi -- i've seen geometry/topology material from argentina, colombia, uruguay, brazil, australia, england, singapore, finland, spain, france, and germany.
every single one of those sources has agreed with the american definition of "intersect" -- i.e., any point(s), 1 or more, that the figures have in common.

[AmunaGmat]

here's a drawing of several different ways to get each number of intersection points:
http://postimage.org/image/3f6p1ttw/

Thank you for the image Ron, I appeared before this question (hahahaha, the forum's language) in the exam and I couldn't make sense of any explanation. The image made it so clear.