Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Schools: HBS(08) - Ding. HBS, Stanford, Kellogg, Tuck, Stern, all dings. Yale - Withdrew App. Emory Executive -- Accepted, Matriculated, Withdrewed (yes, I spelled it wrong on purpose). ROSS -- GO BLUE 2011.

Which of the following lists a number of points at which a circle intersects 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 only

Circle can intersect triangle at one of the vertices - 1 point of intersection; Circle can intersect triangle at two of the vertices - 2 points of intersection; Circle can intersect triangle at three of the vertices (inscribed triangle or inscribed circle) - 3 points of intersection; Circle can intersect triangle at two of the vertices and two sides - 4 points of intersection; Circle can intersect triangle at one of the vertex and cut three sides (one side twice and other two once) two sides - 5 points of intersection; Circle can cut all three sides twice - 6 points of intersection.

Hence circle can intersect triangle at 1, 2, 3, 4, 5 or 6 points. (The examples I provided are not the only possible cases of intersection points, just these examples prove that there can be from 1 to 6 intersections).

Answer: E.

Below is the diagram showing possible cases of intersections provided by DestinyChild.

Attachment:

TriangleCircleIntersection88639.jpg [ 5.38 KiB | Viewed 46499 times ]

Re: GMAT Prep PS - Circle intersecting triangle [#permalink]

Show Tags

17 Mar 2009, 10:33

4

This post received KUDOS

walker wrote:

Could we consider a tangent a intersection?

point of intersection is a point that satisfies both the eq's (this case the circle and the line i.e the side of the triangle) So, a tangent is a point of intersection.

Re: No clue for this DS question - from gmatprep [#permalink]

Show Tags

03 Sep 2010, 03:58

2

This post received KUDOS

Imagine a triangle ABC. And draw a circle around it. 1 point - Just one side of the triangle is tangential to the circle. 2 pts - The circle is encompassing only one vertex. So it cuts at 2 points. 3 pts - A incircle. A circle where all the sides are tangents to it. Like we have in a in-circle 4pts - Draw a circle which passes through vertex A (pt1), cuts side AB (pt2), is tangential to BC (pt3) and finally cuts side AC (pt4). 5 pts - Gets trickier. Draw a circle which passes through vertex A (pt1), Cuts side AB (pt2), cuts side BC twice (pt3, pt4), and finally cuts side AC (pt5). 6 pts - this is the simplest. Draw a circle which cuts each side twice.

Hand me a kudos if you like my explanation. Thank you. -pH

One side intersects, 2 points. Two sides intersect, 4 points. Three sides intersect, 6 points.

Number of points can't be odd.

If a circle is inside a triangle with each of the three sides a tangent to the circle, then there will be 3 points. Also, if only one side is a tangent to the circle, then number of points will be 1.

And if the circle is inside the triangle and two sides are tangent to the circle, then we have 2 points.

Guess then the answer should be E.

If the point of contact of a tangent is not considered as a point of intersection, then of course I am wrong.

Which of the following lists the number of points at which a [#permalink]

Show Tags

28 Sep 2015, 08:14

1

This post received KUDOS

Absolute Values/Modules tag is not required for this . _________________

When everything seems to be going against you, remember that the airplane takes off against the wind, not with it. - Henry Ford +1 Kudos if you find this post helpful

Last edited by Skywalker18 on 28 Sep 2015, 08:16, edited 1 time in total.

As per wikipedia..
"In plane geometry, a line is tangent to a curve, at some point, if both line and curve pass through the point with the same direction. Such a line is called the tangent line (or tangent)......It is a mistake to think of tangents as lines which intersect a curve at only one single point. ....
Note that in the important case of a conic section, such as a circle, the tangent line will intersect the curve at only one point..."

Re: Geometry question regarding circle and triangle [#permalink]

Show Tags

01 Nov 2010, 21:54

Expert's post

metallicafan wrote:

Hi Bunuel!

Is being tangent considered as intersection ? I thought that an intersection is a line which "cuts" another line. Not only "touches" it.

Thanks!

Yes, if a line is tangent to a circle it's considered that this line intersects the circle (both tangent and intersection points are "common" points of a line and a circle). _________________

Re: Which of the following lists the number of points at which a [#permalink]

Show Tags

22 May 2012, 21:30

as per me the answer should be B....... as the question clearly states that the circle intersects the Triangle.....and the tanget does'nt intersect the triangle ..it touches it........

Re: Which of the following lists the number of points at which a [#permalink]

Show Tags

23 May 2012, 00:19

Expert's post

ankitbansal85 wrote:

as per me the answer should be B....... as the question clearly states that the circle intersects the Triangle.....and the tanget does'nt intersect the triangle ..it touches it........

so answer should be 'B'...

I agree with what AugiTh has posted.......

Answer to this question is E, not B.

If a line is tangent to a circle it's considered that this line intersects the circle (both tangent and intersection points are "common" points of a line and a circle).

Which of the following lists a number of points at which a [#permalink]

Show Tags

17 Jul 2013, 21:53

Which of the following lists a number of points at which a circle intersects 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 only

In the old discussion on this topic, the points where the circle touches the triangle(i.e the side of the triangle is tangential) have also been taken as intersecting.

Is intersection and tangential the same on GMAT?

That post is locked so i could not post my reply there.

Re: Which of the following lists a number of points at which a [#permalink]

Show Tags

17 Jul 2013, 22:15

Expert's post

12bhang wrote:

Which of the following lists a number of points at which a circle intersects 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 only

In the old discussion on this topic, the points where the circle touches the triangle(i.e the side of the triangle is tangential) have also been taken as intersecting.

Is intersection and tangential the same on GMAT?

That post is locked so i could not post my reply there.

Please help.

Merging similar topics. Please refer to the solutions above.

Re: Which of the following lists the number of points at which a [#permalink]

Show Tags

26 Aug 2013, 04:05

Somehow I interpreted intersection as "not touching", but just "crossing", so I chose 2,4,6. But I see that official way is to consider "touching" points as well.

Excellent posts dLo saw your blog too..!! Man .. you have got some writing skills. And Just to make an argument = You had such an amazing resume ; i am glad...

So Much $$$ Business school costs a lot. This is obvious, whether you are a full-ride scholarship student or are paying fully out-of-pocket. Aside from the (constantly rising)...

I barely remember taking decent rest in the last 60 hours. It’s been relentless with submissions, birthday celebration, exams, vacating the flat, meeting people before leaving and of...

Rishabh from Gyan one services, India had a one to one interview with me where I shared my experience at IMD till now. http://www.gyanone.com/blog/life-at-imd-interview-with-imd-mba/ ...