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:

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

Show Tags

27 May 2009, 15:26

Expert's post

I think that depends on what is meant by "intersect". If the point of a triangle touching the circle is considered "intersecting" then the answer is E. But I think the questions means that triangle must poke through the circle, in the case the answer is B

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

Show Tags

27 May 2009, 20:41

Considering tangents as 1 intersection I can draw circle with 1,2,3,4,5 intersection points with a triangle. However I cannot come up with 6 intersections. Looking ate the answer choices only choice which contains 1,2,3,4,5 is E but it also has 6. Anyone has idea about the 6 intersection points??

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

Show Tags

28 May 2009, 18:24

Thanks mkrump. I see now. I drew the triagnle first and then was drawing the circle so as to intersect in 6 points. I now find it somewhat easier if I had drawn the circle first and then the triangle.

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

Show Tags

29 May 2009, 15:53

Sorry - I posted the question and I didn't mean to confuse anyone, but the answer is E per GMAT prep. The question does consider tangent points to be points of intersection.

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

Show Tags

29 May 2009, 16:50

mkrump wrote:

Sorry - I posted the question and I didn't mean to confuse anyone, but the answer is E per GMAT prep. The question does consider tangent points to be points of intersection.

It was an excellent question. I am sure a lot of us got to learn something new.

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

Show Tags

29 May 2009, 22:00

Intersect does mean tangents should be considered. Those that are saying "intersect" cannot mean tangent also do not seem to be considering what is actually happening.

A circle is just a set of points that are equidistance from the origin. A triangle is just lines connecting three points.

If the triangle "intersects" as in, goes THROUGH the circle and is not tangent, then "intersect" means that the triangle and circle share 1 point in common, because remember that lines do not have any width, only our pencils do because we live in a 3D world, and cannot see 1 dimensional objects such as true lines and circles.

Tangent is the sharing of a single point, where going through the circle means that 2 points are shared because triangle goes through one line and "back out" another, therefore sharing 2 points.

There is no difference in theory from a tangent line that shares 1 point in common and no others, than one of the points where a triangle intersects a circle in 2 points. Each point is the same.

Intersect has to include tangent as well as everything else that seems more obvious. _________________

------------------------------------ J Allen Morris **I'm pretty sure I'm right, but then again, I'm just a guy with his head up his a$$.

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

Show Tags

29 May 2009, 22:10

Oh my poor drawing!

In fact, I drew these circles and traingles in less than 2 minuets - I guess. I was rushing to meet another deadline - friday evening/night meeting. _________________

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

Show Tags

02 Oct 2014, 00:08

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________

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

Show Tags

02 Oct 2014, 03:51

3

This post received KUDOS

Expert's post

2

This post was BOOKMARKED

mkrump 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

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:

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

Show Tags

26 Nov 2015, 07:31

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________

MBA Admission Calculator Officially Launched After 2 years of effort and over 1,000 hours of work, I have finally launched my MBA Admission Calculator . The calculator uses the...

Final decisions are in: Berkeley: Denied with interview Tepper: Waitlisted with interview Rotman: Admitted with scholarship (withdrawn) Random French School: Admitted to MSc in Management with scholarship (...

The London Business School Admits Weekend officially kicked off on Saturday morning with registrations and breakfast. We received a carry bag, name tags, schedules and an MBA2018 tee at...