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:
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.
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..."
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.
Re: GMAT Prep PS - Circle intersecting triangle [#permalink]
17 Mar 2009, 09:33
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.
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 38689 times ]
Re: No clue for this DS question - from gmatprep [#permalink]
03 Sep 2010, 02:58
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
Re: Geometry question regarding circle and triangle [#permalink]
01 Nov 2010, 20:54
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]
22 May 2012, 20:30
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]
22 May 2012, 23:19
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]
17 Jul 2013, 20:53
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]
17 Jul 2013, 21:15
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]
26 Aug 2013, 03:05
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.
Re: Which of the following lists the number of points at which a [#permalink]
06 Aug 2015, 15:13
This question should be reworded, "is a tangent also an intersection" because I think more than anything else, that's what it's testing for most test takers.
gmatclubot
Re: Which of the following lists the number of points at which a
[#permalink]
06 Aug 2015, 15:13
You know what’s worse than getting a ding at one of your dreams schools . Yes its getting that horrid wait-listed email . This limbo is frustrating as hell . Somewhere...
As I’m halfway through my second year now, graduation is now rapidly approaching. I’ve neglected this blog in the last year, mainly because I felt I didn’...
Wow! MBA life is hectic indeed. Time flies by. It is hard to keep track of the time. Last week was high intense training Yeah, Finance, Accounting, Marketing, Economics...