Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

It is currently 16 Jul 2019, 09:30

Close

GMAT Club Daily Prep

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.

Close

Request Expert Reply

Confirm Cancel

Which of the following lists the number of points at which a

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Director
Director
avatar
Joined: 09 Aug 2006
Posts: 692
Which of the following lists the number of points at which a  [#permalink]

Show Tags

New post 26 Jun 2007, 03:18
17
1
81
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

58% (01:01) correct 42% (01:20) wrong based on 2389 sessions

HideShow timer Statistics


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 only
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 56244
Re: Geometry  [#permalink]

Show Tags

New post 22 Feb 2010, 11:28
40
37
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
TriangleCircleIntersection88639.jpg [ 5.38 KiB | Viewed 112989 times ]

_________________
Most Helpful Community Reply
Manager
Manager
User avatar
Joined: 15 Dec 2008
Posts: 51
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]

Show Tags

New post 17 Mar 2009, 07:53
113
2
26
Accountant wrote:
Which of the following lists the number of points 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 and 6 only
E) 1,2,3,4,5 and 6

Can somebody help me? I have no idea what this means. I'll post OA later.


This is understanding how geomoetric figures work.

The options are 1,2,3,4,5,6
points that interesect.

I made a nice picture that shows all six options, so the answer is E.
Attachments

circles.JPG
circles.JPG [ 8.8 KiB | Viewed 107288 times ]

General Discussion
Senior Manager
Senior Manager
avatar
Joined: 04 Jun 2007
Posts: 326
  [#permalink]

Show Tags

New post 26 Jun 2007, 03:54
2
vshaunak@gmail.com wrote:
Should be 'B'

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. :-D

If the point of contact of a tangent is not considered as a point of intersection, then of course I am wrong. :)
Manager
Manager
avatar
Joined: 23 Apr 2007
Posts: 128
  [#permalink]

Show Tags

New post 26 Jun 2007, 11:21
2
Yes, tangents need to be considered.

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..."
CEO
CEO
User avatar
B
Joined: 17 Nov 2007
Posts: 3376
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
GMAT ToolKit User
Re: GMAT Prep PS - Circle intersecting triangle  [#permalink]

Show Tags

New post 17 Mar 2009, 08:04
4
Could we consider a tangent a intersection?
_________________
HOT! GMAT TOOLKIT 2 (iOS) / GMAT TOOLKIT (Android) - The OFFICIAL GMAT CLUB PREP APP, a must-have app especially if you aim at 700+ | Limited GMAT/GRE Math tutoring in Chicago
Manager
Manager
avatar
Status: Preparing Apps
Joined: 04 Mar 2009
Posts: 88
Concentration: Marketing, Strategy
GMAT 1: 650 Q48 V31
GMAT 2: 710 Q49 V38
WE: Information Technology (Consulting)
Re: GMAT Prep PS - Circle intersecting triangle  [#permalink]

Show Tags

New post 17 Mar 2009, 10:33
5
2
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.
Manager
Manager
avatar
Status: Keep fighting!
Affiliations: IIT Madras
Joined: 31 Jul 2010
Posts: 186
WE 1: 2+ years - Programming
WE 2: 3+ years - Product developement,
WE 3: 2+ years - Program management
Re: No clue for this DS question - from gmatprep  [#permalink]

Show Tags

New post 03 Sep 2010, 03:58
4
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
Retired Moderator
User avatar
Status: 2000 posts! I don't know whether I should feel great or sad about it! LOL
Joined: 04 Oct 2009
Posts: 1070
Location: Peru
Schools: Harvard, Stanford, Wharton, MIT & HKS (Government)
WE 1: Economic research
WE 2: Banking
WE 3: Government: Foreign Trade and SMEs
Re: Geometry question regarding circle and triangle  [#permalink]

Show Tags

New post 01 Nov 2010, 21:34
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!
_________________
"Life’s battle doesn’t always go to stronger or faster men; but sooner or later the man who wins is the one who thinks he can."

My Integrated Reasoning Logbook / Diary: http://gmatclub.com/forum/my-ir-logbook-diary-133264.html

GMAT Club Premium Membership - big benefits and savings
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 56244
Re: Geometry question regarding circle and triangle  [#permalink]

Show Tags

New post 01 Nov 2010, 21:54
Intern
Intern
avatar
Joined: 21 Feb 2008
Posts: 37
Location: United States
Concentration: Marketing, Nonprofit
Re: Which of the following lists the number of points at which a  [#permalink]

Show Tags

New post 22 May 2012, 21:14
I went with E as well. Circle intersects a triangle twice on each side for a total of 6 sides.
Intern
Intern
avatar
Joined: 01 Apr 2012
Posts: 25
Location: United States
Concentration: Technology, Economics
GMAT Date: 05-13-2012
WE: Consulting (Computer Software)
Re: Which of the following lists the number of points at which a  [#permalink]

Show Tags

New post 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........

so answer should be 'B'...

I agree with what AugiTh has posted.......
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 56244
Re: Which of the following lists the number of points at which a  [#permalink]

Show Tags

New post 23 May 2012, 00:19
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).

Check this for a complete solution: which-of-the-following-92274.html#p691200

Hope it helps.
_________________
Intern
Intern
User avatar
Joined: 30 Mar 2012
Posts: 31
Re: Which of the following  [#permalink]

Show Tags

New post 25 May 2012, 08:07
Its the Option E. Going by the definition of a tangent
Quote:
"A Tangent intersects a circle in only one point."

Its the definition of tangent that did the trick in this question. :)
_________________
This time its personal..
Manager
Manager
avatar
Joined: 25 Mar 2013
Posts: 55
WE: Project Management (Telecommunications)
Re: Which of the following lists the number of points at which a  [#permalink]

Show Tags

New post 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.
Intern
Intern
avatar
Joined: 06 Apr 2013
Posts: 14
Concentration: Marketing, General Management
GMAT 1: 640 Q44 V34
GPA: 3
Re: Which of the following lists the number of points at which a  [#permalink]

Show Tags

New post 24 Oct 2013, 21:52
Hi Bunuel,

Nice explanation. is there any trick to solve such questions without actually checking for every option. I tries to draw and got confused.

Suggest.
Senior Manager
Senior Manager
avatar
Joined: 08 Apr 2012
Posts: 343
Re: Which of the following lists the number of points at which a  [#permalink]

Show Tags

New post 24 Sep 2014, 04:59
Is there any way to do this besides trial and error?
Is there a pattern to follow?
Intern
Intern
avatar
Joined: 21 Jul 2015
Posts: 2
Re: Which of the following lists the number of points at which a  [#permalink]

Show Tags

New post 06 Aug 2015, 16:13
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.
CEO
CEO
avatar
S
Joined: 20 Mar 2014
Posts: 2620
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
GMAT ToolKit User Reviews Badge
Re: Which of the following lists the number of points at which a  [#permalink]

Show Tags

New post 06 Aug 2015, 17:12
hamsterlope wrote:
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.


IMHO, no rewording is required as a tangent 'intersects' a circle at the point of tangency. "Intersection" is determined to happen whenever you get a common point between 2 shapes (circle to circle, a line to circle etc) and as a tangent and the circle share 1 point, the tangent is by definition "intersecting" the circle.

From wolfram : "The intersection of two lines AB and CD is written AB intersection CD. The intersection of two or more geometric objects is the point (points, lines, etc.) at which they concur." (from http://mathworld.wolfram.com/Intersection.html).
Verbal Forum Moderator
User avatar
V
Status: Greatness begins beyond your comfort zone
Joined: 08 Dec 2013
Posts: 2351
Location: India
Concentration: General Management, Strategy
Schools: Kelley '20, ISB '19
GPA: 3.2
WE: Information Technology (Consulting)
GMAT ToolKit User Reviews Badge CAT Tests
Which of the following lists the number of points at which a  [#permalink]

Show Tags

New post Updated on: 28 Sep 2015, 08:16
1
Absolute Values/Modules tag is not required for this . :roll:
_________________
When everything seems to be going against you, remember that the airplane takes off against the wind, not with it. - Henry Ford
The Moment You Think About Giving Up, Think Of The Reason Why You Held On So Long
+1 Kudos if you find this post helpful

Originally posted by Skywalker18 on 28 Sep 2015, 08:14.
Last edited by Skywalker18 on 28 Sep 2015, 08:16, edited 1 time in total.
GMAT Club Bot
Which of the following lists the number of points at which a   [#permalink] 28 Sep 2015, 08:14

Go to page    1   2    Next  [ 31 posts ] 

Display posts from previous: Sort by

Which of the following lists the number of points at which a

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne