Jul 16 03:00 PM PDT  04:00 PM PDT Join a free live webinar and find out which skills will get you to the top, and what you can do to develop them. Save your spot today! Tuesday, July 16th at 3 pm PST Jul 16 08:00 PM EDT  09:00 PM EDT Strategies and techniques for approaching featured GMAT topics. Tuesday, July 16th at 8 pm EDT Jul 19 08:00 AM PDT  09:00 AM PDT The Competition Continues  Game of Timers is a teambased competition based on solving GMAT questions to win epic prizes! Starting July 1st, compete to win prep materials while studying for GMAT! Registration is Open! Ends July 26th Jul 20 07:00 AM PDT  09:00 AM PDT Attend this webinar and master GMAT SC in 10 days by learning how meaning and logic can help you tackle 700+ level SC questions with ease. Jul 21 07:00 AM PDT  09:00 AM PDT Attend this webinar to learn a structured approach to solve 700+ Number Properties question in less than 2 minutes
Author 
Message 
TAGS:

Hide Tags

Director
Joined: 09 Aug 2006
Posts: 692

Which of the following lists the number of points at which a
[#permalink]
Show Tags
26 Jun 2007, 03:18
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
Official Answer and Stats are available only to registered users. Register/ Login.




Math Expert
Joined: 02 Sep 2009
Posts: 56244

Re: Geometry
[#permalink]
Show Tags
22 Feb 2010, 11:28
Which of the following lists a number of points at which a circle intersects a triangleA. 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 112989 times ]
_________________




Manager
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
17 Mar 2009, 07:53
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 [ 8.8 KiB  Viewed 107288 times ]




Senior Manager
Joined: 04 Jun 2007
Posts: 326

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



Manager
Joined: 23 Apr 2007
Posts: 128

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
Joined: 17 Nov 2007
Posts: 3376
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth)  Class of 2011

Re: GMAT Prep PS  Circle intersecting triangle
[#permalink]
Show Tags
17 Mar 2009, 08:04
Could we consider a tangent a intersection?
_________________
HOT! GMAT TOOLKIT 2 (iOS) / GMAT TOOLKIT (Android)  The OFFICIAL GMAT CLUB PREP APP, a musthave app especially if you aim at 700+  Limited GMAT/GRE Math tutoring in Chicago



Manager
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
17 Mar 2009, 10:33
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
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
03 Sep 2010, 03:58
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 incircle 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
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
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/myirlogbookdiary133264.html GMAT Club Premium Membership  big benefits and savings



Math Expert
Joined: 02 Sep 2009
Posts: 56244

Re: Geometry question regarding circle and triangle
[#permalink]
Show Tags
01 Nov 2010, 21:54
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).
_________________



Intern
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
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
Joined: 01 Apr 2012
Posts: 25
Location: United States
Concentration: Technology, Economics
GMAT Date: 05132012
WE: Consulting (Computer Software)

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........
so answer should be 'B'...
I agree with what AugiTh has posted.......



Math Expert
Joined: 02 Sep 2009
Posts: 56244

Re: Which of the following lists the number of points at which a
[#permalink]
Show Tags
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: whichofthefollowing92274.html#p691200Hope it helps.
_________________



Intern
Joined: 30 Mar 2012
Posts: 31

Re: Which of the following
[#permalink]
Show Tags
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.
_________________



Manager
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
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
Joined: 06 Apr 2013
Posts: 14
Concentration: Marketing, General Management
GPA: 3

Re: Which of the following lists the number of points at which a
[#permalink]
Show Tags
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
Joined: 08 Apr 2012
Posts: 343

Re: Which of the following lists the number of points at which a
[#permalink]
Show Tags
24 Sep 2014, 04:59
Is there any way to do this besides trial and error? Is there a pattern to follow?



Intern
Joined: 21 Jul 2015
Posts: 2

Re: Which of the following lists the number of points at which a
[#permalink]
Show Tags
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
Joined: 20 Mar 2014
Posts: 2620
Concentration: Finance, Strategy
GPA: 3.7
WE: Engineering (Aerospace and Defense)

Re: Which of the following lists the number of points at which a
[#permalink]
Show Tags
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
Status: Greatness begins beyond your comfort zone
Joined: 08 Dec 2013
Posts: 2351
Location: India
Concentration: General Management, Strategy
GPA: 3.2
WE: Information Technology (Consulting)

Which of the following lists the number of points at which a
[#permalink]
Show Tags
Updated on: 28 Sep 2015, 08:16
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 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.




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 ]



