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

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

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New post 26 Jun 2007, 03:18
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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
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Re: Geometry  [#permalink]

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New post 22 Feb 2010, 11:28
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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 119998 times ]

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

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New post 17 Mar 2009, 07:53
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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.
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circles.JPG
circles.JPG [ 8.8 KiB | Viewed 114096 times ]

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

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New post 17 Mar 2009, 08:04
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Could we consider a tangent a intersection?
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Re: GMAT Prep PS - Circle intersecting triangle  [#permalink]

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New post 17 Mar 2009, 10:33
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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.
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Re: No clue for this DS question - from gmatprep  [#permalink]

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New post 03 Sep 2010, 03:58
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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.

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

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

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New post 01 Nov 2010, 21:54
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Re: Which of the following lists the number of points at which a  [#permalink]

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

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

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New post 12 Jul 2016, 00:04
Bunuel, this is quite an interesting problem from Geometry. Do you have a list of similar official problems? I don't think I have yet seen another official problem that's very similar.
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Re: Which of the following lists the number of points at which a  [#permalink]

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New post 12 Jul 2016, 03:00
TDK82 wrote:
Bunuel, this is quite an interesting problem from Geometry. Do you have a list of similar official problems? I don't think I have yet seen another official problem that's very similar.


Similar questions to practice:
which-of-the-following-lists-the-number-of-points-at-which-a-138952.html
which-of-the-following-lists-the-no-of-points-at-which-a-circle-can-114013.html
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Which of the following lists the number of points at which a  [#permalink]

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New post 28 Sep 2017, 07:55
Hi GMATters,

Here is my video solution to this problem:



Enjoy!

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

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New post 20 Apr 2018, 14:38
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GK_Gmat wrote:
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



Image

Answer: E

The important takeaway here is that "intersect" does not necessarily mean "pass through"
So, a line that is tangent to a circle (touching the circle but not passing through it) can be said to intersect the circle. To intersect is to share a common point.

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

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New post 21 Jan 2019, 07:32
GK_Gmat wrote:
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

The fact that the figure below is viable (constructible) guarantees the correct answer is (E).

Image


We follow the notations and rationale taught in the GMATH method.

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

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Re: Which of the following lists the number of points at which a   [#permalink] 10 Oct 2019, 04:25
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