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# What is the no. of points a triangle can intersect a circle?

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Manager
Joined: 24 Jan 2005
Posts: 209
Location: Boston
What is the no. of points a triangle can intersect a circle?  [#permalink]

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01 Jun 2005, 16:18
1
What is the no. of points a triangle can intersect a circle?

This is a OG question. I need to know why is touching same as intersecting. To me by intersection, we mean when one figure cuts thru another figure, while touching is not the same it (the circle) can just be a tangent to one of the sides of the triange.

So Ans will be 3 (2,4,6 points) for full intersection

Ans will be 6 (1,2,3,4,5,6 points) if touching is also included.

The OG is 6.

Anu thoughts!!!!!!!!!!!!!!1

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Director
Joined: 18 Apr 2005
Posts: 523
Location: Canuckland

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01 Jun 2005, 20:24
I know what you mean, I had a similar question.

Merriam-Webster definition of 'to intersect' is
Main Entry: inÂ·terÂ·sect
Pronunciation: "in-t&r-'sekt
Function: verb
Etymology: Latin intersectus, past participle of intersecare, from inter- + secare to cut -- more at SAW
transitive senses : to pierce or divide by passing through or across : CROSS
intransitive senses
1 : to meet and cross at a point
2 : to share a common area : OVERLAP

2 doesn't apply since a point has no area

so OG question is indeed misleading.
Director
Joined: 01 Feb 2003
Posts: 788

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01 Jun 2005, 20:28
I do not understand the confusion - isn't the answer 6?

Can you give me the question number in OG?
SVP
Joined: 05 Apr 2005
Posts: 1604

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01 Jun 2005, 20:39
Vithal wrote:
I do not understand the confusion - isn't the answer 6?
Can you give me the question number in OG?

in my understanding, the question is "in geomatry is intersection same as tangant"?
Director
Joined: 18 Apr 2005
Posts: 523
Location: Canuckland

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01 Jun 2005, 20:40
Last one in PS section, or somewhere on the last page of PS
Director
Joined: 18 Apr 2005
Posts: 523
Location: Canuckland

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01 Jun 2005, 20:43
HIMALAYA wrote:
Vithal wrote:
I do not understand the confusion - isn't the answer 6?
Can you give me the question number in OG?

in my understanding, the question is "in geomatry is intersection same as tangant"?

A geometry teacher would always say 'line touches the circle" when the line is a tangent. Intersecting the circle means crossing it.
Senior Manager
Joined: 17 Apr 2005
Posts: 352
Location: India
Re: Triangle intersecting a circle  [#permalink]

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02 Jun 2005, 07:36
anirban16 wrote:
What is the no. of points a triangle can intersect a circle?

This is a OG question. I need to know why is touching same as intersecting. To me by intersection, we mean when one figure cuts thru another figure, while touching is not the same it (the circle) can just be a tangent to one of the sides of the triange.

So Ans will be 3 (2,4,6 points) for full intersection

Ans will be 6 (1,2,3,4,5,6 points) if touching is also included.

The OG is 6.

Anu thoughts!!!!!!!!!!!!!!1

I think the question meant the maximum no. of points a circle can intersect a circle (the no. of possible no. of points is of no consideration )

HMTG.
Manager
Joined: 07 Mar 2005
Posts: 89

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02 Jun 2005, 15:32
look at my drawing. Clearly 6 points of intersection.
Attachments

circle.JPG [ 6.95 KiB | Viewed 2099 times ]

Director
Joined: 18 Apr 2005
Posts: 523
Location: Canuckland
Re: Triangle intersecting a circle  [#permalink]

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02 Jun 2005, 16:52
HowManyToGo wrote:
anirban16 wrote:
What is the no. of points a triangle can intersect a circle?

This is a OG question. I need to know why is touching same as intersecting. To me by intersection, we mean when one figure cuts thru another figure, while touching is not the same it (the circle) can just be a tangent to one of the sides of the triange.

So Ans will be 3 (2,4,6 points) for full intersection

Ans will be 6 (1,2,3,4,5,6 points) if touching is also included.

The OG is 6.

Anu thoughts!!!!!!!!!!!!!!1

I think the question meant the maximum no. of points a circle can intersect a circle (the no. of possible no. of points is of no consideration )

HMTG.

in OG in explanation they they show cases when a circle touches the triangle (3 intersections)

the question itself

441. 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

OA is E
SVP
Joined: 03 Jan 2005
Posts: 2108

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02 Jun 2005, 21:23
If we go by the meaning of intersect as "meet at a point" then tangent would be a special case of interesection.
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Posts: 9420
Re: What is the no. of points a triangle can intersect a circle?  [#permalink]

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08 Jan 2018, 13:18
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