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

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Manager
Joined: 20 Jun 2007
Posts: 157
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Which of the following lists the number of points at which a [#permalink]  12 Jan 2008, 06:15
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Which of the following lists the number of points at which a circle can intersect a triangle?
1) 2 and 6 only
2) 2, 4 and 6 only
3) 1, 2, 3 and 6 only
4) 1, 2, 3, 4 and 6 only
5) 1, 2, 3, 4, 5 and 6
Director
Joined: 12 Jul 2007
Posts: 865
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Re: Geometry PS - GMAT Prep [#permalink]  12 Jan 2008, 07:40

1 Point: Circle just touching 1 side or vertex (leaves us with options 3, 4, 5)

Now we see that options 3, 4, 5 all have 1, 2, 3 in them so now let's test 5 points. If 5 points works then 5 is the only possible answer, if 5 points don't work we go back and test 4 points.

5 Points: Circle that touches the base from the inside of the triangle at one point, then intersects each of the legs twice (from going outside the triangle and coming back in)

and by testing 2 points we see our answer!
CEO
Joined: 29 Mar 2007
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Re: Geometry PS - GMAT Prep [#permalink]  12 Jan 2008, 08:51
Raffie wrote:
Which of the following lists the number of points at which a circle can intersect a triangle?
1) 2 and 6 only
2) 2, 4 and 6 only
3) 1, 2, 3 and 6 only
4) 1, 2, 3, 4 and 6 only
5) 1, 2, 3, 4, 5 and 6

Best to just draw a triangle and a circle.
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Circletriangle.doc [394 KiB]

Re: Geometry PS - GMAT Prep   [#permalink] 12 Jan 2008, 08:51
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# Which of the following lists the number of points at which a

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