Geometry

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singhmaharaj: Senior | Next Rank: 100 Posts; Posts: 38; Joined: Tue Feb 10, 2009 6:24 amFollowed by: 2 members; Location: Hong Kong

by singhmaharaj » Sun Apr 06, 2014 5:51 am

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

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Source: Beat The GMAT — Problem Solving | Sun Apr 06, 2014 5:51 am

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Sun Apr 06, 2014 7:36 am

singhmaharaj 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

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,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Sun Apr 06, 2014 2:14 pm

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

Notice how the answer choices DIFFER.
Only E states that the circle and the triangle can intersect at 5 points.
If it's possible for there to be 5 intersections, A, B, C and D can be eliminated.

Since 5 intersections are possible, eliminate A, B, C and D.

The correct answer is E.

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