Circle intersecting triangle

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Circle intersecting triangle

by psm12se » Sat Feb 23, 2013 7:57 am
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
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by Anurag@Gurome » Sat Feb 23, 2013 8:16 am
psm12se wrote:Which of the following lists the number of points at which a circle can intersect a triangle?
See the following figures:

Image

Hence, correct answer is E.
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by GMATGuruNY » Sat Feb 23, 2013 8:45 am
psm12se 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
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.

Image

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

The correct answer is E.
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by The Iceman » Sat Feb 23, 2013 10:25 am
As a general rule, a polygon with n sides, can intersect a circle at a minimum of 0 to a maximum of 2n points, 0 being the case of no intersection.