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by parallel_chase » Tue Jul 29, 2008 2:54 pm
Yes a circle can intersect a triangle at 2,3,4,5, or 6 points. But the max is 6 points.
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by ricky » Tue Jul 29, 2008 3:10 pm
How is it Possible to intersect at 3 and 5 points? :o
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Re: Geometry

by Ian Stewart » Tue Jul 29, 2008 3:10 pm
ricky wrote:Can a circle intersect a triangle at 3 or 5 points?
Yes to both. You need to consider the possibility that the triangle exactly touches one of the sides in one place only, however. For three points, you can take an equilateral triangle, for example, and draw a circle inside the triangle so it exactly touches each side once. For five points, you can draw a tall triangle, then choose a point on the base- draw a circle beginning from that point of the right size to intersect the other two sides in two points each. Easier to see if you draw a picture!
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by ricky » Tue Jul 29, 2008 3:18 pm
But INTERSECTION is different than TOUCHING..Isn't?
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by Ian Stewart » Tue Jul 29, 2008 5:35 pm
ricky wrote:But INTERSECTION is different than TOUCHING..Isn't?
No, at least not in geometry. If you want to see this discussed elsewhere, see here:

mathworld.wolfram.com/Circle-LineIntersection.html

though don't read the equations after the first paragraph- will not help for GMAT preparation.
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by ricky » Wed Jul 30, 2008 12:03 am
Thanx Ian
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Intersection

by tamadhi » Wed Jul 30, 2008 1:24 am
A Circle can also intersect a triangle at 6 places !
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