Geometry

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ricky: Master | Next Rank: 500 Posts; Posts: 118; Joined: Sun Jun 01, 2008 1:47 pmFollowed by: 1 member; Thanked: 5 times

by ricky » Tue Jul 29, 2008 2:22 pm

Can a circle intersect a triangle at 3 or 5 points?

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Source: Beat The GMAT — Problem Solving | Tue Jul 29, 2008 2:22 pm

parallel_chase: Legendary Member; Posts: 1153; Joined: Wed Jun 20, 2007 6:21 amFollowed by: 2 members; Thanked: 146 times

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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ricky: Master | Next Rank: 500 Posts; Posts: 118; Joined: Sun Jun 01, 2008 1:47 pmFollowed by: 1 member; Thanked: 5 times

by ricky » Tue Jul 29, 2008 3:10 pm

How is it Possible to intersect at 3 and 5 points?

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Ian Stewart: GMAT Instructor; Posts: 2623; Joined: Mon Jun 02, 2008 3:17 amFollowed by: 355 members; Location: Montreal; Thanked: 1090 times; GMAT Score:780

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!

For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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ricky: Master | Next Rank: 500 Posts; Posts: 118; Joined: Sun Jun 01, 2008 1:47 pmFollowed by: 1 member; Thanked: 5 times

by ricky » Tue Jul 29, 2008 3:18 pm

But INTERSECTION is different than TOUCHING..Isn't?

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Ian Stewart: GMAT Instructor; Posts: 2623; Joined: Mon Jun 02, 2008 3:17 amFollowed by: 355 members; Location: Montreal; Thanked: 1090 times; GMAT Score:780

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.

For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

ianstewartgmat.com

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ricky: Master | Next Rank: 500 Posts; Posts: 118; Joined: Sun Jun 01, 2008 1:47 pmFollowed by: 1 member; Thanked: 5 times

by ricky » Wed Jul 30, 2008 12:03 am

Thanx Ian

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tamadhi: Newbie | Next Rank: 10 Posts; Posts: 3; Joined: Sun Jul 27, 2008 10:44 pm

Intersection

by tamadhi » Wed Jul 30, 2008 1:24 am

A Circle can also intersect a triangle at 6 places !

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