Which of the Following Lists the Number of Points at Which a Circle Can Intersect a Triangle?

number of points a circle can intersect a triangle

This topic has expert replies

Which of the post-obit lists the number of points at which a circle can intersect a triangle?

A)two and 6 only
B)2, 4, and 6 only
C)one, 2, 3 and 6 just
D)ane, two, 3, 4 and six simply
Due east)1, 2, iii, 4, 5, and 6

Reply: East

How exercise you solve? I don't even understand this question.

See the following figures:

Hence, correct answer is E.

Terminal edited by [email protected] on Wed Aug 03, 2011 seven:54 pm, edited 1 time in total.

GMATGuruNY

GMAT Instructor

• View User Profile

Posts: 15536

Joined: 25 May 2010

Location: New York, NY

Thanked: 13060 times

Followed by:1901 members

GMAT Score:790

AMat700 wrote:Which of the following lists the number of points at which a circle tin can intersect a triangle?

A)ii and 6 only
B)ii, 4, and half dozen only
C)1, 2, three and 6 only
D)1, two, 3, 4 and 6 only
Due east)one, ii, 3, 4, five, and 6

Answer: E

How do you solve? I don't fifty-fifty understand this question.

The quickest approach is to detect how the reply choices differ. Only answer choice E says that 5 intersections are possible:

Since 5 intersections are possible, eliminate A, B, C and D. No need to attempt any other options.

The correct answer is E.

by Kemmy Grand » Mon May 21, 2012 1:53 pm

@GMATGuruNY,

I beg to differ. For those who don't even sympathise the question (like me!) Your explanation doesn't help at all. What if the testmakers purposely threw in the 5 to confuse those who don't know what to practice? I'll capeesh if you could give a more detailed explanation. Thanks!

Define the difference between intersecting and to be tangent in cases ane three and v...I know the OA, only with all due respect, one, iii and v strictly speaking is not intersecting.

aircraft wrote:Define the difference betwixt intersecting and to be tangent in cases one three and v...I know the OA, simply with all due respect, i, iii and 5 strictly speaking is non intersecting.

"Intersect" does not necessarily mean "pass through."
To intersect is to share a mutual point.
So, a line that is tangent to a circumvolve (touching the circle simply not passing through it) can be said to intersect the circle.

The Official Guide doesn't have a formal definition of "intersect," but nosotros tin infer its meaning from the test-maker's definition of a airtight plane figure (e.g., a rectangle):

A polygon is a airtight plane figure formed past three or more line segments, called the sides of the
polygon. Each side intersects exactly two other sides at their endpoints.

And so, the adjacent sides of a rectangle do not pass through each other, but they are said to intersect.

Cheers,
Brent

AMat700 wrote: ↑

Tue Feb 22, 2011 viii:03 pm

Which of the following lists the number of points at which a circumvolve can intersect a triangle?

A)2 and six simply
B)2, 4, and 6 simply
C)ane, 2, 3 and 6 merely
D)1, ii, 3, 4 and 6 only
E)i, 2, iii, four, 5, and 6

Answer: Due east

Solution:

A circle tin intersect a triangle at ane to 6 points, inclusively (see diagrams below):

(Note: Technically, 0 should be included in choice E since a circle and a triangle don't need to intersect each other.)

Answer: E

strattondurfult.blogspot.com

Source: https://www.beatthegmat.com/number-of-points-a-circle-can-intersect-a-triangle-t76683.html