Problem Solving

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

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

Alternatively, we might recognize that only 1 answer choice (E) suggests that there can be 5 intersection points.
Let's check to see if we can get 5 intersection points:

Yep.
So, the correct answer must be E

Cheers,
Brent

nikhilgmat31 wrote:Identify that triangle & circle intersects 5 points is very tough among 1,2,3,4,6 points.

What is source of this question.

I'm pretty sure it's an official GMAT question

Hi nikhilgmat31,

This question is floating around the 'pool' of questions in GMAC CAT 1.

For what it's worth, if you draw a handful of pictures, then you can prove all of the various options rather easily. If you can see how a triangle can intersect at 2 points and at 3 points, then you can 'combine' those two ideas to see how a triangle could intersect at 5 points.

GMAT assassins aren't born, they're made,
Rich