GMAT PREP II (2) QUESTION 15

[pkw209]

Hey all-

Just finished GMAT Prep II and couldn't figure out the answer to this question:

Q) 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

I'm sure if you know the rule, this is simple. Can someone please provide a brief explanation? Thanks!

[enniguy]

Well, in my opinion this question is as simple as it can get. I am not aware of a rule that describes this method. The only TRAP for which even I fell is the option 4.

So, the number of intersection between a triangle and a circle can be the following numbers:
1: Imagine a triangle tip touching a circle.
2. A triangle with one side outside the circle. (2 sides intersecting the circle).
3: Circumcircle or Incircle ( https://images.google.co.in/images?q=Circumcircle )
4: Imagine a circumcircle scenario with only one vertex (out of 3) outside the circle. The rest two are on the circle.
5: Imagine a circumcircle scenario with two vertices (out of 3) outside the circle. Only one is on the circle.
6: All the vertices of the triangle are outside the circle. Surprisingly, I found an image on google. I dint want to draw one.
( https://garethrees.org/2009/02/19/circle ... /cases.png ) - Check Image 5 for this case 6.