That is correct, a point of tangency counts as a single point of intersection. The answer is [E]

Hey Ryan..Can u explain that further pls??

Hopefully my little diagrams uploaded correctly. The definition of tangency is that a line only intersects a curve at one point. See here for more info, but don't get to bogged down in the higher-end geometry:

https://en.wikipedia.org/wiki/Tangent#

If I know a circle can intersect a triangle in 1 spot, then I can dismiss answer choices A and B.

Strategy wise, I see that 2, 3, and 6 points of intersection are in common with our remaining answer choices (C, D, E) so no need to test for them. My second diagram shows 4 points of intersection (tangent to two triangle legs and two intersection points on the other). The final diagram shows the 5 intersection example.

The key is to understand, geometrically, the way that a line segment (read: triangle leg) can intersect the side of a circle at just one point.

Hope this helps, good luck!

Great explanation Ryan..Thanks a lot!! I completely understand now.

Thanks for the explanation, but where is the 6th point? I only see upto 5 points

Hmmm. I purposely made a triangle that touches the circle 6 times. But, since the question does not ask the MAX number of points, how do we know how to construct the diagram?

The question asks what is "possible". Only one answer choice includes 5 points of intersection, so if it is possible to have exactly 5 points of intersection, that answer (E) can be the only correct answer.

In fact if you noticed that only one answer says that 5 points of intersection is a possibility, it would make sense to start by trying to draw a diagram with 5. Because such a diagram is possible, it's a waste of time to even consider other answers.

This is QID 1334

-Patrick