2001 AMC 10 Problems/Problem 4

Problem

What is the maximum number of possible points of intersection of a circle and a triangle?

\textbf{(A) }2\qquad\textbf{(B) }3\qquad\textbf{(C) }4\qquad\textbf{(D) }5\qquad\textbf{(E) }6

Solution

Here is the picture: http://www.artofproblemsolving.com/Forum/download/file.php?id=6658&

We can draw a circle and a triangle, such that each side is tangent to the circle. This means that each side would intersect the circle at one point.

You would then have points, but what if the circle was bigger? Then, each side would intersect the circle at 2 points.

Therefore, .