2001 AMC 10 Problem 4

What is the maximum number for the 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

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.