Which of the following lists a number of points at which a circle intersects a triangleA. 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 only
Circle can intersect triangle at one of the vertices - 1 point of intersection;
Circle can intersect triangle at two of the vertices - 2 points of intersection;
Circle can intersect triangle at three of the vertices (inscribed triangle or inscribed circle) - 3 points of intersection;
Circle can intersect triangle at two of the vertices and two sides - 4 points of intersection;
Circle can intersect triangle at one of the vertex and cut three sides (one side twice and other two once) two sides - 5 points of intersection;
Circle can cut all three sides twice - 6 points of intersection.
Hence circle can intersect triangle at 1, 2, 3, 4, 5 or 6 points. (The examples I provided are not the only possible cases of intersection points, just these examples prove that there can be from 1 to 6 intersections).
Answer: E.
Below is the diagram showing possible cases of intersections provided by DestinyChild.
Attachment:
TriangleCircleIntersection88639.jpg
Can we take this as "there cannot be more than 6 intersections?"