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?"