Consider a triangle ABC.
1- We can draw a circle which is a tangent to one side of tiangle (say AB).
2- Draw a circle that intersects at two points on side AB.
3- Pick one of the vertices (say C), use it as a pivot and draw a circle cutting two sides of the triangle (say CB and CA).
4- Draw a circle intersecting only two sides of the triangle (say AB and AC)
5- Pick one of the vertices (say C), use it as a pivot and draw a circle cutting all three sides of the triangle (say CB, CA and AB).
(Remember that one of the vertices is counted as one point)
6- Draw a circle intersecting all sides of the triangle.
I couldn't think of 7. So, will go with (E)
To find what you seek in the road of life, the best proverb of all is that which says:
"Leave no stone unturned."
-Edward Bulwer Lytton