Problem Solving

koby_gen wrote:Which of the following lists the number of points at which a circle can intersect a parallelogram ?

(A) 2, 4, and 8 only
(B) 2, 4, 6 and 8 only
(C) 1, 2, 3, 4, 6 and 8 only
(D) 2, 3, 4 , 5, 6, 7 and 8 only
(E) 1, 2, 3, 4, 5, 6, 7 and 8

Note that if a line just touches a circle, i.e. the line is a tangent to the circle, then it is considered that the line intersects the circle at one point. Thus a line can intersect a circle at either 1 or 2 points.

A parallelogram has 4 lines.
Hence, it can intersect a circle at either 1, 2, 3, 4, 5, 6, 7, or 8 points.

The correct answer is E.