TITLE: maximum points of intersection between a circle and rectangle
QUESTION [5 upvotes]: I had today this mathematical question:
What is the maximum number of points of intersection between a circle and a rectangle such that the length of the rectangle is greater than the circle's diameter, and its width is less than the circle's diameter?

REPLY [5 votes]: A circle intersects a straight line in at most two points. Your circle can't intersect your rectangle on all four sides. So the answer is six.