What is the greatest number of points of intersection that can occur when 2 different circles and 2 different straight lines are drawn on the same piece of paper?
Think about this incrementally, adding one shape at a time.
1. Circle, zero intersection
2. Circle, best we can do is 2, making a venn diagram.
3. Line, let's have it be horizontal and cut the venn in half. That's 4 more, so we're at 6.
4. Line, this one can be almost the same as the last one but just a tiny bit off horizontal. It cuts the circles for 4 more intersections, and the existing line for 1 more.
That's 11 total. If we think about each shape individually, this is the best possible result