Problem Solving

I'd think through this one using a practical rather than a mathematical approach. Take 2 coins that are different sizes, such as a penny and a quarter. Play with them for a bit and you'll see that the maximum number of points of intersection is 2. There's just no physical way to make them intersect three times. And "infinite" can only be the answer if the 2 circles are the same size, which they cannot be if they have unequal radii.