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When two circles intersect, they can create a maximum of 2 intersection points. Each straight line can intersect with each of the two circles at a maximum of 2 points, contributing 10 points from the lines and circles. Additionally, the five straight lines can intersect each other, yielding a maximum of ( \binom{5}{2} = 10 ) intersection points. Therefore, the total maximum points of intersection are ( 2 + 10 + 10 = 22 ).
If there are n points then the maximum number of lines possible is n*(n-1)/2 and that maximum is attained of no three points are collinear.
There is no "this statement" associated with the question, but the maximum number of points which lie of the graph of a linear equation in two variables is infinite.
20 points
Minimum 3 points - maximum 12 points.