You can give them any name that you like. Conventionally, points are named by capital Roman letters but you do not have to stick by that. You could, if you wanted to, name them after your best friends!
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The place where two points meet is known as an intersection in math.
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 ).
You need two, or more, curves for points of intersection.