Six (6)
Two distinct lines can intersect at most at one point. If the lines are not parallel, they will cross at a single point. If they are parallel, they will never intersect. Therefore, the maximum number of intersection points for two distinct lines is one.
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 ).
10.
12
If no pair of lines is parallel and if each pairwise intersection is distinct, there will be 10 points of intersection.
discuss the possible number of points of interscetion of two distinct circle
6 maximum points of intersection
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 ).
10.
8
12
If the circle is inside the square, four.
If no pair of lines is parallel and if each pairwise intersection is distinct, there will be 499500 points of intersection.
If no pair of lines is parallel and if each pairwise intersection is distinct, there will be 10 points of intersection.
If no pair of lines is parallel and if each pairwise intersection is distinct, there will be 6 points of intersection.
The intersection of two distinct planes is a line. The set of common points in the line lies in both planes.
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