5circles lie in the same plane. what is the maximum number of points of intersection of them?

20

Step-by-step explanation:

the first circles give you 2 points of intersection. when you add the third circle, you get 4 more points, so you will get 6. basically, whenever 2 circles intersect, it will give you 2 points of intersection. so, using this thing, lets find a pattern. when the first 2 circles intersect, you get 2 points. the third circle can either intersect 1 circle, or 2 circles. we're looking for the greatest possible points of intersection, so we're going for the most. if the third circle intersects 2 circles, you will get 4 points. the 4th circle will intersect the other 3, so you will get 6 points. the 5th circle will intersect the other 4 circles, so you will have 8 points. 2+4+6+8=20.