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The maximum number of intersection points of 4 different circles is...

 Jan 17, 2019
 #1
avatar+23494 
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I believe it is 12 .   That is what I find.

 Jan 17, 2019
 #2
avatar+111357 
+1

Each pair of circles intersect twice

 

So.....we have a set of n circles and we want to choose any two of them  = C (n, 2)

 

And since each pair intersects twice, the number of intersection points = 2 C(n , 2)  =

 

2 n! / [ (n - 2)! * 2! ]   =  n! / ( n - 2)!  =   n ( n - 1)

 

So.....The max intersection points of n circles =  n(n - 1)

 

So.....  4(4 - 1)  =  4 (3)   =  12

 

Just as EP found !!!!

 

 

cool cool cool

 Jan 17, 2019
edited by CPhill  Jan 17, 2019

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