100 BC Circles !

Geometry Level 3

What is the maximum number of intersections that can be made using 100 circles ?


The answer is 9900.

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Gagan Raj by Gagan Raj , 23, India

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1 solution

Gagan Raj
Apr 7, 2015

A simple formula for these type of problems which can be used is I = n ( n − 1 ) I = n(n-1) where n n is the number of circles given.

Here , n = 100 n=100

Thus , the maximum number of intersection is 100 ( 100 − 1 ) = 100 ( 99 ) = 9900 100(100-1)=100(99)=9900

1 Helpful 0 Interesting 0 Brilliant 0 Confused

How this formula come ?? Is this such that number of ways of choosing 2 circles out of 100 is C ( 100 , 2 C(100,2 and two circles can maximum intersect two times so our answer becomes 2 [ C ( 100 , 2 ) ] 2[C(100,2)] =9900 ??

Chirayu Bhardwaj - 4 years, 9 months ago

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