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What is the greatest number of points of intersection that can occur when 2 different circles and 2 different straight lines are drawn on the same piece of paper?

 Jan 24, 2019
 #1
avatar+107520 
+2

Maybe.

 

 Jan 24, 2019
 #2
avatar+24093 
+7

What is the greatest number of points of intersection that can occur when
2 different circles and 2 different straight lines are drawn on the same piece of paper?

 

\(\text{Let $n$ the number of circles }\\ \text{Let $m$ the number of straight lines }\)

 

 

 

 

\(\begin{array}{|rcll|} \hline n &=& 2\\ m &=& 2 \\\\ && \dfrac{1}{2}\cdot m(m-1)+n(2m+n-1)\\ &=& \dfrac{1}{2}\cdot 2(2-1)+2(2\cdot 2+2-1) \\ &=& 1 +2\cdot 5 \\ &\mathbf{=}& \mathbf{11} \\ \hline \end{array} \)

 

The greatest number of points of intersection is 11

 

Source: https://math.stackexchange.com/questions/1241472/the-greatest-number-of-points-of-intersection-of-n-circles-and-m-straight-lines

 

laugh

 Jan 24, 2019
edited by heureka  Jan 24, 2019

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