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?

Guest Jan 24, 2019

#2**+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**

heureka Jan 24, 2019