Question

If $4$ circles and $4$ straight lines intersect each other in a plane, then

• A. Maximum number of intersection points made by lines $=38$
• B. Maximum number of intersection points made by lines $=6$
• C. Maximum number of intersection points made by circles $=44$
• D. Maximum number of intersection points made by circles $=12$

Answer 1

Answer: (A), (C)

The correct options are
A Maximum number of intersection points made by lines $=38$
C Maximum number of intersection points made by circles $=44$

We have $4$ circles and $4$ straight lines.
In such case there would be $3$ types of intersections
$1)$Line and line ${}^4{C}_2\cdot 1=6\cdots \left(i\right)$

$2)$Line and circle ${}^4{C}_1\cdot {}^4{C}_1\cdot 2=32\cdots \left(ii\right)$

$3)$Circle and circle ${}^4{C}_2\cdot 2=12\cdots \left(iii\right)$

So total no. of maximum intersection points would be $\left(i\right)+\left(ii\right)+\left(iii\right)$ $=6+32+12$ $=50$