Question

If the maximum number of points in which $4circles$ and $4straight$ lines intersect is $k$, then write the value of $k$.

Answer 1

we have $4$ circles and $4$ straight line

(1) line and line intersections :-

two line can intersects at $1$ point

$\therefore 4$ lines maximum intersection = ${}^4{C}_2.1=6$

(2) line and circle intersections:-

line and circle can intersects at $2$ point.

$\therefore 4$ lines and $4$ circles maximum intersection = ${}^4{C}_1.{}^4{C}_1.2=32$

(3) circles and circle intersections :

Two circles can intersects at most $2$ points

$\therefore 4$ circles maximum intersection = ${}^4{C}_2.2=12$

total no. of maximum intersection= $6+32+12=50.$