Question

The maximum no. of points into which $4$ circles and $4$ straight lines intersect is :

• A. $26$
• B. $56$
• C. $50$
• D. $72$

Answer 1

The correct option is C

$50$

Explanation for the correct option:

We have $4$ circles and $4$ straight line. There are three types of intersections. They are:

We know that Two-line can intersect at $1$ point.

$\therefore 4$ lines maximum intersection $={}^{4}C_2.1=6$

We know that Line and circle can intersect at $2$ point.

$\therefore 4$ lines and $4$ circles maximum intersection $={}^{4}C_1.{}^{4}C_1.2=32$

We know that Two circles can intersect at most $2$ points.

$\therefore 4$ circles maximum intersection $={}^{4}C_2.2=12$

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

Hence, $\mathrm{Option}\left(\mathrm{C}\right)$ is the correct answer.