Question

The maximum number of points of intersection of $4$ circles and $4$ straight lines is

• A. $25$
• B. $50$
• C. $56$
• D. $72$

Answer 1

The correct option is B $50$

We have

$4$ circles

$4$ straight

In such case there would be 3 types of intersections

line and line

${{}^{4}C}_2.1=\mathrm{6........}\left(i\right)$

Line and circle

$4C.{{}^{4}C}_1.2=\mathrm{32...}\left(ii\right)$

circle and circle

${{}^{4}C}_2.2=\mathrm{12...}\left(iii\right)$

So total no of maximum intersection would be

(i)+(ii)+(iii)

$=6+32+12$

$=50$