Question

Statement-1 : The maximum number of points of intersection of 8 circles of unequal radii is 56.
Statement-2 : The maximum number of points into which 4 circles of unequal radii and 4 non coincident straight lines intersect, is 50.

• A. Statement-1 is true, Statement-2 is true, Statement-2 is a correct explanation for Statement -1
• B. Statement -1 is true, Statement -2 is true ; Statement-2 is NOT a correct explanation for Statement - 1
• C. Statement -1 is false, Statement -2 is true
• D. Statement - 1 is true, Statement- 2 is false

Answer 1

Answer: (B)

Two circles intersect in 2 points.
$\therefore$ Maximum number of points of intersection
$=2\times$ number of selections of two circles from 8 circles
$=2{\times }^8{C}_2=2\times 28=56$
Statement $2:4$ lines intersect each other in ${}^4{C}_2=6$ points
4 circles intersect each other in $2{\times }^4{C}_2=12$ points.
Further, one lines and one circle intersect in two points. So 4 lines will intersect four circles in 32 points.
Maximum number of points $=6+12+32=50$