Question

The maximum number of points of intersection of 8 circles of unequal radii is 56. 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)

Statement -1 is true, Statement -2 is true ; Statement-2 is NOT a correct explanation for Statement - 1

Answer 2

Two circles intersect in 2 points. $\therefore$ Maximum number of points of intersection $= 2 ?$ number of selections of two circles from 8 circles $= 2 ? ^8C_2 = 2 ? 28 = 56$ Statement $2 : 4$ lines intersect each other in $^4C_2 = 6$ points 4 circles intersect each other in $2 ? ^4C_2 = 12$ 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 $= 6 + 12 + 32 = 50$