Question
Question: The maximum number of points of intersection of 7 straight lines and 5 circles when 3 straight lines...
The maximum number of points of intersection of 7 straight lines and 5 circles when 3 straight lines are parallel and 2 circles are concentric, is/are-
A
106
B
96
C
90
D
None of these
Answer
106
Explanation
Solution
Points of intersection due to 7 straight lines = 7C2 –3 = 18
Two concentric circles can intersect these 7 lines at maximum = 14 + 14 = 28 points
Third circle can intersect the given system at maximum
= 14 + 2 + 2 = 18
Fourth circle can intersect the system at maximum
= 14 + 2 + 2 + 2 = 20 points
For fifth circle = 14 + 2 + 2 + 2 + 2 = 22 maximum no. of points of intersection
= 18 + 28 + 18 + 20 + 22 = 106