Find 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

Explanation

Points of intersection of 7 straight lines `= .^(7)C_(2)- .^(3)C_(2)=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
Fifth circle can intersect the system at maximum
=14+2+2+2+2=22 points
`therefore` Maximum number of points of intersection
=18+28+18+20+22=106.