Question

In a plane there are 27 straight lines ,of wch 13 pass through the point A and 11 pass through the point B. Besides, no three lines pass through one point, no line passes through both point A andB and no two are parallel. Find the number of points of intersection of the straight lines

Answer 1

If we consider remaining 3 lines, they will cut all other lines since they are non parallel. maximum lines passing through a point is 2 except A and B.
No. of intersection=26+25+24=75
now Lines passing from A will interce will intersect lines through B
no. of intersection=13×11=143
so total points are= 75+143+2=22O