Question

Maximum and minimum number of points of intersection of three lines are A and B respectively. Find A+B if no pair of lines is parallel.

Answer 1

Three lines can intersect at a maximum of 3 points when they form a closed figure called triangle as shown in the first figure below.

So, A = 3

Minimum number of points of intersection of three lines will be 1 when all the three lines are concurrent as shown in the second figure below.

So, B = 1

Hence, A + B = 3 + 1 = 4