Points A, B and C are collinear. Find the length of the segment BC if AB = 24cm, AC = 32cm.

Points A, B and C are collinear. Find the length of the segment BC if AB = 24cm, AC = 32cm. How many solutions does the problem have?

1. This problem can have two solutions, since the point B can either belong to the segment AC on the straight line, or not, but lie on one straight line.
Solution 1:
a) Point B belongs to the segment AC, therefore:
BC = AC – AB = 32 – 24 = 8 cm;
Solution 2:
Point B does not belong to segment AC, therefore:
a) BC = AC + AB = 32 + 24 = 56 cm;
2. Answer: the problem has two solutions; BC = 8 cm or BC = 56 cm.