Three points A, B, C are given on the straight line, with AB = 83cm, AC = 97cm. Find the length of the segment BC.

Let’s schematically depict the data points A, B and C. Two ways of arranging these points on a straight line, when AB = 83 cm, AC = 97 cm. Let us investigate each case separately.
In the first case, point B is located between points A and C. Therefore, AC = AB + BC. Let’s substitute these values in their places. Then, we get 97 cm = 83 cm + BC, whence BC = 97 cm – 83 cm = 14 cm.
In the second case, point A is located between points B and C. Therefore, BC = AC + AB. Let’s substitute these values in their places. Then, we get BC = 97 cm + 83 cm = 180 cm.
Answers: 1) BC = 14 cm. 2) BC = 180 cm.