# Point A lies on line BC. Find the length of the segment AC if AB -23m BC-9m. How many solutions does the problem have?

Points A, B and C can be located in two ways:
1) A__B ____ C;
2) A ___ C__B.
According to the condition, the segment AB = 23 m, and the segment BC = 9 m.
The third location option (B ___ A__ C) is impossible, since a part of the whole (segment AB = 23 m) cannot be larger than the whole itself (segment BC = 9 m)
1. Consider the first option.
The segment AC is divided by point B into segments AB and BC, then its length is equal to:
AC = AB + BC;
AC = 23 + 9 = 32 (m).
2. Consider the second option.
The segment AB is divided by point C into segments AC and BC, then its length is equal to:
AB = AC + BC;
23 = AC + 9;
AC = 23 – 9 = 14 (m).
Answer: 1. AC = 32 m; 2. AC = 14 m.

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