A and B are two points and C is any point collinear with A and B .If AB=10, BC =5, then AC is equal to :

Options

A. either 15 or 5
B. necessarily 5
C. necessarily 16
D. none of these

Answer

To solve the problem, we need to determine the length of AC given that AB = 10 and BC = 5, with point C being collinear with points A and B.

### Step-by-Step Solution:

1. **Understand the Configuration**:
- We have three points: A, B, and C.
- Points A and B are fixed, and point C is collinear with A and B. This means all three points lie on the same straight line.

2. **Identify the Possible Positions of C**:
- Point C can either be between points A and B or outside of them. This gives us two scenarios to consider:
- **Scenario 1**: C is between A and B.
- **Scenario 2**: C is outside of A and B.

3. **Calculate AC for Scenario 1 (C is between A and B)**:
- If C is between A and B, then the distance AC can be calculated as:
\[ AC = AB + BC \]
- Substituting the known values:
\[ AC = 10 + 5 = 15 \]

4. **Calculate AC for Scenario 2 (C is outside A and B)**:
- If C is outside A and B, then the distance AC can be calculated as:
\[ AC = AB - BC \]
- Substituting the known values:
\[ AC = 10 - 5 = 5 \]

5. **Conclusion**:
- From the two scenarios, we find that AC can be either 15 or 5 depending on the position of point C. Therefore, the possible values for AC are:
- AC = 15 (when C is between A and B)
- AC = 5 (when C is outside A and B)

### Final Answer:
AC can be either 15 or 5.