A, B and C are three points such that AB = 4 cm, BC = 3 cm and AC = 7 cm. Which one of them lies between other two ?

Answer

To determine which point lies between the other two among points A, B, and C, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the lengths of the segments**: We have the following lengths:
- AB = 4 cm
- BC = 3 cm
- AC = 7 cm

2. **Use the triangle inequality**: The triangle inequality states that for any three points A, B, and C, the sum of the lengths of any two sides must be greater than the length of the third side. We will check if the lengths satisfy this condition:
- Check if AB + BC > AC:
- 4 cm + 3 cm = 7 cm, which is equal to AC.
- Check if AB + AC > BC:
- 4 cm + 7 cm = 11 cm, which is greater than 3 cm.
- Check if AC + BC > AB:
- 7 cm + 3 cm = 10 cm, which is greater than 4 cm.

The first condition (AB + BC > AC) is satisfied as an equality, indicating that points A, B, and C are collinear.

3. **Determine the position of the points**: Since AB + BC = AC, we can conclude that point B lies between points A and C. This is because the distance from A to C (7 cm) is exactly equal to the sum of the distances from A to B (4 cm) and from B to C (3 cm).

4. **Conclusion**: Therefore, point B lies between points A and C.

### Final Answer:
Point B lies between points A and C.