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We are given the following information:

- The length of segment \( AD = 25 \) units.
- The length of segment \( AC = 19 \) units.
- The length of segment \( BD = 14 \) units.

We need to determine the length of segment \( BC \).

### Steps to solve:

1. **Determine the length of \( CD \):**
   From the diagram, we know that \( D \) is the endpoint, so:
   \[
   CD = BD - BC
   \]

2. **Relating segments:**
   Since \( AD = AC + CD \), we can express \( CD \) as:
   \[
   CD = AD - AC = 25 - 19 = 6
   \]
   
3. **Determine \( BC \):**
   Since \( BD = BC + CD \), we now know \( CD = 6 \), so:
   \[
   BD = BC + CD = BC + 6
   \]
   Substituting the value of \( BD = 14 \):
   \[
   14 = BC + 6
   \]
   Solving for \( BC \):
   \[
   BC = 14 - 6 = 8
   \]

Thus, the length of segment \( BC \) is \( \boxed{8} \) units.

Would you like any further clarification on this solution?

### Related Questions:
1. If segment \( AB \) was 13 units, how would you solve for the length of \( BC \)?
2. What would be the length of \( BC \) if \( AD = 30 \) units and \( BD = 16 \) units?
3. How does the subtraction method work for solving similar problems in geometry?
4. If the points \( B \) and \( C \) are equidistant, what would be the length of \( AB \) and \( CD \)?
5. Can you apply this method to a problem involving three dimensions?

**Tip:** Always sketch the diagram with labeled points and known values when solving geometric segment problems to keep track of relationships between parts.

Points B and C lie on segment AD. The length of segment AD is 25 units; the segment AC is 19 units long; and the segment BD is 14 units long. How many units long, if it can be determined, is the segment BC?

Learn how to determine the length of segment BC on a line segment AD when given the lengths of segments AD, AC, and BD. This geometry problem covers key concepts such as the segment addition formula and how to solve for unknown line segments.

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