Consider an angle $ \angle DEF$, and the fixed points $ B$ and $ C$ on the semiline $ (EF$ and the variable point $ A$ on $ (ED$. Determine the position of $ A$ on $ (ED$ such that the sum $ AB\plus{}AC$ is minimum.
1. **Reflect Point \( F \) and \( C \):**
   - Let \( G \) be the reflection of point \( F \) in the semiline \( (ED) \).
   - Let \( C' \) be the reflection of point \( C \) in the semiline \( (ED) \).

2. **Position of \( C' \):**
   - Since \( C' \) is the reflection of \( C \) in \( (ED) \), \( C' \) must lie on the semiline \( (EG) \).

3. **Using the Triangle Inequality:**
   - Consider the sum \( AB + AC \).
   - Reflecting \( C \) to \( C' \), we have \( AB + AC = AB + AC' \).

4. **Applying the Triangle Inequality:**
   - By the triangle inequality, \( AB + AC' \geq BC' \).
   - Equality holds when \( A \) is the intersection of \( BC' \) and the semiline \( (ED) \).

5. **Conclusion:**
   - The position of \( A \) on \( (ED) \) that minimizes \( AB + AC \) is the point where \( A \) is the intersection of \( BC' \) and the semiline \( (ED) \).

\[
\boxed{A \text{ is the intersection of } BC' \text{ and the semiline } (ED)}
\]