Point  B
  is the midpoint of  AC⎯⎯⎯⎯⎯,
  and point  C
  is the midpoint of  AD⎯⎯⎯⎯⎯.
  If  CD=12,
  what is  AB?
 

We are given the following:

- Point \( B \) is the midpoint of line segment \( AC \).
- Point \( C \) is the midpoint of line segment \( AD \).
- The length of \( CD = 12 \).

We need to find the length of \( AB \).

### Step-by-step solution:

1. **Relationship between points and segments:**
   - Since \( C \) is the midpoint of \( AD \), the length of \( AC \) is half of \( AD \).
   - Since \( B \) is the midpoint of \( AC \), the length of \( AB \) is half of \( AC \).

2. **Express the lengths:**
   - Let \( x \) represent the length of \( AB \).
   - Since \( B \) is the midpoint of \( AC \), \( AB = BC \). Hence, \( AC = 2x \).
   - Since \( C \) is the midpoint of \( AD \), \( AC = CD \). Therefore, \( CD = 12 \) implies \( AC = 12 \).

3. **Finding \( AB \):**
   - From the previous steps, \( AC = 2x \), and \( AC = 12 \). Thus, \( 2x = 12 \).
   - Solving for \( x \), we get:
     \[
     x = \frac{12}{2} = 6
     \]
   - Therefore, \( AB = 6 \).

### Final answer:
\[
AB = 6
\]

Would you like further clarification or details on any part of the solution?

Here are 5 related questions to expand your understanding:
1. If \( AB = 6 \) and \( BC = 6 \), what is the total length of \( AC \)?
2. How would the answer change if \( CD = 8 \) instead of 12?
3. If \( D \) is located at \( (0, 0) \) and \( A \) at \( (12, 0) \), where would point \( B \) and \( C \) be?
4. What would be the length of \( BD \) in this setup?
5. How do the properties of midpoints help in solving geometric problems like this?

**Tip:** Whenever dealing with midpoints, remember that they divide line segments into two equal parts. This property can simplify the problem significantly.

Point B is the midpoint of AC, and point C is the midpoint of AD. If CD = 12, what is AB?

Learn how to solve a geometry problem involving midpoints. Given that CD = 12, find the length of AB using midpoint properties and basic geometric reasoning. Suitable for students in Grades 6-8.

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