If C be the mid-point of a line segment AB, then AC= BC= (___) AB

Options

A. 3
B. `(1)/(2)`
C. 2
D. `(1)/(4)`

Answer

To solve the problem, we need to determine the relationship between the lengths of segments AC, BC, and AB when C is the midpoint of line segment AB.

### Step-by-Step Solution:

1. **Identify the Midpoint**:
Let A and B be two points on a line segment. C is defined as the midpoint of line segment AB.

2. **Understanding the Midpoint**:
By definition, if C is the midpoint of AB, it means that C divides the segment AB into two equal parts. Therefore, the lengths of segments AC and BC are equal.
\[ AC = BC \]

3. **Expressing AB in terms of AC and BC**:
Since C is the midpoint, we can express the total length of segment AB as the sum of the lengths of segments AC and BC:
\[ AB = AC + BC \]

4. **Substituting Equal Lengths**:
Since we established that AC = BC, we can substitute BC with AC in the equation:
\[ AB = AC + AC = 2 \cdot AC \]

5. **Finding AC in terms of AB**:
To find the length of AC in terms of AB, we can rearrange the equation:
\[ AC = \frac{AB}{2} \]

6. **Conclusion**:
Since AC = BC, we can conclude that:
\[ AC = BC = \frac{1}{2} AB \]
Therefore, the blank in the question can be filled with \( \frac{1}{2} \).

### Final Answer:
AC = BC = \( \frac{1}{2} AB \)