https://file.aiquickdraw.com/mathbot/file/1725364577140ci8x7cq1.jpg

To solve this problem, let's analyze the details provided:

### Problem Breakdown:
- **Given**: 
  - Radius of the circle \( r = 12 \) units.
  - Angle \( \angle AOB = 45^\circ \).
  - The formula for the circumference of a circle: \( C = 2\pi r \).
  - We are to find the length of the minor arc \( AB \) using \( \pi = 3.142 \).

### Steps to Solve:
1. **Calculate the circumference of the circle**:
   \[
   C = 2 \times \pi \times r = 2 \times 3.142 \times 12 = 75.408 \text{ units}
   \]

2. **Determine the fraction of the circle's circumference that corresponds to the minor arc**:
   - The angle \( \angle AOB = 45^\circ \) represents the fraction of the circle given by:
   \[
   \text{Fraction of the circle} = \frac{45^\circ}{360^\circ} = \frac{1}{8}
   \]

3. **Calculate the length of the minor arc \( AB \)**:
   \[
   \text{Length of arc } AB = \text{Fraction of the circumference} \times C = \frac{1}{8} \times 75.408 = 9.426 \text{ units}
   \]

4. **Round the answer to two decimal places**:
   \[
   \text{Length of arc } AB = 9.43 \text{ units}
   \]

### Final Answer:
The correct length of the minor arc \( AB \), to two decimal places, is **9.43** units.

Would you like any further details on this solution, or do you have any other questions? Here are some related questions to explore:

1. What is the length of the major arc \( AB \) in this circle?
2. How would the arc length change if the angle \( \angle AOB \) was doubled?
3. Can you calculate the area of the sector formed by \( \angle AOB \)?
4. What would be the arc length if the radius was changed to 10 units?
5. How does the arc length relate to the angle in radians?

**Tip**: When dealing with problems involving circles, always ensure that the angle is correctly converted (if necessary) and applied as a fraction of the full circle.

The query submitted by the user: Solve it

Learn how to calculate the length of a minor arc AB in a circle with radius 12 units and angle AOB of 45 degrees. Step-by-step solution includes the circumference formula and fraction calculation. Suitable for grades 9-12.

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