https://file.aiquickdraw.com/mathbot/file/17276171594752jp9rd5g.jpg

The image shows a circle with a central angle of \(120^\circ\) and a minor arc \( \overset{\frown}{AB} \) of length 15 units. We are asked to find the circumference of the circle.

### Step-by-step solution:

1. **Relation between arc length and circumference:**
   The length of an arc \( L \) is given by the formula:
   \[
   L = \frac{\theta}{360^\circ} \times C
   \]
   where:
   - \( L \) is the arc length (in this case, 15 units),
   - \( \theta \) is the central angle (120° here),
   - \( C \) is the circumference of the circle.

2. **Substitute the given values:**
   We have:
   \[
   15 = \frac{120^\circ}{360^\circ} \times C
   \]

3. **Simplify the equation:**
   \[
   15 = \frac{1}{3} \times C
   \]
   Multiply both sides by 3 to solve for \( C \):
   \[
   C = 45
   \]

### Final Answer:
The circumference of the circle is **45 units**.

Would you like more details, or do you have any questions?

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Here are 5 related questions to expand your understanding:
1. How do you calculate the radius of the circle if you know the circumference?
2. What is the formula for the area of a sector, and how would it apply here?
3. How can you calculate the area of the entire circle using the circumference?
4. What is the length of the major arc \( \overset{\frown}{AB} \) in this circle?
5. How would the arc length formula change if the angle was given in radians?

**Tip:** For problems involving arcs, always remember that the arc length is proportional to the central angle.

The length of the minor arc AB on the circle above is 15. What is the circumference of the circle?

In this problem, the length of the minor arc AB is 15 units, and the central angle is 120°. Learn how to calculate the circumference of the circle using the formula for arc length and central angle. Suitable for students in Grades 8-10.

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