1. **State the problem:** We need to find the circumference of the circle traversed by wheel 12 in a wheel line irrigation system. 2. **Identify the radius of the circle for wheel 12:** The first wheel is 50 m from the pivot point, and each subsequent wheel is 20 m further along the pipe. 3. **Calculate the radius for wheel 12:** $$\text{Radius}_{12} = 50 + (12 - 1) \times 20 = 50 + 11 \times 20 = 50 + 220 = 270 \text{ m}$$ 4. **Recall the formula for circumference of a circle:** $$C = 2 \pi r$$ where $r$ is the radius. 5. **Calculate the circumference for wheel 12:** $$C_{12} = 2 \pi \times 270 = 540 \pi \text{ m}$$ 6. **Approximate the value:** $$C_{12} \approx 540 \times 3.1416 = 1696.46 \text{ m}$$ **Final answer:** The circumference of the circle traversed by wheel 12 is approximately $1696.46$ meters.