Explanation:

To find the radius of the large circular field:

- Calculate the area of each smaller circle using \(A = \pi r^2\).

- Circle 1: Radius = 8 m, Area = \(\pi \times 8^2 = 64\pi\).

- Circle 2: Radius = 9 m, Area = \(\pi \times 9^2 = 81\pi\).

- Circle 3: Radius = 12 m, Area = \(\pi \times 12^2 = 144\pi\).

- Sum the areas of all smaller fields:

$$64\pi + 81\pi + 144\pi = 289\pi.$$

- Use the total area of \(289\pi\) to find the radius \(R\) of the large circle:

$$ \pi R^2 = 289\pi $$

$$ R^2 = 289 $$

$$ R = \sqrt{289} = 17 \text{ m}. $$

- Option 4: 17 m is correct.