Explanation:

- A circle has a diameter of 10 m, giving it a radius of 5 m.

- Two parallel chords are drawn inside the circle.

- One chord is 8 m long.

- The distance between the two chords is 6 m.

- To find the length of the other chord, we can use the circle's radius and the distance from the center to each chord.

- The perpendicular distance from the center of the circle to the first chord is calculated using the Pythagorean theorem: $$(radius{)}^2=(distancefromcentertochord{)}^2+(halfchordlength{)}^2$$.

- Calculate $distancefromcenter=\sqrt{5^2-4^2}=3m$.

- The other chord's center is 3 + 6 = 9 m away from the center.

- Calculate the other chord: $$\sqrt{5^2-9^2}=0$$.

- This implies the chord is not possible in a normal scenario, suggesting calculations might need checking under different assumptions.

- However, within provided options:

- Option 1: 10 m

- Option 2: 6 m

- Option 3: 4 m

- Option 4: 8 m

- If assumptions of exact physical realization hold, alternatives might be different due to proximity calculation errors or taken assumptions of circle arrangement.

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- The calculations end with discrepancies suggesting reviewed design alternatives might be needed.