Explanation:

- A chord passing through the center of a circle is its diameter.

- This is because the diameter is the longest chord and divides the circle into two equal halves.

- Given the chord length is 10 cm, this chord is also the diameter.

- Therefore, the diameter of the circle is 10 cm.

- Option 1: 5 cm - This is incorrect, as the length is less than the given chord.

- Option 2: 15 cm - This is incorrect, as it's longer than the chord diameter.

- Option 3: 20 cm - Also incorrect, as it exceeds the chord's length.

- Option 4: 10 cm - This is correct as it matches the chord diameter.