Explanation:

- To find the length of the diameter, consider a right triangle formed by the radius, half of the chord, and the perpendicular distance from the center to the chord.

- The chord is 10 cm, so half of it is 5 cm.

- The perpendicular from the center is 12 cm.

- Use the Pythagorean theorem: \(r^2 = 5^2 + 12^2\).

- Solving gives \(r^2 = 25 + 144 = 169\).

- Thus, \(r = \sqrt{169} = 13\) cm.

- The diameter is twice the radius, so \(2 \times 13 = 26\) cm.

- 26 cm (Option 3) is the correct length of the diameter.