Explanation:

- To find the length of a chord, we can use the right triangle formed by the radius, the perpendicular from the center to the chord, and half of the chord.

- The radius of the circle is 13 cm.

- The distance from the center to the chord (perpendicular) is 12 cm.

- Using the Pythagorean theorem:

$$

x^2 + 12^2 = 13^2

$$

$$

x^2 + 144 = 169

$$

$$

x^2 = 25

$$

$$

x = 5

$$

- The chord is twice the length of x, so it is 2 * 5 = 10 cm.

- Correct answer option 2: ? 10 cm.

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