Explanation:

- The problem involves a circle with center O, and an external point P, from which two tangents, PA and PB, of equal length are drawn.

- The given angle between the tangents, ?APB, is 120°.

- The distance from the point P to the center O is 12 cm.

- In the triangle OAP, using the cosine rule: \(OA^2 = OP^2 + AP^2 - 2 \cdot OP \cdot AP \cdot \cos(?APO)\).

- The calculation simplifies as ?APO = ?BPO = 30° because the tangents from a point to a circle are equal and symmetrical.

- Substitute values: \(r^2 = 12^2 + l^2 - 12l \cdot \cos(30°)\).

- Solving for l, we find the correct tangent length.

Correct Answer: Option 2: 6 cm