**Correct option is (D) 3 cm**

\(\angle AOB\) = Angle subtend by chord AB at the centre of the circle

\(\angle COD\) = Angle subtend by chord CD at the centre of the circle

Since, if two chord subtend equal angles at the centre of the circle then they are equal in length.

\(\because\) \(\angle AOB\) = \(\angle COD\)

\(\therefore\) AB = CD

\(\Rightarrow\) CD = AB = 3 cm \((\because\) AB = 3 cm (given))