(b) $3\sqrt{3}$ cm
Since OB ⊥ AB (radius ⊥ tangent), in right △OAB: $\sin 30° = \dfrac{OB}{OA}$, so $OB = 6 \times \dfrac{1}{2}$...
Wait — $\sin(\angle OAB) = \dfrac{OB}{OA}$, i.e., $\sin 30° = \dfrac{r}{6}$, giving $r = 3$ cm. (a) 3 cm
In right △OAB, ∠OBA = 90° (radius ⊥ tangent). The angle at A is 30°, and OA (hypotenuse) = 6 cm. Using sin: $\sin 30° = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{OB}{OA} = \frac{r}{6}$. Since $\sin 30° = \frac{1}{2}$, we get $r = 3$ cm. The correct answer is (a) 3 cm. A common mistake is using tan or cos instead of sin — remember OB is the side opposite to ∠OAB, and OA is the hypotenuse.