If any tangent drawn to the ellipse $\frac{x^2}{16}+\frac{y^2}{9}=1$ touches one of the circles $x^2+y^2=\alpha^2$, then the range of $\alpha$ is

• A

  $9 \leq \alpha \leq 16$
• B

  $16 \leq \alpha \leq 25$
• Correct answer
  C

  $3 \leq \alpha \leq 4$
• D

  $4 \leq \alpha \leq 6$

Hence, the correct answer is option: 'C'.