Let $C_1, C_2$ and $C_3$, be three circles having the same radius $r$, which touch each other externally. Then

• A

  for any circle $C$ which is touched internally by $C_1$ and $C_2, C_3$ lies within $C$.
• B

  there is no circle $C$ touched internally by $C_1, C_2$ and $C_3$.
• Correct answer
  C

  a circle $C$ touched internally by $C_1, C_2$ and $C_3$ has radius $\left(1+\frac{2}{\sqrt{3}}\right) r$.
• Correct answer
  D

  the radius of any circle $C$ touched internally by $C_1$ and $C_2$ is at least $2 r$.

Hence, the correct answer is options: 'C', 'D'.