A circle $S_1$ with centre at $C_1$ and radius $r_1$ touches another circle $S_2$ with centre at $C_2$ and radius $r_2$ internally as shown in the figure. If $r_2>2 r_1$ and a diameter of the bigger circle touches the smaller circle at T , then the length of the segment $\mathrm{C}_2 \mathrm{~T}$ is

• Correct answer
  A

  $\sqrt{r_2^2-2 r_1 r_2}$
• B

  $\sqrt{r_2^2-r_1 r_2}$
• C

  $\sqrt{r_1^2+r_1 r_2}$
• D

  $\sqrt{r_1^2+2 r_1 r_2}$

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