Geometry problem on circle [closed]
You need to use the cosine law.
Let $R_2$ be the center of circle $S_2$. Let $r_2$ be the radius of $S_2$.
First of all, it is easy to obtain that the radius of $S$ is $200$ and that $XO=100, XR_2=r_2$ and $OR_2=200-r_2$. Then notice that $\angle R_2XO=120{^\circ}$.
Hence by cosine law $100^2+{r_2}^2-200r_2\cos(120{^\circ})=(200-r_2)^2$
Now solve for $r_2$ we get ${r_2}^2+100r_2+10000={r_2}^2-400r_2+40000\implies 500r_2=30000\implies r_2=60$.