Solution:
Given the figure below:
To solve for the measure of GS, we use the secant-secant theorem.
According to the secant-secant theorem, we have
This implies that
[tex]ST\times FS=SR\times QS[/tex]
Thus, we have
[tex]\begin{gathered} 9\times\text{\lparen9+21\rparen=10}\times QS \\ 9\times30=10\times QS \\ \Rightarrow\frac{9\times30}{10}=\frac{10\times\text{QS}}{10} \\ thus, \\ QS=27 \end{gathered}[/tex]
Hence, QS is evaluated to be
[tex]27[/tex]
The correct option is C
