Question

Find the measure of QS¯¯¯¯¯¯¯.secant-tangent 29A. 29B. 35C. 27D. 20

Answer 1

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

`ST* FS=SR* QS`

Thus, we have

`\begin{gathered} 9*\text{\lparen9+21\rparen=10}* QS \\ 9*30=10* QS \\ \Rightarrow(9*30)/(10)=\frac{10*\text{QS}}{10} \\ thus, \\ QS=27 \end{gathered}`

Hence, QS is evaluated to be

`27`

The correct option is C