Chapter 9.2, Problem 16WE

To determine

To calculate: To find the value of PQ, PS and ST.

Answer to Problem 16WE

The required values are $PQ=20,PS=18\text{and}ST=16$

Explanation of Solution

Given information: Any $\overline{SR}$ is tangent to $\odot P$ and $\odot Q$ . Also $QT=6,TR=8\text{and}PR=30$ .

Formula used: Applying Pythagoras in triangle $\Delta RTQ$ to find the value of PQ.

Calculation: Here, $\Delta RTQ$ is right angle triangle,

  $\begin{array}{l}Q{R}^2=6^2+8^2\\ Q{R}^2=36+64\\ QR=10\end{array}$

As value of $PR=30$ ,

  $\begin{array}{l}PQ=30-10\\ PQ=20\end{array}$

Let ST be x and SP be y.

Here, $\overline{TQ}\left|\right|\overline{SP}$

Therefore,

  $\begin{array}{l}\frac{8}{10}=\frac{x}{20}\\ x=\frac{8\cdot 20}{10}\\ x=16\end{array}$

Same way,

  $\begin{array}{l}\frac{8}{6}=\frac{24}{y}\\ y=\frac{24\cdot 6}{8}\\ y=18\end{array}$