Chapter 10.7, Problem 10PSB

To determine

Find length of side $PS$ .

Answer to Problem 10PSB

  $PS=24$

Explanation of Solution

Given information:

  

  $PQ=15,QR=20,RS=7$ and $\angle Q$ is right angle.

Calculation:

  $\Delta RQP$ is right triangle to apply Pythagorean theorem to find $RP$ ,

  $\begin{array}{l}Q{R}^2+P{Q}^2=R{P}^2\\ {20}^2+{15}^2=R{P}^2\\ RP=25\end{array}$

If a quadrilateral is inscribed in a circle its opposite angles are supplementary so that,

  $\angle S$ is right angle.

Apply Pythagorean Theorem to find $PS$ ,

  $\begin{array}{l}R{S}^2+P{s}^2=R{P}^2\\ 7^2+P{S}^2={25}^2\\ PS=24\end{array}$

Hence , $PS=24$ .