Chapter 4.6, Problem 18PSC

To determine

To show: The value of ${\left(CA\right)}^2+{\left(AT\right)}^2$ .

Answer to Problem 18PSC

  $16$ .

Explanation of Solution

Given information:

A triangle is given as below.

  

Calculation:

A right angled triangle is given as below.

  

Using Pythagoras theorem,

  $\begin{array}{l}{\left(CA\right)}^2+{\left(AT\right)}^2={\left(CT\right)}^2\\ \Rightarrow {\left(CA\right)}^2+{\left(AT\right)}^2=4^2\left\{\text{Since, }CT=4-0=4\right\}\\ \Rightarrow {\left(CA\right)}^2+{\left(AT\right)}^2=16\end{array}$