Chapter 10.1, Problem 6PSA

To determine

To find: The length of the chord that is 15 cm from the centre of the circuit with the radius of 17 cm.

Answer to Problem 6PSA

The length of the chord is 16.

Explanation of Solution

Calculation:

Consider the diagram for the condition as shown in Figure 1

  

Figure 1

Here, $\mathrm{A}\mathrm{B}=15$ and $\mathrm{A}\mathrm{D}=17$ also $\mathrm{A}\mathrm{B}\perp \mathrm{A}\mathrm{D}$ .

Then, by the Pythagoras theorem.

  $\begin{array}{l}{\mathrm{x}}^2+{15}^2={17}^2\\ {\mathrm{x}}^2+225=289\\ \mathrm{x}=8\\ \mathrm{B}\mathrm{D}=8\end{array}$

Then, the length of the chord is,

  $\begin{array}{c}\mathrm{C}\mathrm{D}=2\mathrm{B}\mathrm{D}\\ =2\left(8\right)\\ =16\end{array}$