Chapter 9.6, Problem 2EX

To determine

To measure: $DE,DB,DF$ and $DC$ and to compute $DE\cdot DB$ and $DF\cdot DC$ .

Answer to Problem 2EX

  $\begin{array}{c}DE\cdot DB=11.88\\ DC\cdot DF=12.24\end{array}$

$DE\cdot DB$ is less than $DF\cdot DC$ because the chords $DB$ is smaller than $DC$ .

Explanation of Solution

Given information:

Given figure,

Calculation:

Consider a circle.

Draw a circle. Choose two points $B$ and $C$ on circle and a point $D$ . Draw $\overline{BD}$ and $\overline{CD}$ like below:

Here the measurements are:

  $\begin{array}{l}DE=2.2\text{cm}\\ DB=5.4\text{cm}\\ DC=6.8\text{cm}\\ DF=1.8\text{cm}\end{array}$

And,

  $\begin{array}{c}DE\cdot DB=\left(2.2\right)\left(5.4\right)\\ =11.88\\ DC\cdot DF=\left(6.8\right)\left(1.8\right)\\ =12.24\end{array}$

Here, $DE\cdot DB$ is less than $DF\cdot DC$ because the chords $DB$ is smaller than $DC$ .