Chapter 9.6, Problem 1EX

To determine

To measure: the lengths of the pieces of the chords and to compute the products $w\cdot x$ and $y\cdot z$ .

Answer to Problem 1EX

  $\begin{array}{c}w\cdot x=3.75\\ y\cdot z=3.75\end{array}$

$w\cdot x$ and $y\cdot z$ given same measurement because the chords length were same.

Explanation of Solution

Given information:

Given figure,

Calculation:

Consider a circle.

Draw a circle. Choose four points on circle and draw two intersecting chords like below:

Here the measurements are:

  $\begin{array}{l}w=2.5\text{cm}\\ x=1.5\text{cm}\\ y=1.5\text{cm}\\ z=2.5\text{cm}\end{array}$

And,

  $\begin{array}{c}w\cdot x=\left(2.5\right)\left(1.5\right)\\ =3.75\\ y\cdot z=\left(2.5\right)\left(1.5\right)\\ =3.75\end{array}$

Here, $w\cdot x$ and $y\cdot z$ given same measurement because the chords length were same.