Chapter 9.4, Problem 27WE

To determine

To Find: The nearest tenth of centimeter for the given circle.

Answer to Problem 27WE

The nearest tenth of centimeter XY=2.82 cm.

Explanation of Solution

Given information:

The three parallel chords are of lengths 20, 16 and 12 cm.

Distance between chords 16 cm and 12 cm is 2 cm.

Consider the given figure;

  

  $\begin{array}{l}PX=2cm\hfill \\ PY=\frac{16}{2}-\frac{12}{2}\hfill \\ =8–6\hfill \\ =2\hfill \end{array}$

The Pythagoras Theorem:

The number of the base square and the height square of the right-angled triangle corresponds to the hypotenuse square of that triangle.

By Pythagoras theorem;

  $\begin{array}{l}XY²=PX²+PY²\hfill \\ =2²+2²\hfill \\ =4+4=8\hfill \end{array}$

And

  $\begin{array}{l}XY=\sqrt{8}\\ XY=2.82\end{array}$

Hence, to the nearest tenth of centimeter $XY=2.82$ cm.