Chapter 13.2, Problem 36SPR

To determine

To find: the value of distance $x$ and round off to nearest tenth id necessary.

Answer to Problem 36SPR

The value of $x$ is $3.2$ .

Explanation of Solution

Given:

  

Concept used:

If two chords intersect in a circle, then the products of the lengths of the chord segments are equal. 

  

  $a\times b=c\times d$ .

Calculation:

If a diameter (or radius) of a circle is perpendicular to a chord, then it bisects the chord and its arc.  The diameter of length  $7$  units bisects the chord, so the length of the chord is  $2x$ . If two chords intersect in a circle, then the products of the lengths of the chord segments are equal. 

  $\begin{array}{l}x\left(x\right)=2\left(5\right).\\ x^2=10.\\ x=\sqrt{10}\approx \mathrm{3.2.}\end{array}$

Hence, the value of $x$ is $3.2$ .