Chapter E, Problem 9.13EX

To determine

To find: The distance from O to chord $\overline{XZ}$ .

Answer to Problem 9.13EX

The distance from O to chord $\overline{XZ}$ is $5$ .

Explanation of Solution

Given information: If $\overleftrightarrow{XA}$ is tangent to Oat X and the radius is $13$ and $XZ=24$ .

Calculation:

If $\overleftrightarrow{XA}$ is tangent to Oat Xand the radius is $13$ and $XZ=24$ .

The radius is $13$ and $XZ=24$ .

  $\begin{array}{l}\because OY\text{ is perpendicular to }XZ,\text{ then }OY\text{ bisects }XZ.\\ \therefore XM=\frac{XZ}{2}\\ XM=\frac{24}{2}\\ XM=12\end{array}$

In a triangleOMX

  $XM=12$

Hypotenuse $\text{=13}$

Use the Pythagorean Theorem to have

  $\begin{array}{l}{13}^2={12}^2+{\left(OM\right)}^2\\ {\left(OM\right)}^2={13}^2-{12}^2\\ {\left(OM\right)}^2=169-144\\ {\left(OM\right)}^2=25\\ OM=5\end{array}$