Chapter 9, Problem 14CR

To determine

To find: the radius.

Answer to Problem 14CR

The value of the radius is 13.

Explanation of Solution

Given information:

Given statement,

If $XE=5$ and $AC=24$ ,

In $\odot X,marcAC=120$ .

Calculation:

Consider the following diagram:

.

As the radius $XB$ is perpendicular bisector of the chord $AC$ .

Then, $AC=2AE=2EC$

Then from the Pythagoras theorem,

  $\begin{array}{c}A{X}^2=X{E}^2+E{A}^2\\ A{X}^2=5^2+{12}^2\\ AX=13\end{array}$

Then the value of the radius is 13.