Chapter 12.2, Problem 9CE

To determine

To find: The numerical value of $XO$ .

Answer to Problem 9CE

The length of $XO$ is equal to $2\sqrt{3}$ .

Explanation of Solution

Given information: The given figure is as follows.

  

Calculation:

From the given figure it can be considered that the triangle $XYZ$ is an equilateral triangle. Each edge of pyramid $XYZ$ is equal to $6$ . Also, the length of $XM$ is $3\sqrt{3}$ .

It is known that the circumcenter divides the altitude in 2:1. So, the length of $XO$ can be determined as:

  $\begin{array}{c}XO=\frac{2}{3}XM\\ =\frac{2}{3}\left(3\sqrt{3}\right)\\ =2\sqrt{3}\end{array}$

Therefore, the length of $XO$ is equal to $2\sqrt{3}$ .