Chapter 9.4, Problem 5CE

To determine

The value of OM from the figure.

Answer to Problem 5CE

The final answer is OM=12.

Explanation of Solution

Given information:

The given figure is,

  

Here, in the figure

PQ=10, radius=13=OP, PQ=2PM

So PM=5

Using Pythagoras theorem.

  $\begin{array}{c}{h}^2=p^2+b^2\\ {\left(OP\right)}^2={\left(OM\right)}^2+{\left(PM\right)}^2\\ {\left(13\right)}^2={\left(OM\right)}^2+{\left(5\right)}^2\\ {\left(OM\right)}^2=169-25\\ OM=\sqrt{144}\\ OM=12\end{array}$

Therefore, value of OM is 12.