Chapter 9.4, Problem 9WE

To determine

The value of CD from figure

Answer to Problem 9WE

The value of CD= $10\sqrt{5}$

Explanation of Solution

Given information:

It is given AB=18, OM=12, ON=10 in the figure,

  

Let the radius of the circle be x

From given data

OA=OD=radius of the circle=x

AB=2AM, CD=2ND

AM=9

Using Pythagoras theorem in triangle AMO

  $\begin{array}{c}{\left(OA\right)}^2={\left(AM\right)}^2+{\left(OM\right)}^2\\ x^2=9^2+{\left(12\right)}^2\\ x^2=81+144\\ x=\sqrt{225}\\ x=15\end{array}$

So OA=OD=15

Using Pythagoras theorem in triangle OND

  $\begin{array}{c}{\left(OD\right)}^2={\left(ND\right)}^2+{\left(ON\right)}^2\\ {\left(15\right)}^2={\left(ND\right)}^2+{\left(10\right)}^2\\ 225={\left(ND\right)}^2+100\\ ND=\sqrt{225-100}\\ ND=\sqrt{125}\\ ND=5\sqrt{5}\end{array}$

So CD= $10\sqrt{5}$