Chapter 9.5, Problem 29WE

To determine

To Find :The distance JK in terms of a, b and c.

Answer to Problem 29WE

The JK in terms of the a, b and c is $\frac{ab}{c}$ .

Explanation of Solution

Given information:

  

Angle C of ΔABC is the right angle.

Consider a right angled triangle ΔABC.

  

Here the circle is smallest circle.

Also, $\angle C=90°$

Side AB is tangent to the circle.

As the circle is tangent to AB . Then the inscribed angle will be half of centered angle. So, the centered angle will be:

  $\angle JOK=180°$

Draw a line from C perpendicular to AB .

  

In triangle ABC and AHC , angle A is common and other angle is right angled.

Therefore, they are similar.

  $\begin{array}{l}\frac{CH}{AC}=\frac{BC}{AB}\hfill \\ \frac{CH}{b}=\frac{a}{c}\hfill \\ CH=\frac{ab}{c}\hfill \end{array}$

Further, CH and JK both is radius.

  $\begin{array}{l}JK=CH \\ =\frac{ab}{c}.\end{array}$