Chapter 10.5, Problem 36HP

To determine

To explain: The following construction steps with reasoning.

Explanation of Solution

Given information:

  

In the step 1and 2:

The circle is drawn with the center $C$ . The point $A$ is a point outside the circle periphery of the circle. Then draw a line which joins the center $C$ and outside point $A$ as $\overline{CA}$ . The perpendicular bisector of is drawn as shown below.

  

Step 3:

A circle is constructed with radius $XC$ and center $X$ as:

  

Step 4:

Here, need to connect $A,D,C$ as $\Delta ADC$ is inscribed in circle

  

Therefore,

  $m\angle CDA=90°$

And

  $\overline{CD}\perp \overline{AD}$

Therefore, $\overline{AD}$ is tangent to the circle $\odot C$ from point $A$ .