Chapter 10.8, Problem 3WE

To determine

To draw: an angle $XYZ$ and to construct a circle, with radius $a$ , that is tangent to side of $\angle XYZ$ .

Explanation of Solution

Given Information:

Use figure,

  

Calculation:

Consider an angle $XYZ$ ,

  

Consider an angle $XYZ$ bisect the $\angle XYZ$ , $YW$ is bisecting line.

Construct a perpendicular on $\overline{YZ}$ at $P$ .

Make an arc of length $a$ from $P$ .

Construct a perpendicular on $\overline{QP}$ at $Q$ , line $l$ is parallel to $\overline{YZ}$ and at a units.

  $O$ is the intersecting point of bisector $\overline{YW}$ and line $l$ .

Construct a circle with radius $a$ at $O$ .

This circle makes tangents at the sides of $\angle XYZ$ and has radius $a$ .