Chapter 10.8, Problem 4WE

To determine

To construct: a circle, with radius $a$ , that passes through $N$ is tangent to line $k$ .

Explanation of Solution

Given Information:

Use figure,

  

  

Calculation:

Consider a line $k$ and point $N$ .

Construct a perpendicular on line $k$ at $X$ , cut and arc length $a$ from point $X$ on the perpendicular line again construct a perpendicular at $P$ on line $\overline{PX}$ , $l$ is parallel to $k$ .

Draw an arc of length $a$ from $N$ .

The intersection point of line $l$ and arc is the center $O$ of circle.

Draw a circle with radius $a$ and center $O$ , this circle touches the point $N$ and tangent to line $k$ .