Chapter 14.2, Problem 10PSB

To determine

To find the locus of points that are at given distance from the center and lie on it.

Answer to Problem 10PSB

The locus of the points is the empty set $\varphi$ .

Explanation of Solution

Given:

A regular pentagon.

Calculation:

The following figure describes the locus of points that are at given distance from the pentagon’s center and lie on it.

  

The blue circles are equal distance from the center of pentagon but do not intercept the pentagon. The locus of the points is the empty set $\varphi$ . The green circle is equal distance from the center of the pentagon, and the vertices lie on it. The locus of points is $5$ points. The orange circle is equal distance from the center also, and it intersects the pentagon in $10$ places. The locus of points is $10$ points.