Chapter 14, Problem 6RP

To determine

To sketch the locus of the center of the given circle.

Answer to Problem 6RP

Shown in figure.

Explanation of Solution

Given:

The circle of given radius rolls around the perimeter of a given equilateral triangle.

Calculation:

The following is the sketch of the locus of the center of the circle that rolls around the perimeter of a given equilateral triangle-

  

If the side of the equilateral triangle is $1$ unit, the perimeter of the equilateral triangle will be $3$ units, therefore the circle will have to make total $4$ turns.