   Chapter 7.1, Problem 20E Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

Note: Exercises preceded by an asterisk are of a more challenging nature.In Exercises 11 to 22, sketch and describe each locus in the plane.Given that congruent circles O and P have radii of length 4 in. and that the line of centers has length 6 in., find the locus of points that are 1 in. from each circle.

To determine

To find:

The locus of points that are 1 in. from the congruent circles O and P of radii 4 in. and the line of centers is of length 6 in.

Explanation

Approach:

The locus of points in a plane that are equidistant from the endpoints of a line segment is the perpendicular bisector of that line segment.

Calculation:

Step 1: Construct a circle O of radius 4 in. It is given that the O and P are congruent, and the length of the line joining the centres is 6 in. Also, the locus of points are 1 in. from the circles.

Step 2: At 6-1=5 in. locate a point P and draw a second circle of radius 4 in.

From the figure, we find that the coordinates for the points are as follows:

Point O=0, 0

Point Q=2, 0

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