   Chapter 7.CR, Problem 12CR 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

In Review Exercise 7 to 13, sketch and describe the locus in a plane.Find the locus of the centers of all circles passing through two given points.

To determine

To find:

The locus of the centers of all circles passing through two given points.

Explanation

Consider the figure.

Let the two points be A and B.

So, any circle passing through both A and B will have AB as its chord.

Let there be two circles 1 and 2 with centers C1 & C2 respectively, satisfying above condition.

By theorem that perpendicular bisector of a chord of a circle passes through its center.

Therefore, perpendicular bisector of chord AB with respect to circle-1, passes through C1.

Similarly, perpendicular bisector of chord AB with respect to circle-2, passes through C2

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