   Chapter 7.CR, Problem 12CR ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698

#### Solutions

Chapter
Section ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
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# 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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