Chapter 7.CR, Problem 12CR

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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

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

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

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