Elementary Geometry for College Students (7th Edition) Clone

Published by Cengage
ISBN 10: 978-1-337-61408-5
ISBN 13: 978-1-33761-408-5

Chapter 6 - Section 6.3 - Line and Segment Relationships in the Circle - Exercises - Page 304: 6

Answer

The distance between B and A sets the length of overlap between the two circles, and the common chord AC prevents a change in the two circles' angular placements in relation to one another. Because these structures are in place - one involving angle, and one length - the congruence of the common chord and line segment of centers provides a right angle which establishes the structure of an equilateral square ABCD due to the length- and angle-similarities which occur as a result.

Work Step by Step

The problem asks for an explanation instead of a proof, so the reasoning is outlined above.
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