Elementary Geometry for College Students (5th Edition)

Published by Brooks Cole
ISBN 10: 1439047901
ISBN 13: 978-1-43904-790-3

Chapter 6 - Section 6.3 - Line and Segment Relationships in the Circle - Exercises - Page 309: 45

Answer

By definition, the midpoint of a chord other than a diameter is parallel to the circle directly behind that chord. If a line is drawn through the center of a circle and through the midpoint of the chord, it is perpendicular to the point on the circle that the chord is parallel to. Thus, by substitution, we obtain that the line is perpendicular to the chord.
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