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Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

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Chapter
Section
BuyFindarrow_forward

Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

In Review Exercises 15 to 22, state whether the statements are always true (A), sometimes true (S), or never true (N).

If two chords of a circle are not congruent, then the shorter chord is nearer the center of the circle.

To determine

To state: Whether the statement is always true (A), sometimes true (S), or never true (N).

Explanation

Theorem:

1) In a circle (or in congruent circles) containing two unequal arcs, the largest arc corresponds to the larger central angle.

2) A radius that is perpendicular to a chord bisects the chord.

3) In a circle (or in congruent circles) containing two unequal arcs, the shorter chord is at the greater distance from the center of the circle.

4) Congruent chords are located at the same distance from the center of a circle.

Calculation:

Given that

If two chords of a circle are not congruent, then the shorter chord is nearer the center of the circle.

In a circle, congruent chords are equidistant from the center

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