   Chapter 6.CR, Problem 19CR Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section 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 a parallelogram is inscribed in a circle, then each of its diagonals must be a diameter.

To determine

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

Explanation

Approach:

Theorem:

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

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

Calculation:

Given that

If a parallelogram is inscribed in a circle, then each of its diagonals must be a diameter.

In a parallelogram, opposite sides are equal and parallel.

Let O be the center of the two circles and AB and CD be chords.

Also, AB = CD; ABCD and AC = BD, ACBD.

Since congruent chords are located at the same distance from the center of a circle, OQ = OP.

And AO = OD = CO = OB are radii

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