Chapter 6.CR, Problem 19CR

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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;

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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