Chapter 6.1, Problem 34E

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6th Edition

Daniel C. Alexander + 1 other

ISBN: 9781285195698

Textbook Problem

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*In Exercises 32 to 37, write a paragraph proof.*

Congruent chords are located at the same distance from the centre of a circle.

To determine

**To prove:**

The statement “Congruent chords are located at the same distance from the center of a circle”.

Explanation

**Given:**

The provided statement is “Congruent chords are located at the same distance from the center of a circle”

**Theorem used:**

A radius that is perpendicular to the chord bisects the chord.

Hypotenuse leg theorem:

If the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and one leg of another right triangle, then the triangles are congruent.

**Proof:**

Consider a circle with center *O.*

Let

Construct two line segments

We know that, the radius that is perpendicular to the chord bisects the chord.

Therefore

Since we have

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