Chapter 6.4, Problem 38E

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7th Edition

Alexander + 2 others

ISBN: 9781337614085

Textbook Problem

Prove: In a circle containing two unequal chords, the longer chord corresponds to the larger central angle.

(*HINT: You may use any theorems stated in this section.)*

To determine

**To prove:**

The given statement.

Explanation

**Given:**

The given statement:

“In a circle containing two unequal chords, the longer chord corresponds to the larger central angle.”

Assume

The angle corresponding to chord

**To Prove:**

To prove that the given statement is correct

“In a circle containing two unequal chords, the longer chord corresponds to the larger central angle.”

To prove that

**Theorems Used:**

In a circle (or in congruent circles) containing two unequal chords, the longer chord corresponds to the greater minor arc.

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

**Proof:**

Using the theorem,

The chords are unequal and

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