Chapter 6.4, Problem 36E

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7th Edition

Alexander + 2 others

ISBN: 9781337614085

Textbook Problem

Explain why the following statement is incorrect:

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

To determine

**To explain:**

The reason the given statement is incorrect.

Explanation

**Given:**

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

**To Prove:**

To prove that the given statement is incorrect:

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

Assume two chords

The major arc of chord

To prove that

**Theorem Used:**

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

**Proof:**

Assume the minor arc of chord

Applying the theorem,

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

And since the minor arcs are unequal i.e.

The chord corresponding to minor arc

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