   Chapter 6.4, Problem 38E 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

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 O with two chords AB¯, BC¯ and mAB¯>mBC¯.

The angle corresponding to chord mAB¯ is mAOB and the angle corresponding to arc mBC¯ is mBOC.

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 mAOB>mBOC.

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 mAB¯>mCD¯.

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