   Chapter 6.4, Problem 8E 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

In Exercises 1 to 8, use the figure provided.If Q N : Q M = 5 : 6 , write an inequality that compares m A B ⌢ to m C D ⌢ . To determine

To write:

An inequality that compares mAB to mCD.

Explanation

Given:

QN:QM=5:6 and the figure given below

Theorem:

In a circle (or in congruent circles) containing two unequal chords, the chord nearer the center of the circle has the greater length.

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

Calculation:

Since, QN:QM=5:6, it means that QM¯<QN¯.

Using the theorem.

Since the chords are unequal and the distance of chords from center is also unequal i.e. QM¯<QN¯ and from the given figure.

The chord CD is at distance QN and the chord AB is at distance QM, we conclude that CD¯<AB¯

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