   Chapter 6.4, Problem 3E 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 m C D ⌢ < m A B ⌢ , write an inequality that compares Q M and Q N . To determine

To write:

An inequality that compares QM and QN.

Explanation

Given:

mCD<mAB and the figure given below

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.

In a circle (or in congruent circles) containing two unequal chords, the shorter chord is at the greater distance from the center of the circle.

Calculation:

Using the theorem.

And since the arcs are unequal i.e. mCD<mAB and from the given figure,

The chord corresponding to arc mCD is CD and the chord corresponding to mAB is AB, we conclude that CD¯<AB¯

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