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Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698

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Chapter
Section
BuyFindarrow_forward

Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem

In Exercises 1 to 8, use the figure provided.

If m C Q D < m A Q B , write an inequality that compares C D to A B .

To determine

To write:

An inequality that compares CD to AB.

Explanation

Given:

mCQD<mAQB and the figure given below.

Theorem:

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

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.

Calculation:

Using the theorem.

Since the angles are unequal i.e. mCQD<mAQB and from the given figure.

The arc corresponding to angle mCQD is mCD and the arc corresponding to angle mAQB is mAB, we conclude that mCD<mAB

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