   Chapter 6.4, Problem 26E 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 ⊙ O , A B = 6 c m and B C = 4 c m .a) How are m ∠ A O B and m ∠ B O C related?b) How are m A B ⌢ and m B C ⌢ related? To determine

(a)

To find:

The relation between mAOB and mBOC.

Explanation

Given:

O, AB=6cm and BC=4cm. The figure given below,

Theorem 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.

Calculation:

Using the theorem,

Since the chords AB=6cm and BC=4cm are unequal and AB>BC.

From the given figure,

The arc corresponding to chord AB is mAB and the arc corresponding to chord BC is mBC, we conclude that mAB>mBC

To determine

(b)

To find:

The relation between mAB and mBC.

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