   Chapter 6.4, Problem 28E 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

Triangle A B C is inscribed in circle O ; A B = 5 , B C = 6 , and A C = 7 .a) Which is the largest minor arc of ⊙ O : A B ⌢ , B C ⌢ , or A C ⌢ ?b) Which side of the triangle is nearest point O ? To determine

(a)

To find:

The largest minor arc.

Explanation

Given:

Triangle ABC is inscribed in circle O; AB=5, BC=6, and AC=7.

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.

Calculation:

Using the theorem,

Since the chords AB=5, BC=6, and AC=7 are unequal and AB<BC<AC.

To determine

(b)

To find:

The side of the triangle that is nearest point O.

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