   Chapter 6.4, Problem 30E 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

Given that m A C ⌢ : m B C ⌢ : m A B ⌢ = 4 : 3 : 2 in circle O :a) Which arc is largest?b) Which chord is longest? To determine

(a)

To find:

The largest arc.

Explanation

Given:

mAC:mBC:mAB=4:3:2 in circle O. The figure given below

Theorem Used:

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

Calculation:

Since, mAC:mBC:mAB=4:3:2 and the sum of the arcs is 360°, we get

mAC+mBC+mAB=360°

or 4x+3x+2x=360°

To determine

(b)

To find:

The longest chord.

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