   Chapter 6.4, Problem 31E 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 : m ∠ B : m ∠ C = 2 : 4 : 3 in circle O :a) Which angle is largest?b) Which chord is longest? To determine

(a)

To find:

The largest angle.

Explanation

Given:

mA:mB:mC=2:4:3 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, mA:mB:mC=2:4:3 and the sum of the angles of a triangle is 180°, we get

mA+mB+mC=180°

Or 2x+4x+3x=180°

So

To determine

(b)

To find:

The longest chord.

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