   Chapter 6.CR, Problem 25CR 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

G i v e n :                               D F - ≅ A C -   i n   ⨀ O                                                                       O E = 5 x + 4                                                                     O B = 2 x + 19 F i n d :                                             O E To determine

To Find:

The value of OE, if DF-AC- in  O, OE=5x+4 and OB=2x+19 Explanation

Approach:

Theorem 6.1.1:

A radius that is perpendicular to a chord bisects the chord.

Theorem 6.1.8:

Congruent chords are located at the same distance from the center of a circle.

Calculation:

Given that DF-AC- in O

So, DF and AC are congruent chords.

So, by Theorem 6.1.8:

Congruent chords are located at the same distance from the center of a circle.

DF and AC are at the same distance from the center of a circle  O.

So, OE=OB

But it is given that, OE=5x+4 and OB=2x+19

So, 5x+4=

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