   Chapter 6.3, Problem 14E ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698

#### Solutions

Chapter
Section ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
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# In the figure for Exercises 7 to 16, O is the center of the circle. See Theorem 6.3.5.Given: A E = x 2 , E B = x 3 , D E = 5 x 6 ,     a n d     E C = 6 Find: x and DE. To determine

To find:

To find x and DE

Explanation

Given that, AE=x2,EB=x3,DE=5x6,andEC=6

The diagrammatic representation is given below,

Theorem:

If two chords intersect within a circle, then the product of the lengths of the segments (parts) of one chord is equal to the product of the lengths of the segments of the other chord.

By using the theorem to get the following,

AEEB=DEEC

Substitute the values AE=x2,EB=x3,DE=5x6,andEC=6 in the above equation to get the following,

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