   Chapter 6.CT, Problem 15CT 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

In ⊙ P (not shown), the length of radius   P A ¯ is 5. Also, chord A B ¯ ∥   c h o r d C D ¯ . If A B = 8 and C D = 6     , find the distance between A B ¯ and C D ¯ if these chordsa) lie on the same side of center P .b) lie on opposite sides of center P .

To determine

a)

To find:

The distance between AB¯ and CD¯ chords if it lie on the same side of center P.

Explanation

Given:

A circle of length of radius PA¯= 5.

Chord AB¯chord CD¯.

If AB=8 and CD=6.

Calculation:

Consider the circle with center P with radius PA¯= 5 and chord AB¯chord CD¯ which lie on the same side of center P be,

Here,

M and N are the mid points of the line AB¯ and CD¯ therefore AM¯=4=MB¯ and CN¯=3=ND¯.

PO¯ is also a radius.

Let consider ΔPAM.

Using Pythagoras theorem,

To determine

b)

The distance between AB¯ and CD¯ chords if it lie on opposite sides of center P.

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