   Chapter 6.CR, Problem 14CR 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

Two parallel chords of a circle each have length 16. The distance between these chords is 12. Find the length of the radius of the circle.

To determine

To find: The length of the radius of the circle.

Explanation

Theorem:

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

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

3) If a line through the centre of a circle bisects a chord other than a diameter, then it is perpendicular to the chord.

Calculation:

Given that the length of the chords of the circle = 16.

The distance between the chords = 12.

Let O be the center of the two circles and AB and CD be chords.

Also, AB = CD = 16.

Also, PQ = 12

Since, congruent chords are located at the same distance from the center of a circle.

Since AB and CD are congruent, they are at the same distance from the centre.

So, PO = QO and PQ = 12

So, PO = QO = 122 = 6

Since, a radius that is perpendicular to a chord bisects the chord

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