   Chapter 6.CR, Problem 2CR 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

Find the length of a chord that is 8 cm from the center of the circle that has a radius length of 17 cm.

To determine

To find: The length of the chord.

Explanation

Theorem:

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

2) 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 radius of a circle is 17 cm.

The distance from the center of the circle to the chord = 8 cm

Let the length of the chord be x cm.

Let O be the center of the circle and AB be a chord.

So, AB = x cm and OB = radius = 17 mm

The distance from the center of the circle to the chord = OP = 8 cm.

By theorem, OPAB.

So, ◿OPB is a right triangle.

By theorem, AP=PB or AB = 2AP = 2AB.

So, AP=12AB.

So, AP=PB=12x=x2cm

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