   Chapter 6.CR, Problem 1CR 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

The length of the radius of a circle is 15 mm. The length of a chord is 24 mm. Find the distance from the center of the circle to the chord.

To determine

To find: The distance from the center of the circle to 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 15 mm.

The length of the chord is 24 mm.

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

So, AB = 24 mm and OB = radius = 15 mm

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

By theorem, OPAB.

So, ◿OAB is a right triangle.

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

So, AP=12AB.

So, AP=PB=1224=12 mm

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