Chapter 6.CR, Problem 13CR

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7th Edition

Alexander + 2 others

ISBN: 9781337614085

Textbook Problem

Two circles are concentric. A chord of the larger circle is also tangent to the smaller circle. The lengths of the radii are 20 and 16, respectively. Find the length of the chord.

To determine

**To find: **The length of the chord of the larger circle.

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 larger circle is 20.

The length of the radius of a smaller circle is 16.

Let O be the center of the two circles and AB be a chord.

Also, AB be a tangent to the smaller circle at C

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

The distance from the center of the larger circle to the chord = OC.

By theorem,

So,

By theorem,

So,

So,

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