Elementary Geometry for College Students (7th Edition) Clone

Published by Cengage
ISBN 10: 978-1-337-61408-5
ISBN 13: 978-1-33761-408-5

Chapter 8 - Section 8.5 - More Area Relationships in the Circle - Exercises - Page 390: 26

Answer

A=12$\pi$$\approx$37.9 in$^2$

Work Step by Step

There is a right triangle formed by the radius of the larger circle, half of the chord, and the radius of the smaller circle. Since the radius of the smaller circle is half of the radius of the larger circle (short leg of the triangle is half of the hypotenuse), this is a 30 60 90 triangle. Therefore the angle between the two radii is 60$^{\circ}$. The measure of the minor arc formed by the chord is equal to twice that angle, which is 120$^{\circ}$. A=$\frac{120}{360}$$\pi$(6)$^2$ A=12$\pi$$\approx$37.9 in$^2$
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