Elementary Geometry for College Students (6th Edition)

Published by Brooks Cole
ISBN 10:
ISBN 13:

Chapter 8 - Review Exercises - Page 386: 37

Answer

The area of the circumscribed circle is twice the radius of the inscribed circle.

Work Step by Step

The circumscribed circle has a radius that is equal to half the diagonal of the square, for it touches each vertex of the square. Using 45-45-90 triangles in the square, we know that this is the same as: $R = d/2 = \frac{s \sqrt{2}}{2}$ The radius of the inscribed circle is equal to half the length of the side. Thus, we create our proportion: $ = \frac{ (s \sqrt{2}/2)^2}{(s/2)^2} = 2 $
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