Elementary Geometry for College Students (5th Edition)

Published by Brooks Cole
ISBN 10: 1439047901
ISBN 13: 978-1-43904-790-3

Chapter 6 - Section 6.3 - Line and Segment Relationships in the Circle - Exercises - Page 308: 39

Answer

8.7

Work Step by Step

While we could do some complex geometry to solve this problem, the tangent to both happens to be a 30-60-90 triangle. Thus, its length is $\sqrt{3}$ times the lengths of each side. Thus: $AB = \sqrt{3}(2+3) = 5\sqrt3 = 8.7$
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