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 6 - Section 6.2 - More Angle Measures in the Circle - Exercises - Page 296: 34

Answer

5.67 mm

Work Step by Step

We know that OE is 5 mm. In addition, since OE equals ED, and EF is half of ED, it follows that EF is half of 5, which is 2.5. Since OFE is a right angle, we use the Pythagorean theorem: $OF^2 + 2.5^2 = 5^2 \\ OF = 4.33 mm$ Since OF plus FC equals 10, this means that FC equals $10 - 4.33 = 5.67$.
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