Elementary Geometry for College Students (7th Edition)

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

Chapter 6 - Section 6.1 - Circles and Related Segments and Angles - Exercises - Page 287: 43



Work Step by Step

The measure of an inscribed angle is equal to half of measure of the angle of the arc it inscribes. Thus, the measure of angle Z is 90 degrees. Since the measure of XO equals the measure of OY, we find that the measure of XY equals 10. Using the Pythagorean thorem, we obtain that YZ equals $\sqrt{10^2 - 6^2} = 8$. Since XW is congruent to WY, we find: $6^2 + WZ^2 = (8 - WZ)^2 \\ 36 = 64 - 16WZ \\ WZ = 1.75$
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