Elementary Geometry for College Students (5th Edition)

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

Chapter 6 - Section 6.2 - More Angle Measures in the Circle - Exercises - Page 298: 24

Answer

By the definition of perpendicular lines, it follows that CDA and CDB are both right angles. Thus, because right angles are congruent, these two angles are congruent. In addition, CD is congruent to itself by the identity property. Finally, since they correspond to congruent arcs, we obtain that angle C and angle B are congruent. Thus, by SAS, triangle ADC is congruent to triangle DCB. Since corresponding parts of similar triangles are proportional, we obtain: $\frac{AD}{CD} = \frac{CD}{DB}$.
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