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 309: 47

Answer

We must prove that triangle TWV is similar to triangle TXV. Both triangles share a common angle T and a common side TV, which are congruent to themselves by the identity property. In addition, angles V and W are congruent, for they are inscribed angles for the same arc. Thus, the triangles are similar by ASA, so we use proportions: $\frac{TV}{TW}=\frac{TX}{TV} \\TV^2 =TWTX$
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