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 295: 23

Answer

BD is twice the measure of BC.

Work Step by Step

The measure of arc BC is equal to double the measure of angle A, for when a pair of two tangent lines intersect an arc, the measure where these lines intersect is equal to half of the measure of the arc that is intersected. Since angle BCD is twice the measure of angle B, its arc, BD, is four times the measure of angle B. Since angle A is congruent to B, this means that arc BD is four times the measure of A. Since BC is twice the measure of A, it follows that the measure of BD is twice the measure of BC.
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