Elementary Geometry for College Students (6th Edition)

Published by Brooks Cole
ISBN 10: 9781285195698
ISBN 13: 978-1-28519-569-8

Chapter 6 - Section 6.2 - More Angle Measures in the Circle - Exercises - Page 288: 45


We can use the same generalized example as we used in problem 44, for this will address both cases. We consider a line that creates a third side to the triangle in which the line is congruent to the original line going through the circle. This is an inscribed angle, so it is half of the length of the arc that it corresponds to, which is the same as the arc that the other angle corresponds to. Since both angles are part of the base of an isosceles triangle, the two angles are congruent. Thus, if the inscribed angle is half of the measure of the corresponding arc, it follows that the angle created by the chord and the tangent line is also half of its corresponding arc.
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