Elementary Geometry for College Students (6th Edition)

Published by Brooks Cole
ISBN 10:
ISBN 13:

Chapter 6 - Section 6.4 - Some Constructions and Inequalities for the Circle - Exercises - Page 302: 32

Answer

Angle T and side EQ are the largest. The smallest angle and side cannot be determined from the given information.

Work Step by Step

The angle created by a radius and a tangent line at the point of tangency is equal to 90$^{\circ}$. Since angle T is a right angle it must be the largest in the triangle and therefore side QE across from it is the largest side since it is the hypotenuse. The shortest angle and side depends on whether or not the tangent line, ET, is longer than the radius of the circle.
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