   Chapter 6.2, Problem 4E Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

Find m R T ⌢ if m ∠ R S T : m ∠ R S W = 1 : 5 To determine

To find:

mRT if mRST:mRSW=1:5.

Explanation

Theorem:

The radius drawn to a tangent at the point of tangency is perpendicular to the tangent at that point.

Corollary:

The measure of an angle formed by a tangent and a chord drawn to the point of tangency is one-half the measure of the intercepted arc.

Calculation:

To find: mRSW.

Diameter is RS¯ and tangent is SW.

By theorem,

mRSW=90°

mRST:mRSW=1:5

mRSTmRSW=15mRSW=5mRST90°=5mRST

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