   Chapter 6.2, Problem 44E 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

In Exercises 39 to 47 , provide a paragraph proof. Be sure to provide a drawing, Given, and Prove where needed.Prove Case 2 of Corollary 6.2 . 4 : 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. (See Figure 6.29 (b) on page 291 .)

To determine

To provide:

A paragraph proof for the statement “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”.

Explanation

Calculation:

Consider the below figure,

Proof:

 Given: DC¯ tangent.Prove: m∠BCD=mBC⌢2 Given: AC¯⊥DC¯ The radius to the tangent at the point of tangency is perpendicular to the tangent of that point. m∠ACD=mABC⌢2 Since,m∠ACD=90∘mABC⌢=180∘

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