   Chapter 6.CR, Problem 5CR 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 Review Exercises 5 to 10, B A → is tangent to the circle at point A in the figure shown. m ∠ B = 25 ° ,   m A D ^ = 140 ° ,     m D C ^ = ? To determine

To find: mDC^

Explanation

Theorem:

1) The measure of an angle formed when two secants intersect at a point outside the circle is one-half the difference of the measures of two intercepted arcs.

2) The measure of an inscribed angle of a circle is one-half the measure of its intercepted arc.

Calculation:

Given that

mB=25°, mAD^=140° and BA is tangent to the circle at point A.

By theorem, the measure of an angle (mB) formed when two secants (BD and BA) intersect at a point (B) outside the circle is one-half the difference of the measures of two intercepted arcs AD^ and AC^ .

25°=12(140°-mAC)^

50°=140°-mAC^

Subtract 50 from each side

50°-50°=140°-mAC^-50°

0=90°-mAC^

Add mAC^ to both the sides

0+mAC^=90°-mAC^+mAC^

mAC^=90°

By theorem, The measure of an inscribed angle D of a circle is one-half the measure of its intercepted arc mAC^.

Therefore, mD=12mAC^

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

What is 834 of \$12,000?

Elementary Technical Mathematics

Solve the equations in Exercises 112 for x (mentally, if possible). x1=cx+d(c1)

Finite Mathematics and Applied Calculus (MindTap Course List)

Evaluate the integrals in Problems 1-26. 14.

Mathematical Applications for the Management, Life, and Social Sciences

Domain Find the domain of the function. 77. h(x) = ln x + ln(2 x)

Precalculus: Mathematics for Calculus (Standalone Book)

Find the general indefinite integral. 1+x+xxdx

Single Variable Calculus: Early Transcendentals, Volume I

Find the center of A4.

Elements Of Modern Algebra

Which graph is best described by a linear model?

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

In Exercises 1-8, construct a truth table for each compound proposition. ~p~q

Finite Mathematics for the Managerial, Life, and Social Sciences 