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Math
GeometryElementary Geometry for College Students6th Edition

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Chapter 6.CR, Problem 8CR
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Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698

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Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
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In Review Exercises 5 to 10, B A → is tangent to the circle at point A in the figure shown.

m ∠ D = 40 ° ,   m D C ^ = 130 ° ,     m ∠ B = ?

Chapter 6.CR, Problem 8CR, In Review Exercises 5 to 10, BA is tangent to the circle at point A in the figure shown.

To determine

To find: m∠B

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

m∠D=40°, mDC^=130° and BA→ is tangent to the circle at point A.

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

So, m∠ADC=12mAC^

40°=12mAC^

40°×2=12mAC^×2

80°=mAC^

Therefore, mAC^=80°

Now, mAD^+mAC^+m<

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Sect-6.1 P-1ESect-6.1 P-2ESect-6.1 P-3ESect-6.1 P-4ESect-6.1 P-5ESect-6.1 P-6ESect-6.1 P-7ESect-6.1 P-8ESect-6.1 P-9ESect-6.1 P-10E
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