   Chapter 6.CR, Problem 9CR 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. G i v e n :           C   i s   t h e   m i d p o i n t   o f   A C D ^   a n d     m ∠ B = 40 °       F i n d :             m A D ^ ,   m A C ^ , m D C ^ To determine

To find: mAD^,mAC^, 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=40° and C is the midpoint of mACD^ 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^ .

Since, C is the midpoint of mACD^, mAC^=mDC^

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