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Transcript
```Chapter 10
LESSON
10.4
NAME _________________________________________________________ DATE ____________
Practice with Examples
For use with pages 621–627
GOAL
Use angles formed by tangents and chords to solve problems in
geometry and use angles formed by lines that intersect a circle to
solve problems
VOCABULARY
Theorem 10.12
If a tangent and a chord intersect at a point on a circle, then the measure
of each angle formed is one half the measure of its intercepted arc.
Theorem 10.13
If two chords intersect in the interior of a circle, then the measure of
each angle is one half the sum of the measures of the arcs intercepted by
the angle and its vertical angle.
Theorem 10.14
If a tangent and a secant, two tangents, or two secants intersect in the
exterior of a circle, then the measure of the angle formed is one half the
difference of the measures of the intercepted arcs.
EXAMPLE 1
Finding Angle and Arc Measures
Line m is tangent to the circle.
a. Find m1
b. mACB
90
B
A
1
2
m
SOLUTION
1
2
C
a. m1 90 45
b. Because 1 and 2 are a linear pair,
m2 180 m1 180 45 135. So,
mACB 2135 270.
190
Geometry
Practice Workbook with Examples
LESSON
Practice with Examples
Chapter 10
10.4
CONTINUED
NAME _________________________________________________________ DATE ____________
For use with pages 621–627
Exercises for Example 1
Find the value of each variable.
1.
2.
B
3.
M
m
P
x
156
z
2x
C
1
EXAMPLE 2
x
2
x
y A
Q
m
m
y
N
Using Theorem 10.13
Find the value of x.
SOLUTION
A
1 x mAB
mCD
2
Apply Theorem 10.13. 60
B
1
x 60 20 Substitute.
2
x 40
x
D
20
C
Simplify.
Exercises for Example 2
Find the value of x.
4.
5.
A
N
135
M
6.
30
P
W
x
2x
45
B
C
x
D
110
100
Y
x
Z
X
Q
Geometry
Practice Workbook with Examples
191
Chapter 10
LESSON
10.4
CONTINUED
EXAMPLE 3
NAME _________________________________________________________ DATE ____________
Practice with Examples
For use with pages 621–627
Using Theorem 10.14
Find the value of x.
A
D
B
x
SOLUTION
85
E
1
x mBC mDE
2
Apply Theorem 10.14.
1
x 171 85
2
Substitute.
x 43
171
C
Simplify.
Exercises for Example 3
Find the value of x.
7.
8.
x
9.
30
136
60
38 x 2x
8x
170
192
Geometry
Practice Workbook with Examples