Angle Relationships in Circles

1
11-5
Angle Relationships in Circles
Warm Up
Lesson Presentation
Lesson Quiz
Holt Geometry
2
Warm Up 1. Identify each line or segment that
intersects ?F. Find each measure. 2.
m?NMP 3. m?NLP
110
55
3
Objectives
Find the measures of angles formed by lines that
intersect circles. Use angle measures to solve
problems.
4
(No Transcript)
5
Example 1A Using Tangent-Secant
and Tangent-Chord Angles
Find each measure.
m?EFH
65
6
Example 1B Using Tangent-Secant
and Tangent-Chord Angles
Find each measure.
7
Check It Out! Example 1a
Find each measure.
m?STU
83?
8
Check It Out! Example 1b
Find each measure.
9
(No Transcript)
10
Example 2 Finding Angle Measures Inside a Circle
Find each measure.
m?AEB
126?
11
Check It Out! Example 2a
Find each angle measure.
m?ABD
12
Check It Out! Example 2b
Find each angle measure.
m?RNM
m?RNM 180 ?MNQ
m?RNM 180 158 22
13
(No Transcript)
14
Example 3 Finding Measures Using Tangents and
Secants
Find the value of x.
40?
63?
15
Check It Out! Example 3
Find the value of x.
50 83 x
x 33
16
Example 4 Design Application
17
Check It Out! Example 4
18
(No Transcript)
19
Example 5 Finding Arc Measures
If a tangent and a secant intersect on a ? at the
pt. of tangency, then the measure of the ? formed
is half the measure of its intercepted arc.
Multiply both sides by 2.
Subtract 68 from both sides.
20
Example 5 Continued
Thm. 11-5-3
Substitute the given values.
Multiply both sides by 2.
Add 66 to both sides.
21
Check It Out! Example 5
22
Lesson Quiz Part I
Find each measure. 1. m?FGJ 2. m?HJK
41.5
65
23
Lesson Quiz Part II
3. An observer watches people riding a Ferris
wheel that has 12 equally spaced cars. Find x.
30
24
Lesson Quiz Part III
4. Find mCE.
12