Other Angle Relationships in Circles Section 10.4 Goal: - To solve problems using angles formed by...
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Transcript of Other Angle Relationships in Circles Section 10.4 Goal: - To solve problems using angles formed by...
![Page 1: Other Angle Relationships in Circles Section 10.4 Goal: - To solve problems using angles formed by tangents, chords and lines that intersect a circle.](https://reader036.fdocuments.us/reader036/viewer/2022082917/55159532550346486b8b5a45/html5/thumbnails/1.jpg)
Other Angle Relationships in Circles
Section 10.4
Goal:
- To solve problems using angles formed by tangents, chords and lines that intersect a circle.
![Page 2: Other Angle Relationships in Circles Section 10.4 Goal: - To solve problems using angles formed by tangents, chords and lines that intersect a circle.](https://reader036.fdocuments.us/reader036/viewer/2022082917/55159532550346486b8b5a45/html5/thumbnails/2.jpg)
Theorem 10.12
C
A
B
2
1 11 and 2
2 2m mAB m mBCA
If m 1=80 , then ?
If 200, then m 2=?
mBA
mBCA
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.
1
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Example Find: m CBD and mBAD
AB
4 50x 3x
D
C
![Page 4: Other Angle Relationships in Circles Section 10.4 Goal: - To solve problems using angles formed by tangents, chords and lines that intersect a circle.](https://reader036.fdocuments.us/reader036/viewer/2022082917/55159532550346486b8b5a45/html5/thumbnails/4.jpg)
Lines Intersecting On, Inside, or Outside a Circle
On the circle Inside the circle Outside the circle
Case 1 Case 2 Case 3
An inscribed angle
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Lines, or chords, intersecting inside a circle
Theorem 10.13
1
B
A
C
11
2m mCD mAB
D
2
If two chords intersect in the interior of a circle, then the measures of each angle is one half the sum of the measures of the arcs intercepted by the angle and its vertical angle.
12
2m mBC mAD
![Page 6: Other Angle Relationships in Circles Section 10.4 Goal: - To solve problems using angles formed by tangents, chords and lines that intersect a circle.](https://reader036.fdocuments.us/reader036/viewer/2022082917/55159532550346486b8b5a45/html5/thumbnails/6.jpg)
Chords, intersecting inside a circle Example
x
B
A
C
Find x
D
40
120
![Page 7: Other Angle Relationships in Circles Section 10.4 Goal: - To solve problems using angles formed by tangents, chords and lines that intersect a circle.](https://reader036.fdocuments.us/reader036/viewer/2022082917/55159532550346486b8b5a45/html5/thumbnails/7.jpg)
Lines Intersecting Outside a CircleThree scenarios!
tangent-secant tangent-tangent secant-secant
![Page 8: Other Angle Relationships in Circles Section 10.4 Goal: - To solve problems using angles formed by tangents, chords and lines that intersect a circle.](https://reader036.fdocuments.us/reader036/viewer/2022082917/55159532550346486b8b5a45/html5/thumbnails/8.jpg)
Tangent - Secant
1
B
A
C
Tangent-Secant
11
2m mBC mAC
1 210 and 40Find m if mBC mAC
![Page 9: Other Angle Relationships in Circles Section 10.4 Goal: - To solve problems using angles formed by tangents, chords and lines that intersect a circle.](https://reader036.fdocuments.us/reader036/viewer/2022082917/55159532550346486b8b5a45/html5/thumbnails/9.jpg)
Tangent - Tangent
1
Q
P
R
Tangent-Tangent
11
2m mPQR mPR
1 300 and 60Find m if mPQR mPR
![Page 10: Other Angle Relationships in Circles Section 10.4 Goal: - To solve problems using angles formed by tangents, chords and lines that intersect a circle.](https://reader036.fdocuments.us/reader036/viewer/2022082917/55159532550346486b8b5a45/html5/thumbnails/10.jpg)
Secant - Secant
1
B
A
D
Secant-Secant
11
2m mBC mAD
1 190 and 30Find m if mBC mAD
C
![Page 11: Other Angle Relationships in Circles Section 10.4 Goal: - To solve problems using angles formed by tangents, chords and lines that intersect a circle.](https://reader036.fdocuments.us/reader036/viewer/2022082917/55159532550346486b8b5a45/html5/thumbnails/11.jpg)
Example
78
B
A
C
Find x:
204
x
![Page 12: Other Angle Relationships in Circles Section 10.4 Goal: - To solve problems using angles formed by tangents, chords and lines that intersect a circle.](https://reader036.fdocuments.us/reader036/viewer/2022082917/55159532550346486b8b5a45/html5/thumbnails/12.jpg)
Example
96
Find x:
x
![Page 13: Other Angle Relationships in Circles Section 10.4 Goal: - To solve problems using angles formed by tangents, chords and lines that intersect a circle.](https://reader036.fdocuments.us/reader036/viewer/2022082917/55159532550346486b8b5a45/html5/thumbnails/13.jpg)
Example
31
Find x:
57
x
![Page 14: Other Angle Relationships in Circles Section 10.4 Goal: - To solve problems using angles formed by tangents, chords and lines that intersect a circle.](https://reader036.fdocuments.us/reader036/viewer/2022082917/55159532550346486b8b5a45/html5/thumbnails/14.jpg)
Example
27
Find x:
88
x