Notes on 10-4,10-6

1. Section 10-4, 10-6
Jim Smith JCHS
3108.4.39
3108.4.40

2. Central Angles Are Equal To The
Measure Of The Intercepted Arc
Central Angles
1
63°
1 = 63°

3. Inscribed Angles
The Vertex Of An Inscribed Angle Is
On The Circle And The Sides Are
Contained In Chords.
1 2
4
3

4. The Measure Of An Inscribed Angle
Is Equal To ½ The Measure Of The
Intercepted Arc
1
100°
1 = ½ ( 100 )
1 = 50°
2
4
3
2 = ½ (180 )
2 = 90°

5. Any Angle With It’s Vertex
On The Circle Is Equal
To ½ Of The Arc.
2 secants
A secant and
a tangent

6. The opposite angles of an inscribed
quadrilateral are supplementary
1
2
< 1 + < 2 = 180

7. If The Vertex Is Somewhere
Inside The Circle But Not At The
Center, The Angle Is Equal To
½ The Sum Of The Arcs
8
150°
80°
8 = ½ (150 + 80)
8 = ½ ( 230 )
8 = 115°

8. If The Vertex Is Outside
(A Distance Away From) The
Circle, The Angle Is Equal To
½ The Difference Of The Arcs.
120°
50°
5
5 = ½ (120 - 50)
5 = ½ ( 70 )
5 = 35°

9. 2
1
3
4
= arc =1/2 arc
=1/2 (sum of
2 arcs)
=1/2 (difference
of 2 arcs)

10. D
C
B
A
F
E
AC is a diameter
CD = 100°
CB = AE
BE = 50° 1
2
3
4
5
Find the
Measures of
the angles
AF is a tangent

11. D
C
B
A
F
E
AC is a diameter
CD = 100°
CB = AE
BE = 50° 1
2
3
4
5
AF is a tangent
100°
80°
50°
130/2 =65
65°
65°

12. D
C
B
A
F
E
1
2
3
4
5
100°
80°
50°
65°
65°
1 = 80°

13. D
C
B
A
F
E
1
2
3
4
5
100°
80°
50°
65°
65°
2 =1/2 (65)
2 = 32 ½ °

14. 3 =1/2 (180+50)
3 =1/2 (230)
3 = 115°
D
C
B
A
F
E
1
2
3
4
5
100°
80°
50°
65°
65°

15. D
C
B
F
E
1
2
3
4
5
100°
80°
50°
65°
65°
4 =1/2 (65+50)
4 =1/2 (115)
4 = 57 ½ °
A

16. 5 =1/2 (180-65)
5 =1/2 (115)
5 =57 1/2°
D
C
B
A
F
E
1
2
3
4
5
100°
80°
50°
65°
65°