CIRCLES

1. 10.2 Arcs and Chords
Central angle
Minor Arc
Major Arc

2. Central angle
A central angle is an angle which vertex is
the center of a circle

3. Minor Arc
An Arc is part of the circle.
A Minor Arc is an arc above the central
angle if the central angle is less then 180°

4. Major Arc
A Major Arc is an arc above the central
angle if the central angle is greater then
180°
ADB
Arc
Major
AB
Arc
Minor

5. Semicircle
If the central angle equals 180°, then the arc
is a semicircle.

6. Semicircle
If the central angle equals 180°, then the arc
is a semicircle.

7. Measure of an Arc
The measure of an Arc is the same as the
central angle.

 30
AC

8. Measure of an Arc
The measure of an Arc is the same as the
central angle.

120
AB






240
120
360
ADB
ADB
D
A
B

9. Postulate: Arc Addition
Arcs can be added together.






110
27
83
QR
RP
QP

83

27

10. Congruent Arcs
If arcs comes from the same or congruent
circles, then they are congruent if then
have the same measure.
A
B
K
G

85

85
KG
AB 

11. Congruent chords Theorem
In the same or congruent circles, Congruent
arcs are above congruent chords.
CD
AB
CD
AB


if
only
and
if

12. Theorem
If a diameter is perpendicular to a chord ,
then it bisects the chord and its arc.
BC
AC
BE
AE



13. Theorem
If a chord is the perpendicular bisector of
another chord (BC), then the chord is a
diameter.
EC
BE
DC
BD



14. Solve for y




140
90
AB
AMO
m
y
2

15. Solve for y




140
90
AB
AMO
m
y
2




35
70
2
y
y

16. Theorem
In the same or congruent circles, two chords
are congruent if and only if they are an
equal distance from the center.
RS
PQ
BO
AO
Since

 ,

17. Solve for x, QT
UV = 6; RS = 3; ST = 3

18. Solve for x, QT
UV = 6; RS = 3; ST = 3
x = 4,
Since Congruent
chord are an
equal distance
from the center.

19. Solve for x, QT
UV = 6; RS = 3; ST = 3
x = 4,
5
9
16
3
4 2
2
2





QT
QT 4

20. Find the measure of the arc
Solve for x and y

52

52
 
 6
2y
 
10
x

21. Find the measure of the arc
Solve for x and y

52

52
 
 6
2y
 
10
x
23
2
46
)
6
2
(
52
44
10
52









y
y
y
x
x

22. Homework
Page 607 – 608
# 12 - 38

23. Homework
Page 608 -609
# 39 – 47,
49 – 51,
69, 76 - 79