April 15, 2015
Bellringers
C is center
P is point of
tangency
1) solve for x
6
C
x
8
P
8
2) solve for x and y
x
18
y 18
60o
LOOK AT THEOREM 9.1 if necessary
April 15, 2015
WE 1-6,8,10,16,20
CE 1-3,5
1) 2, 2, 2, 2, 1, 0
1) 8 2) 2 34
2) 2, 1, 0, 0, 0, 0
8) 72,72; 18,18; 144; yes
3) b, e
10) os sp;
op, os; 12
16) 20, 18, 16
20) 8
3) 12 4) 15
5) 8.2
12 5
6) 12
April 15, 2015
9-3 Arcs and Central Angles
A CENTRAL ANGLE of a circle is an angle with its vertex at the center of the circle.
An ARC is an unbroken part of a circle.
MINOR ARC is an arc that is in the interior of the central angle.
MAJOR ARC is the remaining arc that is not in the interior of the central angle.
SEMICIRCLES 2 arcs formed by a diameter
April 15, 2015
The MEASURE OF a MINOR ARC is equal to the measure of the central angle.
m AB
70o
The MEASURE OF THE MAJOR ARC is equal to 360 minus the measure of the
minor arc
The MEASURE OF A SEMICIRCLE is 180
ADJACENT ARCS of a circle are the arcs that have exactly one point in
common.
April 15, 2015
Postulate 16 - Arc Addition Postulates: The measure of the arc formed by 2
adjacent arcs is the sum of the measures of the 2 arcs.
April 15, 2015
Congruent Arcs: are arcs in the same or congruent circles that have equal
measures
80
A
E
C
B
o
6
80 o
6 P
D
Q
80 o
F
IDENTIFY ALL CONGRUENT ARCS
S 80 o
3
T
R
April 15, 2015
Theorem 9.3 In the same circle or in congruent circles, 2 minor arcs are
congruent if and only if their central angles are congruent.
50o
50o
C
Name the following: (O is the center)
a) two minor arcs
b) two major arcs
R
O
A
c) two semicircles
S
d) an acute central angle
e) two congruent arcs
April 15, 2015
Round Table Consensus
* Each person chooses a different color pencil
*Everyone does 1st problem -- solve for x -- compare
answers. When you agree on the answer, pass your paper
clockwise.
* Everyone finds the measure of AB -- compare answers.
When you agree on the answer, pass your paper clockwise.
* Continue until you have determined the measure of each
arc.
WE WILL CHECK AS A CLASS
April 15, 2015
Find the measure of each arc:
D
Solve for x first: x =
1
x-
4x
E
4
A) m AB
C
2
B) m CD
2x
3
3x x+1
0
B
C) m BC
D) m DE
A
E) m EA
April 15, 2015
YT is a diameter
Give the measure of each angle or arc:
Y
a) m WX
b) m XY
X
30 o
c) m WOT
O
d)m YZT
e)m YOT
f) m XYT
W
50
o
T
Z
April 15, 2015
QUICK REVIEW
The MEASURE OF a MINOR ARC is equal to the measure of the central angle.
The MEASURE OF THE MAJOR ARC is equal to 360 minus the measure of the minor arc
The MEASURE OF A SEMICIRCLE is 180
ADJACENT ARCS of a circle are the arcs that have exactly one point in
common.
April 15, 2015
Assignment
page 341 CE 1-13 odd
WE 2-6 even; 7, 8, 10, 11, 16
April 15, 2015
Answers to 9.3
2) 50 3) 130 4) 180 5) 230 6) 230 7) 280 8) 60 9) 50 10) 110
11) 110
12) 250
13) 310
April 15, 2015
2)80
4) 50
6) 55
7) 30
8) 4,8
10)
60
30
11)
16) 35
70, 70
2n
3k
56 50 2x
70
50 2x
35 28
34 44
100 88
104 p + q
50 44 50
1/2(p+q)