10­6 Full Day Circles and Arcs 2011
March 02, 2011
Warm Up
Feb 26­12:13 PM
1
10­6 Full Day Circles and Arcs 2011
March 02, 2011
Feb 28­9:46 AM
2
10­6 Full Day Circles and Arcs 2011
March 02, 2011
Feb 26­12:13 PM
3
10­6 Full Day Circles and Arcs 2011
March 02, 2011
Feb 28­9:59 AM
4
10­6 Full Day Circles and Arcs 2011
March 02, 2011
Feb 26­12:13 PM
5
10­6 Full Day Circles and Arcs 2011
March 02, 2011
Feb 26­12:13 PM
6
10­6 Full Day Circles and Arcs 2011
March 02, 2011
What is a circle? ­Up
m
r
a
W
How would you describe a circle in words so I can draw it?
A
A circle is the set of all points equidistant from a given point called the center.
You name a circle by its center.
Feb 26­12:13 PM
7
10­6 Full Day Circles and Arcs 2011
March 02, 2011
Objective: Find the measures of central angles and arcs. Find circumference and arc length.
Feb 26­12:13 PM
8
10­6 Full Day Circles and Arcs 2011
March 02, 2011
How do we define AC? AP?
A radius is a segment that has one endpoint at the center and the other endpoint on the circle.
C
A
P
How do we define PQ? BC?
A diameter is a segment that contains the center of a circle and has both endpoints on the circle.
Q
C
B
A
P
Feb 26­12:13 PM
9
10­6 Full Day Circles and Arcs 2011
March 02, 2011
PAC
A central angle is an angle whose vertex is the center of the circle.
C
A
P
m PAC = mCP
Congruent circles have congruent radii.
C
A
P
Feb 26­12:13 PM
10
10­6 Full Day Circles and Arcs 2011
March 02, 2011
This study shows how people spend their time.
What is the measure, in degrees, of the central angle used for the Entertainment section?
What is the measure, in degrees, of the central angle used for the Sleep and Food section?
Feb 26­12:13 PM
11
10­6 Full Day Circles and Arcs 2011
March 02, 2011
Identifying Arc's.
An arc is a part of a circle.
semicircle
minor arc major arc
Feb 26­12:13 PM
12
10­6 Full Day Circles and Arcs 2011
March 02, 2011
What is the Circumference of a circle?
Apr 12­3:28 PM
13
10­6 Full Day Circles and Arcs 2011
March 02, 2011
What is pi?
Pi is the ratio of the circumference of a circle to its diameter.
=
C
d
How would you solve this equation for C?
Apr 12­3:15 PM
14
10­6 Full Day Circles and Arcs 2011
March 02, 2011
Apr 12­3:32 PM
15
10­6 Full Day Circles and Arcs 2011
March 02, 2011
Circles that lie on the same plane and have the same center are concentric circles.
Apr 12­3:35 PM
16
10­6 Full Day Circles and Arcs 2011
March 02, 2011
A car has a turning radius of 16.1 ft. The distance between the two front tires is 4.7 ft. In completing the outer turning circle, how much farther does a tire travel than a tire on the concentric inner circle?
Apr 12­3:37 PM
17
10­6 Full Day Circles and Arcs 2011
March 02, 2011
The diameter of a bicycle wheel is 22 in. To the nearest whole number, how many revolutions does the wheel make when the bicycle travels 100 ft?
Apr 12­3:44 PM
18
10­6 Full Day Circles and Arcs 2011
March 02, 2011
The measure of an arc is in degrees while the arc length is a fraction of a circle's circumference. What fraction of the circle's circumference is a 60o angle?
Apr 12­3:48 PM
19
10­6 Full Day Circles and Arcs 2011
March 02, 2011
Find the length of each arc shown in pink. Leave your answer in terms of pi.
Apr 12­3:51 PM
20
10­6 Full Day Circles and Arcs 2011
March 02, 2011
Find the length of a semicircle with radius 1.3 m. Leave your answer in terms of pi.
Apr 12­3:54 PM
21
10­6 Full Day Circles and Arcs 2011
March 02, 2011
It is possible for two arcs of different circles to have the same measure but different lengths.
In order for two arcs to be CONGRUENT ARCS, they must have the same measure AND the same length.
Apr 12­3:56 PM
22
10­6 Full Day Circles and Arcs 2011
March 02, 2011
Homework
pg. 569 #1­26, 28­38 even, 42­47, 59, 71
Feb 26­12:13 PM
23
10­6 Full Day Circles and Arcs 2011
March 02, 2011
Feb 28­3:40 PM
24