Unit 10 Circles. This unit addresses circles. It includes central angles, arcs (minor/major/semicircle), arc lengths, sectors, areas of sectors, segments, tangents to circles, circumscribed and inscribed circles, and chords. Standards. SPI’s taught in Unit 10:
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Unit 10 Circles
.
a
m
Other
15%
Sleep
31%
Entertainment
18%
Must Do
7%
Food
9%
Work
20%
How would I figure out how many people are in each category?
A C
O
D E
C
580
D
B
320
O
A
(measure of the arc) X π x D 360
(mXY0/3600)x (π x D)
= 90/360 x (π x 16)
=.25 x (π x 16)
= 4π inches
X
O
900
16 inches
Y
X
O
15 CM
P .
Y
2400
Remember, Diameter = 2 Radii
Of course... There is a way to do it on the calculator…
C
580
D
B
10 inches
320
O
A
R
B (or π R)
(Arc0)/360 x the area of the circle (π R2)
Area of Sector AOB = m(arc AB)/360 x π R2
(Remember, the measure of the arc is the measure of degrees)
A
B
r
O
Z
720
20 cm
M
O
Area of Sector Area of Triangle Area of Segment

=
Make a sector Make a Triangle Calculate area
Given a Segment
A
O
10 in.
B
Hint: Convert Percent to a decimal
Hint: What is the area of the circle?
Radius = 15 inches
(x,y)
same as
x2, y2
y
r
r = √ (xh)2 + (yk)2 Revised Distance Formula
r2= (xh)2 + (yk)2 Square both sides
(xh)2 + (yk)2 = r2  Rewrite in the “equation of a circle” format
(h,k)
same as
x1, y1
x
0
O
A
P
A
B
O
O
N L
1170
X0
M
E D
X0
.
O
380
N
25
M
7
24
L
B
D
E
A
C
F
B
8 cm
D
E
O
C
A
15 cm
F
10 cm
B
D
E
17 cm
A
C
F
15 cm
P
O
Q
P
A
X0
X0
B
Q
9
a
9
9
12.5
18
16
X
36
18
K
r
3
L
M
14
N
6.8
4
X
Warning track (180 degree arc)
5 ft
320 Feet
Home Plate
measure of arc ac
A
B
C
m
a
600
n
q
300
b
p
1
2
250
3
600
4
6
800
5
B
D
C
300
n
m
300
.
p
b
c
w
a
600
d
in other words, you take the
average of 2 angles
600
1
500
you subtract them and then
divide by 2 –what is angle 1?
1
300
1000
950
Z0
460
200
X
900
X
400
a
x
c
w
t
d
b
y
z
y
z
6
8
7
y
z
8
16
6.5
3
7
a