10-6: Circles and Arcs
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Transcript 10-6: Circles and Arcs
10-6: Circles and Arcs
Goal: Be able to find the measures of central angles
and arcs, and to find the circumference and arc length
of circles.
circle – the set of all points ______________
equidistant
center
from a given point, the __________.
This is A
(circle A)
A
center
radius – a segment that has one __________
endpoint
center and the other endpoint
at the __________
circle
on the _________.
diameter – a segment that contains the
center of a circle and has both
__________
endpoints the circle.
__________on
C
A B is a radius.
A C , A D are also radii.
A
B
CD
D
is a diameter.
central angle – an angle whose _________
vertex
center of the circle.
is at the __________
C
CAB
A
B
is a central angle.
B A D is a central angle.
D
There are ________
360 degrees in a circle.
The following information was determined from a survey determining how people really spend their
time.
How People Spend Their Time
7%
31%
18%
Sleep
Other
Food
Work
Entertainment
20%
Must Do
15%
9%
Directions: Find the measure of each central angle to the nearest whole number.
Find the corresponding percent of 360.
1.) Sleep .31(360 ) 1 1 2
4.) Work .20(360 ) 7 2
2.) Other .15(360 ) 5 4
5.) Entertainment .18(360 ) 6 5
3.) Food .09(360 ) 3 2
6.) Must Do .07 (360 ) 2 5
arc – part of a _________.
circle
C
A
E
B
D
is a minor arc.
AB
0 m AB 180
H
F
G
FGH
is a semicircle.
m FG H 180
CDE is a major arc.
180 m C D E 360
***The measure of a
equals
minor arc __________
the measure of its
corresponding
central angle.
______________
Identify the following in circle C.
M
Y
C
W
D
X
X D , D Y , YM , M W , X W
a.) two minor arcs _____________________________
D YW , D YX , YM X , YM D , M W D
b.) two major arcs _____________________________
YM W , M W X , W X Y
c.) two semicircles _____________________________
Find the measure of each arc.
M
84°
Y
C
40°
W
56° 84°
D
56°
84°
X
1 .) X D
m XD m D C X 56
2 .) X Y
m XY m XD m D Y
3 .) M W X
so, m XY 56 40 96
M W X is a semicircle. So, m M W X 180
so,
m D XM 56 180 236
4 .) D X M
m DXM m DX m XW M
5 .) YM
mYM 180 m XY 180 96 84
6.) m X C W m XCW m XW 84
circumference of a circle – the ___________
distance
around the circle.
r
C d
or C 2 r
d
Circles that lie in the same plane and have
concentric circles
the same center are ___________________.
A car has a turning radius of 16.1 feet. 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?
To find the radius of the inner circle, subtract 4.7 ft from the
turning radius.
circumference of outer circle: C 2 r 2 (16.1) 32.2
radius of the inner circle: 1 6 .1 4 .7 1 1 .4
circumference of inner circle: C 2 r 2 (11.4) 22.8
The difference of the two distances: 3 2 .2 2 2 .8 9 .4 2 9 .5
A tire on the turning circle travels about 29.5 ft farther than
a tire on the inner circle.
Arc Length – fraction of the_______________
circumference
of a circle.
C
B
length of B C
r
r
CD ?
2 r
360
A
Is AB
m BC
No.
C
105
105
105
D
B
m A B m C D , but AB C D
They are part of different circles
with different radii.
Congruent arcs – arcs that have the _________________
same measure
in the same circle or ___________________.
in congruent circles.
and are __________________
Find the length of the arcs.
C
1 .) B C
5 cm
B
m BC
60
2 r
360
60
2 (5)
360
5
m AD B 360 150 210
cm
B
3
2.) A D B
m ADB
150
A
2 r
360
210
360
18 cm
2 (18) 21 cm
D