10.6 and
10.7
Circles and
Sectors
Words…
Circle: the set of all points equidistant from a given point called the
center (name a circle by its center)
radius
P
Central angle – an angle whose
vertex is the center of the circle.
diameter
Arcs…
Semicircle – an arc that is half the circle
Minor arc – smaller than a
semicircle
Major arc – greater than a
semicircle
Identify…
Minor arcs:
Semicircles:
Major arcs that
contain point A:
Measures…
Name and find the measure of a minor arc:
Name and find the measure of a major arc:
Arc Length…
THEOREM 10.9: Circumference of a Circle
The circumference of a circle is  times the diameter.
C  d or C  2r
THEOREM 10.10: Arc Length
marc AB 
Length of arc AB 
 2r
360
Arc Length…
Find the length of each arc shown in red. Leave your answer in
terms of  .
Area…
THEOREM 10.11: Area of a Circle
The area of a circle is the product of  and the square
of the radius.
A  r
2
THEOREM 10.12: Area of a Sector of a Circle
marc AB  2
Area of sector AOB 
 r
360
Area…
Find the area of a circle
with a 12-inch diameter.
Find the area of sector
ZOM. Leave your answer
in terms of  .
Recap…
Use the circle to the right to answer the following.
1) Find mABC
2) Find mAOC
3) Find the area of circle O.
4) Find the length of ABC
5) Find the area of sector AOC
10.6 and
10.7
Circles and
Sectors
HW:
p. 570
#9-31 odd,
34-39
p. 577
#1-4, 7-12
QUIZ TMW