Introduction to Circles
Lesson 9.2
Find the circumference and
area of this circle.
Diameter
Radius
7in.
C=2

r

C = 14  in.
C = 2(7)
Leave in terms of
otherwise stated
A=

r2
 
A = 49 in2
A = 72
 unless

Symbol for a circle
Named with a letter

P

C

 D


An arc is made up of
two points on a circle
and all points of the
circle needed to
connect those two
points by a single path.
The red portion of the circle is called arc
CD. CD symbol

P
The measure of an arc is
equivalent to the number of
degrees it occupies. A complete
circle has 360 degrees.
The length of an arc is a fraction of
a circle’s circumference, so it is
expressed in linear units, such as
feet, centimeters, or inches.
y-axis
Find the measure and
the length of AB.
A(6,0)
x-axis
Since the arc is one fourth
of the
1
circle, its measure is 4 (360), or 90.
B (0,-6)
The arc’s length (l) can be expressed as

a part of the circle’s circumference.
d
=
 12
= 3  or 

1
4

=
1
4

l
90
= 360 C
9.42 units
(0,6)
90º
(6,0)
A sector of a circle is a region
bounded by two radii and an arc
of the circle. The figure at the
left shows sector CAT of  A.

Find the area of the sector CAT.
Since we know that CT has a measure of 90º, we
can calculate the area of the sector CAT as a
fraction of the area of  A .

Area of sector CAT =
90
(area
360
= ( 1 62)
=9

A)

 u or 28.27 u
4


of
2
2
A chord is a line segment
joining two points on a circle.
B
A diameter is a chord that
passes through the center of
the circle.
A
C
An inscribed angle is an angle
whose vertex is on a circle and
whose sides are determined by
two chords of the circle
AB and AC are chords, and <BAC is an inscribed angle.
<BAC is said to intercept BC.
(An intercepted arc is an arc whose
endpoints are on the sides of an angle and whose other points all lie within the
angle. Although <BAC intercepts only one arc, in Chapter 10 you will deal with
some angles that intercept two arcs of a circle.)
Reflection Review:
y
H’ (-4,9)
 H (4,9)
T(10,2)


Reflect point H over the y-axis to H’.
Find the slope of TH’.
Slope = -7/14 = -1/2

x