Introduction to Circles

1
Introduction to Circles

• Lesson 9.2

2
Find the circumference and area of this
circle. Leave in terms of unless otherwise
stated
Diameter
Radius
7in.
C 2 r C 2(7) C 14 in.
A r2 A 72 A 49 in2
3
Symbol for a circle Named with a letter P
P
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.
C
D
The red portion of the circle is called arc CD.
CD symbol
4
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 circles
circumference, so it is expressed in linear
units, such as feet, centimeters, or inches.
5
y-axis
Find the measure and the length of AB.
A(6,0)
x-axis
Since the arc is one fourth of the circle, its
measure is (360), or 90.
B (0,-6)
The arcs length (l) can be expressed as a part
of the circles circumference.
l

C
d


12
3 or 9.42 units
6
(0,6)
90º
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.
(6,0)
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 (area of A)
( 62) 9 u2 or 28.27 u2
7
A chord is a line segment joining two points on a
circle. A diameter is a chord that passes through
the center of the circle. An inscribed angle is
an angle whose vertex is on a circle and whose
sides are determined by two chords of the circle
B
A
C
AB and AC are chords, and ltBAC is an inscribed
angle.
ltBAC 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 ltBAC intercepts only one
arc, in Chapter 10 you will deal with some angles
that intercept two arcs of a circle.)
8
Reflection Review
y
H (-4,9)
H (4,9)
T(10,2)
x
Reflect point H over the y-axis to H. Find the
slope of TH.
Slope -7/14 -1/2