Download Circles - Northwest ISD Moodle

Circles
Definitions
Chord
a segment whose endpoints lie
on a circle
A
AB
B
Arc
an unbroken part of a circle
Minor Arc
an arc that is
less than half
of a circle
to name, use
2 points
Major Arc
an arc that is
more than
half of a
circle
to name, use
3 points
Central Angle
an angle whose vertex is at the
center of a circle
Inscribed Angle
an angle whose vertex is on a
circle and whose sides are chords
of the circle
Tangent
a line, ray, or segment that is in
the same plane as the circle, but
intersects the circle in only one
point
Secant
a line, ray, or segment that
contains a chord
Warm Up #1
Write an example of each of
the following:
A. Radius ____
B. Secant ____
C. Tangent ____
D. Chord ____
E. Diameter ____
F. Minor arc ____
G.Major arc ____
H. Central angle ____
I. Inscribed angle ____
J. Center ____
Circles
Central and Inscribed
Angles
1. The measure of an arc is the same as the measure
of its central angle.
y
x
If x = 63,
Then y = 63
y
80
x
70
x = 70
y = 360 – (80 + 70) = 210
2. The measure of an inscribed angle is equal to half
the measure of the intercepted arc.
60
z
y
x
n
z
w
40
x
115
x = 60/2 = 30
z = 115 X 2 = 230
r = 360 - 230 = 130
OR
180-115 = 65
65 X 2 = 130
160
x = 160 / 2 = 80
y = 40 X 2 = 80
z = 180 - 120 = 60
w = 60 X 2 = 120
or
w = 360 - 240 = 120
3. A tangent and a radius form a 90 degree angle.
Quadrilateral = 360
50
x
90 + 90 + 50 = 230
x = 360 – 230 = 130
4. The measure of an angle formed by secants tangents
or one of each is equal to half the difference of the
intercepted arcs.
xº
85
xº
250
15
125
110
150
X = (125-85) /2 = 20
120
xº
X = (120-15) /2 = 52.5
X = (250-110)/2 = 70
5. The measure of the angle formed by two chords is
equal to half the sum of the intercepted arcs.
xº
50
80
102
88
y
78
xº
56
X = (50+80)/2 = 65
xº
Y = (102 + 88) /2 = 95
180-95 = x = 85
(78+x)/2 = 56
(78+x) = 112
X = 34
Congruent chords =
Congruent arcs
60
x
y
45
x
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