Download Day66Inscribed Angles

What angle relationships are
created from the special segments
inside and outside of circles?
Agenda:
– Warmup – finish packet from Friday
– Notes/Practice Inscribed Angles
– TEST Friday
Day 3
Definition – An inscribed angle is an
angle whose vertex is on a circle
and whose sides contain chords of
the circle.
A
B
O
C
AC is the
intercepted
arc
Day 3
ABC is an inscribed angle of circle O.
Theorem: The measure of an
inscribed angle is equal to half the
measure of its intercepted arc.
Day 3
Ex1.
Ex2.
A
G
C
T
D
O
If mCAT = 70°,
If mDG = 62°,
then mCT = 140°.
then mDOG = 31°.
Central Angles vs. Inscribed Angles
Central Angle:
-Vertex at the Center of
the Circle
Inscribed Angle:
-Vertex on the Circle
-Angle formed by two radii -Angle formed by two chords
-Measure is equal to the
intercepted arc
A
-Measure is half the measure
of the intercepted arc
G
If mAQB D
= 120°, then
Q
mAB = 120 °
B
Q is the center of the circle.
C
F
If mDCF = 85°,
then mDGF = 170°
Example
G
150°
Example
A
110°
C
100°
75°
110°
B
D
55°
Q 110°
F
Q is the center of the circle.
mABC = 75°, mAB =
100°
Find mGF and mGDF.
Find: mAC, mBC
mAC = 150°
mGF = 110°
mBC = 110°
mGDF = 55°
Corollary 2: An angle inscribed in a
semicircle is a right angle.
Given: PG is a diameter of circle I.
mPIG = 180°
mPLG = 180°
P
therefore, mPQG = 90°.
Day 3
L
I
G
Q
Day 3
Check for Understanding
1.
2.
100
A
y°
z°
x°
30
50
O
B
z°
x°
60
65
55
y°
x = 30°
y = 25°
z = 15°
AB is a
diameter
x = 130°
y = 120°
z = 110°
O is the center of the circle. Find the values for x, y, and z.
Day 3
Check for Understanding
3.
4.
z°
B
x°
O
A
x = 90°
y°
AB is a
diameter
z°
x°
y°
70
55
55
140
x = 70°
y = 90°
y = 110°
z = 90°
z = 110°
O is the center of the circle. Find the values for x, y, and z.
Day 3
Check for Understanding
5.
76°
6.
38°
O
x°
y°
A
x°
B
y°
50°
90°
x = 38°
x = 25°
y = 38°
y = 65°
AB is a
diameter
Day 3
Check for Understanding
7.
8.
40°
150°
40°
75° x°
y°
y°
x°
80°
x =75°
x = 70°
y = 65°
y = 70°