Download 12.3 Notes (Inscribed Angles)

12-3 Inscribed Angle
An inscribed angle is an angle whose vertex is on a
circle and whose sides contain chords of the circle.
mFG = ________
m∠FOD = ________
70°
F
D
m∠FDG = ________
O
m∠FGD = ________
m∠DFG = ________
G
If an angle is inscribed in a circle, then its measure is
half the measure of its intercepted arc.
150°
Q
A
50°
B
R
O
S
C
m∠ABC = ________
m∠QRS = ________
P
160°
90°
m∠PRQ = ___________
m∠PQR = ___________
R
m∠QPR = ___________
Q
If two inscribed angles of a circle intersect the same
arc, then the angles are congruent.
A
∠ABD ≅ ___________
B
C
D
If the vertices of a polygon lie on a circle, the polygon is
inscribed and the circle is circumscribed.
120°
m∠A = ________
m∠B = ________
A
90°
B
m∠C = ________
70°
m∠D = ________
C
80°
D
If a quadrilateral is inscribed in a circle, then the
opposite angles are supplementary.
Q
90°
110°
R
S
T
m∠S = __________
m∠T = __________
m∠XYZ = ___________
O
Z
X
∠XYZ is a(n) __________ angle.
Y
If the arc that an inscribed angle intercepts is a
semicircle, then the angle is a right angle.
x __________
A
B
80°
x°
D
C
If two arcs are cut by parallel chords, then the arcs
are congruent.
x°
80°
85°
x°
y°
z°
60°
y°
110°
1. x = __________
2. x = __________
y = __________
y = __________
z = __________
x°
K
100°
L
80°
O
M
3. x = __________
4. KM = 10
mKM = 60
length of the radius =
5. x = __________
5x-5
6x+5
y = __________
4x+25
y
m∠A = __________
B
A
6. AB = BC = CD = DE = EF = FA
C
F
E
D
7. Find the measure of each angle.
m∠VRW =
R
W
m∠RTV =
m∠RVW =
140°
60°
O
m∠TRV =
m∠RVT =
m∠RWV =
m∠ROT =
V
T
80°
8. GF is tangent to
O
D
AD || BC
C
m∠AOE =
80°
m∠DOE =
m∠DAE =
m∠CAD =
m∠EAF =
m∠ACB =
m∠GAC =
O
100°
B
G
E
A
F