Inscribed Angles

1
Section 11-3

• Inscribed Angles

2
Terms

• Inscribed Angle
• Intercepted Arc

A
Inscribed Angle
B
Intercepted Arc
C
3
Theorem 11-9 Inscribed Angle Theorem

• The measure of an inscribed angle is half the
  measure of the intercepted arc.

A
mltB ½m AC
B
C
4
Using Inscribed Angle Theorem

• Find x

X ½ AC X ½ 110 X 55
A
110
X
B
C
5
Corollaries to the Inscribed Angle Theorem

• Two inscribed angles that intercept the same arc
  are congruent.
• An angle inscribed in a semicircle is a right
  angle.
• The opposite angles of a quadrilateral inscribed
  in a circle are supplementary.

6
Using corollaries

• Find x and y

70 ½ x 140x y ½(140) Y70
x
70
y
7
Using corollaries

• Find w, x, y, and z

Y½(65 120) Y92.5 XY 180 X 92.5 180 X
87.5 W½(30 120) W75 W Z 180 75 Z
180 Z105
65
w
x
120
y
z
30
8
Theorem 11-10

• The measure of an angle formed by a tangent and a
  chord is half the measure of the intercepted arc.

A
mltB ½m BDA
D
C
B
Note BC must be a tangent!
9
Apply theorem 11-10

• Find mltABC

m AB 2 ( 50)100 mltABC ½ m AB mltABC
½(100) mltABC 50
A
C
B
50
10
Apply it all

• Find each variable

x100 y180-10080 z½(80)40 r180-50-4090 s½(8
0)40
z
50
x
y
r
s
11
Homework

• Page 601
• 1-3, 6-20even, 24, 51-53