11-3 Inscribed Angles

1
11-3Inscribed Angles

• Objective To find the measure of an inscribed
  angle.

2
Central Angle
Definition
An angle whose vertex lies on the center of the
circle.
NOT A Central Angle (of a circle)
Central Angle (of a circle)
Central Angle (of a circle)
3
Central Angle Theorem
The measure of a center angle is equal to the
measure of the intercepted arc.
Center Angle
Intercepted Arc
Give is the diameter, find the value of x
and y and z in the figure.
Example
4
Vocabulary
A
Intercepted Arc
Inscribed Angle
C
B
5
Theorem 11-9 (Inscribed Angle Theorem)

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

A
B
C
6
Example 1 Using the Inscribed Angle Theorem

P
ao
60o
T
Q
30o
S
bo
60o
R
7
Example 2 Find the value of x and y in the
figure.
8
Corollaries to the Inscribed Angle Theorem

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

9
An angle inscribed in a semicircle is a right
angle.
P
180?
90?
S
R
10
Example 3 Using Corollaries to Find Angle Theorem

• Find the diagram at the right, find the measure
  of each numbered angle.

120o
1
60o
2
4
80o
3
100o
11
Example 4 Find the value of x and y.
85 x 180 x 95 80 y 180 y 100
yo
xo
85o
80o
12
Theorem 11-10

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

B
B
D
D
C
C
13
Example 5 Using Theorem 11-10

• Find x and y.

J
90o
Q
35o
xo
yo
L
K
14
Assignment
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