Transcript Angles Inside a Circle

Other Angles
Lesson 9.6
Geometry Honors
Objective: Student will be able to solve
problems involving angles formed by
chords, secants, and tangents.
Page 357
Lesson Focus
This lesson studies the relationships among
the arcs of a circle and the angles formed by
chords, secants, and tangents.
Theorem 9-9
The measure of an angle formed by two chords that intersect
inside a circle is equal to half the sum of the measures of the
intercepted arcs.
A
mAOD 

1
»
m»
AD  mBC
2

D
O
B
C
Theorem 9-10
The measure of an angle formed by two
secants, two tangents, or a secant and a
tangent drawn from a point outside a circle is
equal to half the difference of the measures of
the intercepted arcs.
Theorem 9-10: Case 1
Two secants
mA 

1 »
»
mED  mBC
2

E
B
A
C
D
Theorem 9-10: Case 2
Two tangents
B
mA 

1 ¼
»
mBDC  mBC
2

D
A
C
Theorem 9-10: Case 3
a secant and a tangent
mA 

1 ¼
»
mBED  mBC
2

E
B
A
C
D
InClass Exercises
Problem Set Classroom Exercises, p. 358: # 1 – 9.
Written Exercises 9.6, p.359: # 1 – 24
Homework Exercises
Handout 9-6