Transcript CHAPTER 9 CIRCLES - Castro Valley High School

CHAPTER 9
CIRCLES
9.6
OTHER ANGLES
THEOREM 9-9
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
C
m
1 = ½ (mAB + mCD)
1
B
D
THEOREM 9-10
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
1. Two Secants
x°
y°
m
1 = ½ (x – y)
1
THEOREM 9-10
2. Two Tangents
2
x°
y°
m
2 = ½ (x – y)
THEOREM 9-10
3. A Secant and a Tangent
y°
x°
m
3 = ½ (x – y)
3
UT is tangent to the circle.
Complete.
U
30°
110°
1. 40
2. m TVS=
2. 105
3. m
3. 75
W
V
R
1. mWT=
T
S
100°
RVS=
4. mRS=
4. 110
AB is tangent to circle O; AF is a diameter;
mAG = 100; mCE = 30; mEF = 25
D
B
6
C
30°
E
25°
8
A
O
3
7
100°
2
1
G
5
4
F
1.
2.
3.
4.
5.
6.
7.
8.
m
m
m
m
m
m
m
m
1
2
3
4
5
6
7
8
1.
2.
3.
4.
5.
6.
7.
8.
80
100
27.5
117.5
62.5
35
90
62.5
CLASSWORK/HOMEWORK
9-6 ASSIGNMENT
• Pgs. 358-359, Classroom Exercises 1-9
• Pgs. 359-360, Written Exercises 1-10, 1220 even