WARM UP

70

80

z

120

x

y

90

y

x

z

100

1)2)

Section 9.6

Other Angles

OTHER Angles in a Circle• You know two types of Angles:

– Central angles– Inscribed angles

• FOUR OTHER TYPES

1) Two Chords

2) Two Secants

3) Two Tangents

4) One Secant and One Tangent

#1 TWO CHORDS

1) Draw a circle2) Draw two intersecting chords3) Label one chord with T and O4) Label the other chord Y and M5) Label point where they intersect as K

How do you find the measure of an interior angle of a circle?

112

m mTY mMO

T

O

M

Y

K1

Find the m∠1 and m∠2.

56

97

472

1o

o

o m∠2 = ½(56 + 97)

m∠2 = ½(153)

m∠2 = 76.5o

m∠1 = 180 – 76.5

m∠1 = 103.5o

#2 TWO SECANTS1) Draw a circle2) Plot point W outside of

the circle3) Draw two secant lines

starting at point W going through the circle.

4) Label the intercepting arcs x and y.

How do we find the measures of these arcs? 1

12

m x y

W

xo

yo

1

Find the m∠1.

12392 o

o

m∠1 = ½(92 – 23)

m∠1 = ½(69)

m∠1 = 34.5o

#3 TWO TANGENTS

1) Draw a circle

2) Plot point J outside of the circle

3) Draw two tangent lines starting at point J

4) Label the intercepting arcs x and y

How do we find the measures of these arcs?

12

2m x y

J

xo

yo

2

Find the missing measure

x 102 78ooo

78o = ½(x – 102)

78(2) = x – 102

156 = x – 102

258 = x

#4 A SECANT and A TANGENT

1) Draw a circle2) Plot point F outside of the

circle3) Draw one tangent and

one secant from F 4) Label the intercepting

arcs x and y.

How do we find the measures of these arcs?

132

m x y

F

xo

yo

3

Find the missing measures

3765x

oo

o

37o = ½(x – 65)

37(2) = x – 65

74 = x – 65

139o = x

Problemas!

• Page 358-359 • Classroom Exercises #1-9

•DRAW the DIAGRAMS