WARM UP1) A secant and a tangent to a circle intersect in

a 42 degree angle. The two arcs of the circle intercepted by the secant and tangent have measures in a 7:3 ratio. Find the measure of the third arc.

2) Find the measures of angle 1 and 2.

2

62

16051

1

20

30

90

7

45

6

2

381

109

D

E

CA

B Z

130

90

9 10

1 83

2

654

7

90

30

20

K

J

GH

I

Z

25o

90o60o

30o

90o 60o

65o

55o

125o

90o

35o

Section 9.7

Circles and Lengths of Segments

Interior SegmentsDraw the following.

ac = bd

d c

ba

Find the value of x.

2 x -2

x

12

x(x - 2) = 12(2)

x2 – 2x = 24

It’s a quadratic so set it = 0

x2 – 2x – 24 = 0

(x – 6)(x + 4) = 0

x – 6 = 0 and x + 4 = 0x = 6 and x = - 4

TWO SECANTS

Draw the following.

kg = jh

k

j

h

g

Find the measure of x.

x

39

10

10x = 12(3)

10x = 36

x = 3.6

One Secant and One Tangent

Draw the following.

r2 = stt

s

r

x

4

10

Find the missing measure

2 40x

40x

2 10x

x2 = 10(4)

x2 = 40

4 10x

Practice Problems• Page 363 - 364

• Classroom Exercises #1 - 6

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