a

bc

d ab = cd

part part = part part

9

2

6x

x = 3

3

2

12

x

x = 8

3

26

x

x = 1

Example 1:

Example 2: Find x

8

12

2x

3x

2x 3x = 12 8

6x2 = 96x2 = 16

x = 4

E A B

C

D

EA • EB = EC • EDoutside whole = outside whole

EA

B

C

D

713

4

x

7 (7 + 13) 4(4 + x)=

Example 3:

140 = 16 + 4x124 = 4x

x = 31

E

A

B

CD 8

5

6

x

6 (6 + 8) 5(5 + x)=

Example 4:

84 = 25 + 5x59 = 5x

x = 11.8

Tangent Segment

Secant Segment

External

Segment

Notice that on the tangent

segment, the outside

is the whole!

E

A

B C

EA2 = EB • ECoutside whole = outside whole

E

A

B C

24

12 x

outside whole = outside whole 242 = 12 (12 + x)576 = 144 + 12x x = 36

Example 5:

E

A

B

C

15

5

x

outside whole = outside whole x2 = 5 (5 + 15)

x2 = 100 x = 10

Example 6:

What you should know by now…

Given two chords, USE

Given two secants OR a tangent and a secant, USE

part part = part part

outside whole = outside whole