Thursday, November 14th

WARM UPFind

1. Z

2. M<U

Homework Answers

Do you know your formulas?!!

P

A

B

Case I: Central Angle: Vertex is AT the center

Central Angle is equal to the ______________

Arc = ___________ the inscribed angle

Angle =

CASE IV. Vertex is OUTSIDE circle

ANGLE

LARGE ARC

small

ARC

small

ARC small

ARC

ANGLE

ANGLE

LARGE ARC

LARGE ARC

Angle =

Tune: If You’re Happy and You Know It

• If the vertex is ON the circle half the arc. <clap, clap>

• If the vertex is INside the circle half the sum. <clap, clap>

• But if the vertex is OUTside, then you’re in for a ride, cause it’s half of the difference anyway. <clap, clap>

Today’s Goal

Secants and tangentsSide Lengths

Segment Lengths in Circles

Find the lengths of segments of chords

Find the lengths of segments of tangents and secants

a

bc

d ab = cd

part part = part part

9

2

6x

x = 3

Solve for x.

Find the length of DB.

8

12 2

x3x

x = 4DB = 20

A

B

C

D

Find the length of each chord.

x = 8AC = 13DB = 14

x5

x - 4

10

A

B

C

D

E A B

C

D

EA • EB = EC • EDoutside whole = outside whole

EA

B

C

D

7 13

4

x

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

Ex: 3 Solve for x.

140 = 16 + 4x124 = 4x

x = 31

E

A

B

CD 8

5

6

x

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

Ex: 4 Solve for x.

84 = 25 + 5x59 = 5x x = 11.8

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

Ex: 5 Solve for x.

E

A

B

C15

5

x

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

x2 = 100x = 10

Ex: 6

Practice Problems