Warm-up

1. Name a segment tangent to

circle A.

2. What is the

3. If BD = 36, find BC.

4. If AC = 10 and BD = 24, find AB.

5. If AD = 7 and BD = 24, find BE.

A

D

E

C

Bm ACB ?

Unit Question: What happens when line

segments intersect a circle?Today’s Question:

How do you find the measure of angles formed by secant and tangent lines?

Secant Anglesand

Secant – Tangent Angles

measure of an arc = measure of central angle

A

B

C

Q 97

m AB

m ACB

m AE

E

=

=

=

97°

263°

83°

Case I: Vertex is ON the circle

ANGLE = ARC

2ANGLE

ARCANGLE

ARC

A secant line intersects the circle at exactly two points.

Ex. 1 Find m1. AB

C124°

1

m<1 = 620

Ex. 2 Find m1.

84°

1

m<1 = 420

Remember, a straight angle is 180 degrees!

Ex. 3 Find m1.108°

1

m<1 = 1260

Case II: Vertex is inside the circleA

B

C

D

ANGLE = (ARC + ARC)

2

ANGLE

ARC

ARC

Ex. 4 Find m1.A

B

CD

1

93°

113°

m<1 = 1030

Ex. 5 Find mQT.N

Q

TM

920840

mQT = 1000

Case III: Vertex is outside the circle

A

B

C

D

ANGLE = (Large ARC Small ARC)

2

ANGLE

LA

RGE

AR

C

small

ARC

ANGLELA

RG

E

AR

C

sm

all A

RC

small A

RC

LARGE

ARC

AN

GL

E

A

B

D

1

Ex. 6 Find m1.

65°

15°

m<1 = 250

A

B

Ex. 7 Find mAB.

27°

70°

m AB = 160

1

Ex. 8 Find m1.24

0°

m<1 = 600