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