CIRCLESEverything you wanted to know and then some!!

Parts of a CircleCircle – set of all points _________ from a given point called the _____ of the circle.

C

Symbol:

equidistant

center

C

Secant Line

A secant line intersects the circle at exactly TWO points.

TANGENT: a LINE that intersects the circle exactly ONE

time

Name the term that best describes the line.

Secant

Radius

DiameterChordTangent

If a line (segment or ray) is tangent to a circle, then it is perpendicular to the radius drawn to the point of tangency.

Point of Tangenc

y

More Pythagorean Theorem type problems! Yeah!!

a2 + b2 = c2

x = 1592 + 122 = x2

R

S

T

TSRS If two segments from

the same exterior point are tangent to a circle, then they are

congruent.

Party hat problems!

A

C

B152 x

x14

15x

P

A

BC

Central Angle : An Angle whose vertex is at the center of the

circleMinor ArcMajor Arc

Less than 180°

More than 180°

ABACBTo name:

use 2 letters

To name: use 3 letters

APB is a Central Angle

measure of an arc = measure of central angleA

B

C

Q 96

m AB

m ACBm AE

E

=

==

96°

264°84°

Tell me the measure of the following arcs.

80100

40

140A

B

C

DR

m DAB =m BCA =

240

260

Inscribed Angle: An angle whose vertex is on the circle and whose sides are chords of the circle

INSCRIBEDANGLE

INTERCEPTED

ARC

2 ArcdIntercepteAngleInscribed

160

80

To find the measure of an inscribed angle…

120

x

What do we call this type of angle?What is the value of x?

y

What do we call this type of angle?How do we solve for y?The measure of the inscribed angle is HALF the measure of the

inscribed arc!!

Examples3. If m JK = 80, find m JMK.

M

Q

K

S

J

4. If m MKS = 56, find m MS.

40

112

Case I: Vertex is ON the circle

ANGLE = ARC2

ANGLE

ARCANGLE

ARC

Ex. 2 Find m1.

84°

1

m1 = 42

Case II: Vertex is inside the circleA

B

CD

ANGLE = (ARC + ARC)2

ANGLE

ARC

ARC

Ex. 4 Find m1. AB

CD

1

93°

113°

m1 = 103

Case III: Vertex is outside the circleA

B

C

D

ANGLE = (Large ARC Small ARC)2

ANGLE

LARGE ARC

small

ARC

ANGLELARGE

ARC

small ARC sm

all ARCLARGE

ARC

ANGL

E

A

B

Ex. 7 Find mAB.

27°

70°

mAB = 16

1

Ex. 8 Find m1.26

0°

m1 = 80

a

bc

d ab = cd

part part = part part

9

2

6xx = 3

32

12

x

x = 83

26

x

x = 1

Ex: 1 Solve for x.

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 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.