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# Unit Question: What are the properties and characteristics of circles? - PowerPoint PPT Presentation

Unit Question: What are the properties and characteristics of circles?. Today’s Question: How does the measure of an arc compare to the measure of its central angle?. Chapter 11 Circles. C. 11.1 Parts of a Circle.

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Unit Question: What are the properties and characteristics of circles?

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Unit Question:What are the properties and characteristics of circles?

Today’s Question:

How does the measure of an arc compare to the measure of its central angle?

Circles

11.1 Parts of a Circle

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

equidistant

C

center

Symbol:

RADIUS= distance from the _____ to a point on the circle

center

P

DIAMETER: distance ______ the circle through its ______

across

P

center

Also known as the longest chord.

r =

OR

D =

½ D

2 r

D = ? of a circle?

24

32

12

r = ?

16

r = ?

4.5

6

D = ?

12

9

Q of a circle?

R

P

S

T

Use P to determine whether each statement is true or false.

Same center but different radii of a circle?

Concentric Circles

Q of a circle?

R

P

S

T

Ex. 4

14

Q of a circle?

R

P

S

T

Ex. 5

18

Arcs and of a circle?

Section 11.2

Central Angles

Central Angle of a circle? : An Angle whose vertex is at the center of the circle

ACB

AB

A

Minor Arc

Major Arc

Less than 180°

More than 180°

P

To name: use 3 letters

C

B

To name: use 2 letters

<APB is a Central Angle

EDF of a circle?

Semicircle: An Arc that equals 180°

E

D

P

F

To name: use 3 letters

A circle has 360 degrees

A semicircle has 180 degrees

Vertical Angles are Equal

EB is a diameter.

m AB

m ACB

m AE

A

E

96

=

96

Q

=

264

B

C

=

84

m DAB = angle

Tell me the measure of the following arcs.

240

D

A

140

m BCA =

260

R

40

100

80

C

B