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


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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?. 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?


Chapter 11

Circles


C

11.1 Parts of a Circle

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

equidistant

C

center

Symbol:


11.1 Parts of a Circle

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

center

P


CHORD: a segment whose ________ are on the circle

endpoints


Diameter

DIAMETER: distance ______ the circle through its ______

across

P

center

Also known as the longest chord.


What is the relationship between the diameter and the radius of a circle?

r =

OR

D =

½ D

2 r


D = ?

24

32

12

r = ?

16

r = ?

4.5

6

D = ?

12

9


Q

R

P

S

T

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


Same center but different radii

Concentric Circles


Q

R

P

S

T

Ex. 4

14


Q

R

P

S

T

Ex. 5

18


Arcs and

Section 11.2

Central Angles


Central Angle : 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

Semicircle: An Arc that equals 180°

E

D

P

F

To name: use 3 letters


Measure of an arc is equal to the measure of the central angle


THINGS TO KNOW AND REMEMBER ALWAYS

A circle has 360 degrees

A semicircle has 180 degrees

Vertical Angles are Equal


Find the measure of an the following arcs.

EB is a diameter.

m AB

m ACB

m AE

A

E

96

=

96

Q

=

264

B

C

=

84


m DAB =

Tell me the measure of the following arcs.

240

D

A

140

m BCA =

260

R

40

100

80

C

B


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