learning target: i can find the measures of central angles and arcs. i can find circumference and...

Learning Target:

I can find the measures of central angles and arcs.

I can find circumference and arc length.

A CIRCLE is the set of all points equidistant from a given point

called the center.

Circle P

P

A CENTRAL ANGLE of a circle is an angle with its vertex at the

center of the circle.

Central angle

An arc is a piece of a circle’s circumference.

Arc

One type of arc, a semicircle, is half of a circle.

P

A

C Semicircle ABC

m ABC = 180

B

A minor arc is smaller than a semicircle. A major arc is greater than a semicircle.

AC

D

minor arcs

EO

AC

CE

DE

AD

AC

D

semicircles

EO

ACE

CAD

AC

D

major arcs containing point A

EO

ACD

CEA

DEA

ADC

AC

D

central angles containing D

EO

AOD

DOE

AC

D

radius

EO

AO

DO

EO

CO

AC

D

diameter

EO

AE

DC

The measure of a central angle is equal to its

intercepted arc.

53o

53o

O P

R

m ROP = 53°

m RP = 53°

Find the measure of each arc.

1. BC = 32 °

2. BD = 90 °

3. ABC = 180 °

4. AB = 148 °

1. BC =

2. BD =

3. ABC =

4. AB =

The circumference of a circle is the distance around the

outside of the circle.

or

The arc length of a circle is the length of an arc; a piece of the

circumference.

or

Concentric Circles are circles within the same plane (coplanar) that have

the same center.