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?

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

C

Symbol:

equidistant

center

C

11.1 Parts of a Circle

P

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

center

CHORD: a segment whose ________ are on the circle

endpoints

Diameter

P

DIAMETER: distance ______ the circle through its ______

center across

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 = ?

r = ?

r = ? D = ?

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

P

Q

R

TS

diameter. a is .1 RT False

radius. a is .2 PS True

chord. a is .3 QT True

Same center but different radii

P

Q

R

TS

Ex. 4QT. find 7, QP If diameter. a is QT

14

P

Q

R

TS

Ex. 5

Find the measure of radius

PR if PR 3 and QT 5x 6.x

18

P

A

BC

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

circleMinor ArcMajor Arc

Less than 180°More than

180°ABACB

To name: use 2 letters

To name: use 3 letters

<APB is a Central Angle

P

E

F

D

Semicircle: An Arc that equals 180°

EDFTo 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.

A

B

C

Q 96m AB

m ACB

m AE

E

=

=

=

96264

84

Tell me the measure of the following arcs.

80100

40

140A

B

C

D

R

m DAB =

m BCA =

240

260