Holt CA Course 1

9-3 Circles

MG3.1 Identify and construct basic elements of geometric figures (e.g., altitudes, midpoints, diagonals, angle bisectors, and perpendicular bisectors; central angles, radii, diameters, and chords of circles) by using a compass and straightedge.

California Standards

Holt CA Course 1

9-3 Circles

A circle is the set of all points in a plane that are the same distance from a given point, called the center of a circle. This distance is called the radius of the circle.

A circle is named by its center. For example, if point A is the center of a circle, then the name of the circle is circle A. There are special names for the different parts of a circle.

Holt CA Course 1

9-3 Circles

ArcPart of a circle named by its endpoints

RadiusLine segment whose endpoints are the centerof a circle and any point on the circle

Diameter

Line segment that passesthrough the center of a circle, and whose endpoints lie on the circle

ChordLine segment whose endpoints are any twopoints on a circle

Holt CA Course 1

9-3 Circles

Name the parts of circle M.

Additional Example 1: Identifying Parts of Circles

O

N

P

Q

R

M

A. radii:

B. diameters:

C. chords:

MN, MR, MQ, MO

NR, QO

NR, QO, QN, NP

Radii is the plural form of radius. Reading Math

Holt CA Course 1

9-3 Circles

Name the parts of circle M.

Check It Out! Example 1

A. radii:

B. diameters:

C. chords:

GB, GA, GF, GD

BF, AD

A

B

C

D

EF

G

H

AH, AB, CE,

BF, AD

Holt CA Course 1

9-3 Circles

)

Central angle

SectorA central angle of a circleis an angle formed by tworadii. A sector of a circle is the part of the circleenclosed by two radii and anarc connecting them.

The sum of the measures of allof the central angles in a circleis 360°. We say that there are 360° in a circle.

Holt CA Course 1

9-3 Circles

The circle graph shows the results of a survey about favorite types of muffins. Find the central angle measure of the sector that shows the percent of people whose favorite type of muffin is blueberry.

Additional Example 2: Problem Solving Application

Holt CA Course 1

9-3 Circles

11 Understand the Problem

Additional Example 2 Continued

List the important information:

• The percent of people whose favorite muffin is blueberry is 40%.

Holt CA Course 1

9-3 Circles

22 Make a Plan

The central angle measure of the sector that represents this group is 40% of the angle measure of the whole circle. The angle measure of a circle is 360°. Since the sector is 40% of the circle graph, the central angle is 40% of the 360° in the circle.

40% of 360° = 0.40 · 360°

Solve33

0.40 · 360° = 144° Multiply.

The central angle of the sector measures 144°.

Additional Example 2 Continued

Holt CA Course 1

9-3 Circles

Look Back44

The 40% sector is less than half the graph, and 144° is less than half of 360°. Since 144° is close to 180°, the answer is reasonable.

Additional Example 2 Continued

Holt CA Course 1

9-3 Circles

The circle graph shows the results of a survey about favorite types of muffins. Find the central angle measure of the sector that shows the percent of people whose favorite type of muffin is banana nut.

Check It Out! Example 2

Holt CA Course 1

9-3 Circles

11 Understand the Problem

List the important information:

• The percent of people whose favorite muffin is banana nut is 35%.

Check It Out! Example 2 Continued

Holt CA Course 1

9-3 Circles

22 Make a Plan

The central angle measure of the sector that represents this group is 35% of the angle measure of the whole circle. The angle measure of a circle is 360°. Since the sector is 35% of the circle graph, the central angle measure is 35% of the 360° in the circle.

35% of 360° = 0.35 · 360°

Solve33

0.35 · 360° = 126° Multiply.

The central angle of the sector measures 126°.

Check It Out! Example 2 Continued

Holt CA Course 1

9-3 Circles

Look Back44

The 35% sector is about one-third the graph, and 126° is about one-third of 360°. Since 126° is close to 120°, the answer is reasonable.

Check It Out! Example 2 Continued