# 9.3: Arcs in Circles

**At Grade**Created by: CK-12

**Practice**Arcs in Circles

What if the Ferris wheel below had equally spaced seats, such that the central angle were

If the radius of this Ferris wheel is 25 ft., how far apart are two adjacent seats? Round your answer to the nearest tenth. *The shortest distance between two points is a straight line.* .

### Arcs in Circles

A **central angle** is the angle formed by two radii of the circle with its vertex at the center of the circle. In the picture below, the central angle would be **arcs** (an **arc** is a section of the circle). In this case the arcs are

If

**Semicircle:**An arc that measures180∘ .

**Minor Arc:**An arc that is less than180∘ .

**Major Arc:**An arc that is greater than180∘ .use 3 letters to label a major arc.*Always*

Two arcs are **congruent** if their central angles are congruent. The measure of the arc formed by two adjacent arcs is the sum of the measures of the two arcs (**Arc Addition Postulate**). An arc can be measured in degrees or in a linear measure (cm, ft, etc.). In this chapter we will use degree measure. ** The measure of the minor arc is the same as the measure of the central angle** that corresponds to it. The measure of the major arc equals to

#### Measuring Arcs

Find

#### Identifying and Measuring Minor Arcs

Find the measures of the minor arcs in

Because

#### Using the Arc Addition Postulate

Find the measures of the indicated arcs in

Use the Arc Addition Postulate.

a)

b)

c)

#### Ferris Wheel Problem Revisited

Because the seats are

The total distance apart is 8.6 feet.

### Examples

#### Example 1

List the congruent arcs in

#### Example 2

Are the blue arcs congruent? Explain why or why not.

a)

b)

The two arcs have the same measure, but are not congruent because the circles have different radii.

#### Example 3

Find the value of

The sum of the measure of the arcs is

### Review

Determine if the arcs below are a minor arc, major arc, or semicircle of

ABˆ ABDˆ BCEˆ CAEˆ ABCˆ EABˆ - Are there any congruent arcs? If so, list them.
- If
mBCˆ=48∘ , findmCDˆ . - Using #8, find
mCAEˆ .

Determine if the blue arcs are congruent. If so, state why.

Find the measure of the indicated arcs or central angles in

DEˆ DCˆ ∠GAB FGˆ EDBˆ ∠EAB DCFˆ DBEˆ

** Algebra Connection** Find the measure of

- What can you conclude about
⨀A and⨀B ?

### Review (Answers)

To view the Review answers, open this PDF file and look for section 9.3.

### Notes/Highlights Having trouble? Report an issue.

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arc

A single section of the circle, that describes a particular angle.central angle

An angle formed by two radii and whose vertex is at the center of the circle.major arc

An arc that is greater than .minor arc

An arc that is less than .semicircle

An arc that measures .Arc Addition Postulate

Arc addition postulate states that the measure of the arc formed by two adjacent arcs is the sum of the measures of the two arcs.Diameter

Diameter is the measure of the distance across the center of a circle. The diameter is equal to twice the measure of the radius.### Image Attributions

Here you'll learn the properties of arcs and central angles of circles and how to apply them.

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