Lesson 8-1: Circle Terminology 1

Lesson 9-1

Circle Terminology

Lesson 8-1: Circle Terminology 2

Circle DefinitionCircle : The set of points coplanar points equidistant from a

given point.

The given point is called the CENTER of the circle.

The distance from the center to the circle is called the RADIUS.

Center

Radius

Lesson 8-1: Circle Terminology 3

DefinitionsChord : The segment whose endpoints lie on the circle.

Chord

Diameter : A chord that contains the center of the circle.

DiameterSecant : A line that contains a chord.Secant

Tangent : A line in the plane of the circle that intersects the circle in exactly one point.

Point of Tangency :

The point where the tangent line intersects the circle.

Tangent

Lesson 8-1: Circle Terminology 4

Example: In the following figure identify the chords, radii, and diameters.

, ,AB BF CEChords:

Radii:

Diameter:

O

D

A

B

F

C

EFB

Lesson 8-1: Circle Terminology 5

Circles that have congruent radii.

22

Circles that lie in the same plane and have the same center.

Definitions

Concentric circles :

Congruent Circles :

Lesson 8-1: Circle Terminology 6

Polygons

A polygon inside the circle whose vertices lie on the circle.

Inscribed Polygon:

Circumscribed Polygon :

A polygon whose sides are tangent to a circle.

Lesson 8-1: Circle Terminology 7

ARCSThe part or portion on the circle from some point B to C

is called an arc.

A

B

CBC

Arcs :

Semicircle: An arc that is equal to 180°.

Example:

OA

B

CExample: ABC

Lesson 8-1: Circle Terminology 8

Minor Arc & Major Arc

AB

Minor Arc : A minor arc is an arc that is less than 180°

A minor arc is named using its endpoints with an “arc” above.

A

B

Example:

Major Arc: A major arc is an arc that is greater than 180°.

A major arc is named using its endpoints along with another point on the arc (in order).A

B

CExample: ABC

O

Lesson 8-1: Circle Terminology 9

Example: ARCSIdentify a minor arc, a major arc, and a semicircle, given that

is a diameter. , , ,DE EC CF DF

A

C

D

E

F

Minor Arc:

CD

Major Arc: , , ,CEF EDC DFE FCD

Semicircle: , , ,CED CFD EDF ECF

Lesson 8-2: Formulas 10

Lesson 8-2

Formulas•Circumference•Arc Length•Area•Sector

Lesson 8-2: Formulas 11

Central AngleA central angle is an angle whose vertex is at the center of the circle.

mBC

The measure of a minor arc is the measure of its central angle.

The measure of a major arc is 360 minus the measure of its central angle.

The arc measure is written as

mBC m BAC

Central Angle

A

B

CBAC

Lesson 8-2: Formulas 12

CIRCUMFERENCE:Circumference is the distance around the circle.

2C r C d2d r

Formula: Or

Example: Find the circumference of the following circle.

3 cm

2 (3)C6C

18.85C cm

where

Lesson 8-2: Formulas 13

Arc LengthArc length is the distance around an arc.

236072

2 4360

ar

The circumference multiplied by the ratio of the center angle and 360°.

Formula:

Example:

2 cm

72 B

C

A

0.8 2.51 cm

Arc Length

Lesson 8-2: Formulas 14

Area of a CircleArea of a circle is the number of unit squares that can fit into a circle.

2(3)A

2A r

Example: Find the area of the following circle.

3 cm

9A 228.27A cm

Formula:

Lesson 8-2: Formulas 15

Area of a SectorArea of a sector is the area of a section of the circle.

B C

A

The area multiplied by the ratio of the center angle and 360°

Formula:

Example:

3 cmB C

A

65°

21.625 5.11 cm

Sector 2

2

36065

3360

ar