7.1B – Circumference and Arc Length

R.4.G.5 Investigate and use the properties of angles ( central tangents , and and inscribed secants involving circles ) arcs , chords to solve problems ,

Circle Vocabulary

• • • Center: The middle…duh… Radius: A line segment drawn from the center to any point on the circle Diameter: A line segment drawn across a circle that passes through the center (twice the radius)

2

Circumference

• Circumference is: The distance around the outside of the circle • Circumference formulas: C = 2 π r C = π d

3

Examples

Find the circumference of the circle: 8 m 21 m

4

Arcs

• • Definition: An arc is an unbroken part of a circle Minor Arc: Shortest path between two points Name of minor Arc: Measure of minor Arc:

R

45 o

T S 5

Arcs (cont.)

• Major Arc: The longest path between two points

R

Name of major arc: Measure of major arc: 45 o

T S 6

Arc Length

• • An arc’s length is based on the Circumference of the circle and the Measure of its arc.

Formula for Arc Length: Arc Length = or…

7

Example

Find the length of arc AB. Leave your answer in terms of π.

A

120 ° 6 in

arclength



m

360 

C

B C 8

Example

Find the length of arc ACB. Leave your answer in terms of π.

A

120 ° 6 in

arclength



m

360 

C

C B 9

Now You Try…

Find the length of arc MP. Leave your answer in terms of π.

45 ° M P

10 cm

L 10

Now You Try…

Find the length of arc MLP. Leave your answer in terms of π.

45 ° M P

10 cm

L 11