CIRCLES9.6

- Angle whose vertex is the center.

- Segment or distance from center to circle.

- Segment that connects one point on circle to another.

Circle -The set of infinite points equidistant from

a center point.A

O

X

M

OAO - Center

- Radius

XM- Chord

- Chord that passesthrough the center.

XY - Diameter

Y

C

XOA - Central Angle

2(RADIUS) = DIAMETER2R=D

CIRCUMFERENCE OF A CIRCLE IS THE OUTSIDE PERIMETER

CIRCUMFERENCE FORMULAS

WHAT IS PI ( ) ?

MARCH 14

Relationship Between Diameter and Circumference

- Two easiest things to measure on a circle.

Silver DollardiameterCircumference C:d Ratio of

3.8 cm 12.0 cm3.82

12.0 3.1413...

12.0 cm 37.7 cm12.037.73.1416...

Compact Disc

Table Top

200 cm 628.3 cm200

628.33.1415...

Relationship Between Diameter and Circumference

Silver Dollar

Compact Disc

Table Top

C:d Ratio of

3.8212.0 3.14136...

12.037.73.1416...

200628.33.1415...

Regardless of the sizeof the circle, the ratioof the circumference to the diameter remainsconstant.

dC

dC

3.141592...

(d) (d)

Circumference of a Circle

d

C

Find the circumference of a circle with a diameter of 7 inches.

C d

Use 3.14.

C d C 7 C (3.14) 7 C 21.98 inches

Find the missing information.

radius diameter Circumference

5 in. d = 2r

10 in.

4 m 8 m

Use 3.14.

C d C (3.14) 10 C 31.4 in.C d C (3.14) 8 C 25.12 mC 62.8 ft.C d

62.8 3.14 d 3.14 3.14

62.8 d3.14

20 ft. d

r 10 ft.

MAKING CIRCLE GRAPHS

Central Angle- an angle whose vertex is in the center of the circle

There are 360 degrees in a circle

Use proportions to find the degree of each central angle

%

100 360

x

EXAMPLE: FIND THE MEASURE OF THE CENTRAL ANGLES

Swimming

Soccer

27

100 360

x

97.2x

30

100 360

x

108x

YOUR TURNFIND THE CENTRAL ANGLE OF …

Track

Tennis

20

100 360

x

72

12

100 360

x

43.2

HOMEWORK

Page 472 (1-18) all You may use a calculator but you need to still

show work Use 3.14 for pi Round to three decimal places if need be