9.1 – 9.2 Exploring Circles

Geometry

Objectives/Assignment

• Find the circumference of a circle• Use circumference to solve other

problems

Definitions

• Circle – is the set of all points in a plane that are equidistance from a given point on that plane

• Center- “The given“ point on the plane• Radius- A segment that has one endpoint

at the center of a circle and the other end point on the circle itself

Definitions• Chord – A segment that has both

endpoint on a circle• Diameter - Is a chord that contains

the center of the circle.• Circumference - The distance around

the circle

Finding circumference

• The circumference of a circle is the distance around the circle.

• For all circles, the ratio of the circumference to the diameter is the same.

• This ratio is known as or pi.

Circumference of a Circle

• The circumference C of a circle is C = d or C = 2r, where d is the diameter of the circle and r is the radius of the circle.

diameter d

Example #1

Example # 2

Find • a. the circumference of a circle with

radius 6 centimeters • b. the radius of a circle with

circumference 31 meters.

Solution:C = 2r = 2 • • 6 = 12 37.70

So, the circumference is about 37.70 cm.

C = 2r31 = 2r31 = r

4.93 rSo, the radius is

about 4.93 cm.

2

a.

b.

Practice

Take Notes

Take Notes

C = 2 *3.14* 7 = 44D = 2 * r = 14

C = 2 *3.14* 16.2 = 101.8R = D / 2 = 16.2

Take Notes

116.5 = 2 * 3.14 * r116.5 = 6.28 * r R = 18.6

D = 2 * r = 18.6 * 2 = 37.1

Take Notes

C = 2 * 3.14 * 12C = 6.28 * 12 C = 75.4

D = 2 * r = 2* 12 = 24

Take Notes

C = 2 * 3.14 * 14 C = 43.9

D² = 10² + 24² D² = 100+ 576D = 26C = 26* 3.14 = 81.7

D² = 5² + 5² D² = 25 +25D = 7.1C = 7.1* 3.14 = 22.2

And… Sum Of Central Angles

Practice

4x + 35 = 9x +530 = 5xX = 6

AE = = 4 * 6 + 35 = 59

ED = = 9 * 6 + 5 = 59

62 =59- 59- 180 , 180 = 3ے + 2ے + 1ے

4ے = 3ے ( vertical) = 62

121 =62 + 59 = 3ے + 1ے

121 = 62+ 59 = 2ے + 4ے

242 = 4ے + 3ے + 2ے + 1ے

= = 118

4ے + 3ے + 2ے + 1ے - 360 ,

360-59-59-62-62 = 118

DC = 62 = 3ے

180 = 3ے + 2ے + 1ے