introduction of circle

By:Bagoes Darmawan, S.Pd

Definiton of CicleDefiniton of Cicle

The Element of The CircleThe Element of The Circle

Radius and DiameterRadius and Diameter

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Radius and DiameterRadius and Diameter

CircumferenceCircumference

Area of The CircleArea of The Circle

Sector And Arc From The CircleSector And Arc From The Circle

Definition

The set of all points on a plane that are a fixed distance from a center. (mathisfun.com)

(“Himpunan titik-titik yang berjarak sama dari pusat pusat

lingkaran”)

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THE ELEMENT OF CIRCLE

Consider the Following Figure!

C E O is the center of the circle

D OA is radii (r) of the circle

A O B AB is diameter (d) of the circle

DO is apothem

arc

chord sector

sector

DO is apothem

The area i.e on the AOC, COE, and

OEB is sector

The area on the chord and arc is

segment

apothem

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Example:

Notice the following figure!

A B

C

D F E

Answer:

Determine:a. Radiusb. Diameterc. Arcd. Chorde. Sector

Answer:

a. AC, CE, BC, and CD are radius of the circle

b. BD and AE are diameter of the circle

c. AD, AB, BE, and DE are arc of the circle

d. AD and DE are chord of the circle

e. ACD, ACB,BCE, and DCE are sector of the circle

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J

Copyright�2011 by Bagoes Darmawan-the circle

Determine:a. Radiusb. Diameterc. Arcd. Chorde. Sectore. Sector

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RADIUS AND DIAMETER

The Radius is the distance from the center to the edge.

The Diameter starts at one side of the circle, goes through the center and ends on the other side.ends on the other side.

So the Diameter is twice the Radius:

Diameter = 2 × Radius

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CIRCUMFERENCE The Circumference is the distance around the edge of the

circle. Circumference = π × Diameter And so these are also true: Circumference / Diameter = π Circumference can determine with formula Circumference can determine with formula

orCircumference = 2 × π × Radius

Circumference = π × diameter

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AREA The area of a circle is π times the Radius squared, which is

written:

Or, in terms of the Diameter:

A = π × r2

A = (π/4) × D2

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Example

1. Given a circle

The circle has diameter 14 cm. What is its circumferenceThe circle has diameter 14 cm. What is its circumference

Answer:

Use the formula C = .d, where d is the diameter

d = 14 cm and =22/7

So, circumference is 44 cm.

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2. Given a circle!

What is the area of the circle?AnswerAnswer

Use the formula A = .r2, where r is the radius

d = 14, r = 7, and = 22/7

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2. Given a circle!

The circumference and the area of the

circle is....3.5cm

CDE


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if the length of ab is 20 cmand = 3.14, determinea. sector of aob? b. circumferencec. area? a o bd. the length ofd. the length of


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3. Notice the following figure!

A B

C

When The length of diameter is 28 cm, the area of sector ABC is ... cm2ABC is ... cm2

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Consider the following figureA

Determine:a. The area of circle

B O b. The circumferencec. The sector of AOBc. The sector of AOBd. The area of triangle AOBe. The area of segment AB

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SECTOR AND ARC OF THE CIRCLE

Consider the following figure!A From the above picture, we know that

The circle has sector, the sector is AOB. O B The area of sector

determined by formula

n

determined by formula

And then, arc of AB determined by formula:

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Example:

Consider the following figure!

A If the length of OA is 10 cm,

determine the length of

O a. Sector AOB60°O a. Sector AOB

B b. Arc AB


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60°

3. Notice the following figure!

A B

C

When The length of diameter is 28 cm, the area of sector When The length of diameter is 28 cm, the area of sector ABC is ... cm2


introduction of circle

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