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By: Bagoes Darmawan, S.Pd


Definiton of Cicle The Element of The Circle Radius and Diameter Circumference Area of The Circle Sector And Arc From The Circle www.mawan24.wordpress.com


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 lingkaran”)

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THE ELEMENT OF CIRCLE Consider the Following Figure! C E O is the center of the circle arc D sector OA is radii (r) of the circle sector chord A O B AB is diameter (d) of the circle DO is apothem apothem The area i.e on the AOC, COE, and OEB is sector The area on the chord and arc is segment Back to menu www.mawan24.wordpress.com


Example: Notice the following figure! A B Determine: a. Radius b. Diameter C c. Arc d. Chord D F E e. 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 Back to menu www.mawan24.wordpress.com


Copyright2011 by Bagoes Darmawanthe circle

J

Determine: a. Radius b. Diameter c. Arc d. Chord e. 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. 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 or Circumference = 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: A = π × r2

Or, in terms of the Diameter:

A = (π/4) × D2

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Example 1. Given a circle

The circle has diameter 14 cm. What is its circumference Answer: Use the formula C = ď °.d, where d is the diameter d = 14 cm and ď ° =22/7 So, circumference is 44 cm. Back to menu www.mawan24.wordpress.com


2.

Given a circle!

What is the area of the circle? Answer Use the formula A = ď °.r2, where r is the radius d = 14, r = 7, and ď ° = 22/7

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2.

Given a circle! The circumference and the area of the circle is.... C

3.5cm

D E

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Copyright2011 by Bagoes Darmawan-the circle


if the length of ab is 20 cm and ď ° = 3.14, determine a. sector of aob? b. circumference c. area? a d. the length of

o

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Copyright2011 by Bagoes Darmawan-the circle

b


3. Notice the following figure! A

B C

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

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Consider the following figure A

B

O

Determine: a. The area of circle b. The circumference c. The sector of AOB d. The area of triangle AOB e. 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. On B The area of sector 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 60째 a. Sector AOB B b. Arc AB

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3. Notice the following figure! A

B 60째

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

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Introduction of circle