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# The circle, the circumference and their elements. The central angle

## 1. The circle, the circumference and their elements. The central angle.

“БІЛІМ-Инновация”Халықаралық қоғамдық қоры

CHAPTER no 4

GEOMETRY

The circle, the circumference and

their elements. The central angle.

4-term

Week no 1

2019-2020

## 2.

The circle, the circumference and their elements. TheCHAPTER no 4 central angle.

You will be able to:

• know the definitions of a circumference and a circle,

and their elements (center, radius, diameter, chord);

• know and apply definition and properties of central

angle;

• prove and apply the perpendicular diameter-chord

theorem;

• know the definition of a locus.

Geometry

4-term

Week no 1

2019-2020

2

## 3.

The circle, the circumference and their elements. TheCHAPTER no 4 central angle.

Key Terms:

circle – шеңбер - окружность

center - центр

radius - радиус

diameter - диаметр

chord - хорда

central angle – центрлік бұрыш – цетральный угол

locus – нүктелердің геометриялық орны –

геометрическое место тосек

Geometry

4-term

Week no 1

2019-2020

3

## 4.

The circle, the circumference and their elements. TheCHAPTER no 4 central angle.

You can see many circular or ring-shaped geometric figures all

around you.

Geometry

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Week no 1

2019-2020

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## 5.

The circle, the circumference and their elements. TheCHAPTER no 4 central angle.

It is easy to recognize a circle, but

how can we define it as a shape?

Let us look at a geometric

definition.

Note:

The word ‘circle’ is

derived from the latin

word circus, which

means ‘ring’ or

‘racecourse’.

Geometry

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Week no 1

2019-2020

5

## 6.

The circle, the circumference and their elements. TheCHAPTER no 4 central angle.

Definition:

A CIRCLE is the set of all the points in a

plane that are at the same distance from a

fixed point in the plane and the fixed point

is called the center of the circle.

Geometry

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Week no 1

2019-2020

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## 7.

The circle, the circumference and their elements. TheCHAPTER no 4 central angle.

Definition:

The RADIUS is the distance from the center

The DIAMETER goes straight across the circle,

through the center

The CHORD is a line segment which

joins two different points on a circle.

Geometry

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Week no 1

2019-2020

7

## 8.

The circle, the circumference and their elements. TheCHAPTER no 4 central angle.

Definition:

Circumference is the distance once around the circle

Circumference = π × Diameter

Geometry

4-term

Week no 1

2019-2020

8

## 9.

The circle, the circumference and their elements. TheCHAPTER no 4 central angle.

Example:

You walk around a circle which has a

diameter of 100m, how far have you

walked?

Solution:

Distance walked = Circumference = π × 100m

= 314m (to the nearest m)

Geometry

4-term

Week no 1

2019-2020

9

## 10.

The circle, the circumference and their elements. TheCHAPTER no 4 central angle.

Example:

The length of the diameter of a circle is 20 cm and

the radius is 2x – 4. Find x.

Solution:

Diameter = 2 ⋅ Radius

d=2⋅r

20 = 2 ⋅ (2x – 4)

2x – 4 = 10

2x = 14

x = 7 cm

Geometry

4-term

Week no 1

2019-2020

10

## 11.

The circle, the circumference and their elements. TheCHAPTER no 4 central angle.

Definition:

An ARC of a circle consists of two points on the circle and the

unbroken part of the circle between these two points.

NOTE:

Any two points of a circle divide the

circle into two arcs. If the arcs are

unequal, the smaller arc is called the

minor arc and the larger arc is called

the major arc.

Geometry

4-term

Week no 1

2019-2020

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## 12.

The circle, the circumference and their elements. TheCHAPTER no 4 central angle.

Definition:

A CENTRAL ANGLE of the circle is an angle

whose vertex is at the center of a circle.

NOTE:

The measure of a minor arc

is equal to the measure of

its central angle.

Geometry

4-term

Week no 1

2019-2020

Central Angle = Minor Arc

∠APB = A͡B

12

## 13.

The circle, the circumference and their elements. TheCHAPTER no 4 central angle.

Examples:

Find the measure of the indicated central angle of each

circle.

Geometry

4-term

Week no 1

2019-2020

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## 14.

The circle, the circumference and their elements. TheCHAPTER no 4 central angle.

Theorem:

If a diameter or radius is perpendicular to a chord,

then it bisects the chord and its arc.

Example:

In the figure, if [OH] ⊥ [AB] then

|AH| = |HB|.

Geometry

4-term

Week no 1

2019-2020

## 15.

The circle, the circumference and their elements. TheCHAPTER no 4 central angle.

Example:

A chord of length 10 cm is 12 cm away from the center of a

circle. Find the length of the radius.

Solution:

Look at the figure.

In ΔAHO, r² = 5² + 12²

r² = 25 + 144

r² = 169

r = 13 cm.

Geometry

4-term

Week no 1

2019-2020

## 16.

The circle, the circumference and their elements. TheCHAPTER no 4 central angle.

Definition:

LOCUS is the set of all points that share a property. This usually results in a curve

or surface.

Example:

A Circle is "the locus of points on a plane that are a certain distance from a central

point".

Geometry

4-term

Week no 1

2019-2020

## 17.

The circle, the circumference and their elements. TheCHAPTER no 4 central angle.

Activity:

Put a pin in a board, put a loop of string around it,

and insert a pencil into the loop. Keep the string

stretched and draw the circle!

Geometry

4-term

Week no 1

2019-2020

## 18.

The circle, the circumference and their elements. TheCHAPTER no 4 central angle.

Resources :

https://www.mathsisfun.com/geometry/circle.html

https://www.onlinemathlearning.com/diameter-of-circle.html

https://www.mathemania.com/lesson/the-definition-and-basics/

https://www.khanacademy.org/math/basic-geo/basic-geo-area-and-perimeter/areacircumference-circle/v/parts-of-a-circle

https://www.mathplanet.com/education/geometry/circles/basic-information-about-circles

https://www.brainfuse.com/jsp/alc/resource.jsp?s=gre&c=37818&cc=108830

Geometry

4-term

Week no 1

2019-2020