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Circumference of a Circles

- REVIEW

NAME MY PARTS

Tangent Line which intersects the circle at

exactly one point. Point of Tangency the

point where the tangent line

and the circle intersect (C)

L

D

Secant Line which intersects the circle at

exactly two points. e.g. DL

C

M

NAME EACH OF THE FOLLOWING

1. A Circle

C

B

D

Answer Circle O

O

A

E

NAME EACH OF THE FOLLOWING

2. All radii

C

B

D

Answer AO, BO, CO DO, EO

O

A

E

NAME EACH OF THE FOLLOWING

3. All Diameters

C

B

D

Answer AD and BE,

O

A

E

NAME EACH OF THE FOLLOWING

4. A secant

C

B

D

Answer BC

O

A

E

k

NAME EACH OF THE FOLLOWING

5. A Tangent

C

B

D

Answer EK

O

A

E

k

NAME EACH OF THE FOLLOWING

5. Point of Tangency

C

B

D

Answer E

O

A

E

k

CIRCUMFERENCE

Circumference is a distance around a

circle. Circumference of a Circle is determined

by the length of a radius and the value of

pi. The formula is C 2?r or C ?d

r

P

EXAMPLE 1

WHAT IS THE CIRCUMFERENCE OF A CIRCLE IF RADIUS

IS 11 cm?

Solution C 2?r C 2?( 11 cm) C 22?cm or C

69.08 cm

R

11 cm

EXAMPLE 2

THE CIRCUMFERENCE OF A CIRCLE IS 14?cm. HOW LONG

IS THE RADIUS?

Solution C 2?r 14?cm 2?r Dividing both

sides by 2 ?. 7 cm r or r 7 cm

R

r?

(No Transcript)

AREA of a Circles

INVESTIGATION

IS IT POSSIBLE TO COMPLETELY FILLED THE CIRCLE

WITH A SQUARE REGIONS?

NO.

R

INVESTIGATION

HOW IS THE AREA OF THE CIRCLE MEASURED?

In terms of its RADIUS.

R

INVESTIGATION

TAKE A CIRCULAR PIECE OF PAPER CUT INTO 16 EQUAL

PIECES AND REARRANGE THESE PIECES

WHAT IS THE NEW FIGURE FORMED?

r

NOTICE THAT THE NEW FIGURE FORMED RESEMBLES A

PARALLELOGRAM.

The BASE is approximately equal to half the

circumference of the circular region.

- 14

- 6

- 2

- 8

- 10

- 12

- 4

h r

r

- 11

- 9

- 13

- 3

- 1

- 5

- 7

base C or b ?r

Area of 14 pieces area of the //gram bh

?r( r) ?r²

- 14

- 6

- 2

- 8

- 10

- 12

- 4

h r

r

- 11

- 9

- 13

- 3

- 1

- 5

- 7

base C or b ?r

EXAMPLE 1

WHAT IS THE AREA OF A CIRCLE IF radius IS 11 cm?

Solution A ?r ² ?( 11 cm)² A 121?cm²

or 379.94 cm²

R

11 cm

EXAMPLE 2

WHAT IS THE AREA OF A CIRCLE IF radius IS 4 cm?

Solution A ?r ² ?( 4 cm)² A 16?cm² or

50.24 cm²

R

4 cm

EXAMPLE 3

THE CIRCUMFERENCE OF A CIRCLE IS 14?cm. WHAT IS

THE AREA OF THE CIRCLE?

Solution Step 1. find r. C 2?r 14?cm

2?r Dividing both sides by 2 ?. 7 cm r or r

7 cm

Step 2. find the area A ?r ² ?( 7 cm)² A

49?cm² or 153.86 cm²

EXAMPLE 4

THE CIRCUMFERENCE OF A CIRCLE IS 10?cm. WHAT IS

THE AREA OF THE CIRCLE?

Solution Step 1. find r. C 2?r 10?cm

2?r Dividing both sides by 2 ?. 5 cm r or r

5 cm

Step 2. find the area A ?r ² ?( 5 cm)² A

25?cm² or 78.5 cm²

TRUE OR FALSE

- 1. All radii of a circle are congruent.

- ANSWER
- TRUE

TRUE OR FALSE

- 2. All radii have the same measure.

- ANSWER
- FALSE

TRUE OR FALSE

- 3. A secant contains a chord.

- ANSWER
- TRUE

TRUE OR FALSE

- 4. A chord is not a diameter.

- ANSWER
- TRUE

TRUE OR FALSE

- 5. A diameter is a chord.

- ANSWER
- TRUE

AREAS OF REGULAR POLYGONS

REGULAR POLYGONS

6 SIDES

3 SIDES

4 SIDES

5 SIDES

7 SIDES

8 SIDES

9 SIDES

10 SIDES

Given any circle, you can inscribed in it a

regular polygon of any number of sides.

The radius of a regular polygon is the distance

from the center to the vertex.

The central angle of a regular polygon is an

angle formed by two radii.

It is also true that if you are given any regular

polygon, you can circumscribe a circle about it.

This relationship between circles and regular

polygons leads us to the following definitions.

The center of a regular polygon is the center of

the circumscribed circle.

The apothem of a regular polygon is the

(perpendicular) distance from the center of the

polygon to a side.

2

1

APOTHEM( a)

NAME THE PARTS

THE CENTER

THE RADIUS

CENTRAL ANGLE

2

1

ANGLE 1 AND ANGLE 2

NAME THE PARTS

APOTHEM

AREAS OF REGULAR POLYGONS

The area of a regular polygon is equal to HALF

the product of the APOTHEM and the PERIMETER.

A ½ap where, a is the apothem and p is the

perimeter of a regular polygon.

FIND THE AREA OF A REGULAR HEXAGONS WITH A 9 cm

APOTHEM.

REMEMBER Each vertex angle regular hexagon is

equal to 120. each vertex ? S n

HINT A radius of a regular hexagon bisects the

vertex angle.

9 CM

FIND THE AREA OF A REGULAR HEXAGONS WITH A 9 cm

APOTHEM.

SOLUTION Use 30-60-90 ? ½s 3 Multiply

both sides by 2 S 6

9 CM

60

½ s

So, perimeter is equals to 36

FIND THE AREA OF A REGULAR HEXAGONS WITH A 9 cm

APOTHEM.

SOLUTION A ½ap ½( 9cm)36 cm ½(

324 cm² ) 162 cm²

9 CM

60

½ s

So, perimeter is equals to 36

FIND THE AREA OF A REGULAR triangle with radius 4

4 CM

60

½ s