Circumference of a Circles

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Circumference of a Circles

• REVIEW

2
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
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NAME EACH OF THE FOLLOWING
1. A Circle
C
B
D
AnswerCircle O
O
A
E
4
NAME EACH OF THE FOLLOWING
2. All radii
C
B
D
AnswerAO, BO, CO DO, EO
O
A
E
5
NAME EACH OF THE FOLLOWING
3. All Diameters
C
B
D
AnswerAD and BE,
O
A
E
6
NAME EACH OF THE FOLLOWING
4. A secant
C
B
D
AnswerBC
O
A
E
k
7
NAME EACH OF THE FOLLOWING
5. A Tangent
C
B
D
AnswerEK
O
A
E
k
8
NAME EACH OF THE FOLLOWING
5. Point of Tangency
C
B
D
AnswerE
O
A
E
k
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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
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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
11
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?
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(No Transcript)
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AREA of a Circles
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INVESTIGATION
IS IT POSSIBLE TO COMPLETELY FILLED THE CIRCLE
WITH A SQUARE REGIONS?
NO.
R
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INVESTIGATION
HOW IS THE AREA OF THE CIRCLE MEASURED?
In terms of its RADIUS.
R
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INVESTIGATION
TAKE A CIRCULAR PIECE OF PAPER CUT INTO 16 EQUAL
PIECES AND REARRANGE THESE PIECES
WHAT IS THE NEW FIGURE FORMED?
r
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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 orb ?r
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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 orb ?r
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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
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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
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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
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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
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TRUE OR FALSE

• 1. All radii of a circle are congruent.

• ANSWER
• TRUE

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TRUE OR FALSE

• 2. All radii have the same measure.

• ANSWER
• FALSE

25
TRUE OR FALSE

• 3. A secant contains a chord.

• ANSWER
• TRUE

26
TRUE OR FALSE

• 4. A chord is not a diameter.

• ANSWER
• TRUE

27
TRUE OR FALSE

• 5. A diameter is a chord.

• ANSWER
• TRUE

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AREAS OF REGULAR POLYGONS
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REGULAR POLYGONS
6 SIDES
3 SIDES
4 SIDES
5 SIDES
7 SIDES
8 SIDES
9 SIDES
10 SIDES
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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)
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NAME THE PARTS
THE CENTER
THE RADIUS
CENTRAL ANGLE
2
1
ANGLE 1 AND ANGLE 2
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NAME THE PARTS
APOTHEM
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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.
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FIND THE AREA OF A REGULAR HEXAGONS WITH A 9 cm
APOTHEM.
REMEMBEREach vertex angle regular hexagon is
equal to 120. each vertex ? S n
HINTA radius of a regular hexagon bisects the
vertex angle.
9 CM
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FIND THE AREA OF A REGULAR HEXAGONS WITH A 9 cm
APOTHEM.
SOLUTIONUse 30-60-90 ?½s 3 Multiply
both sides by 2S 6
9 CM
60
½ s
So, perimeter is equals to 36
36
FIND THE AREA OF A REGULAR HEXAGONS WITH A 9 cm
APOTHEM.
SOLUTIONA ½ap ½( 9cm)36 cm ½(
324 cm² ) 162 cm²
9 CM
60
½ s
So, perimeter is equals to 36
37
FIND THE AREA OF A REGULAR triangle with radius 4
4 CM
60
½ s