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CIRCLE
Prepared by : Pang Kai Yun, Sam Wei Yin,
Ng Huoy Miin, Trace Gew Yee,
Liew Poh Ka, Chong Jia Yi
CIRCLE
A circle is a plain figure enclosed by a curved line, every point on which is equidistant from a point within, called the centre.
DEFINITION
Circumference - The circumference of a circle is the perimeter
Diameter - The diameter of a circle is longest distance across a circle.
Radius - The radius of a circle is the distance from the center of the circle to the outside edge.
CIRCUMFERENCE
C = 2πrC = πd * Where π = 3.142
EXAMPLE (CIRCUMFERENCE)
C = πd = 3.142 x 6 cm = 18.85 cmC = 2πr = 2 x 3.142 x 4 cm = 25.14 cm
AREA OF CIRCLE
* Where π = 3.142A=π r2
EXAMPLE 1 (AREA OF CIRCLE)
= 3.142 x = 3.142 x 36 = 113.11 c
EXAMPLE 2 (AREA OF CIRCLE)
= 3.142 x = 3.142 x 16 = 50.27 c = 4cm
ARC
A portion of the circumference of a circle.
ARC LENGTH (DEGREE)
= 2r* A circle is
EXAMPLE 1 (ARC LENGTH)
= 2r = x 2 x 3.142 x 12 = x 75.41 = 9.43 cm
RADIAN
The angle made by taking the radius and wrapping it along the edge of the circle.
FROM RADIAN TO DEGREEDegree = x Radians
Radians = x DegreeFROM DEGREE TO RADIAN
EXAMPLE (FROM RADIAN TO DEGREE)
1. = x = 2. = x = 3. = x =
EXAMPLE (FROM DEGREE TO RADIAN)
1. = x =
3. = x = 2. = x =
ARC LENGTH (RADIAN)
= r θ* Where θ is radians
EXAMPLE 2 (ARC LENGTH)
= r θ = 4.16 cm x 2.5 rad = 10.4 cm
EXAMPLE 3 (ARC LENGTH)
= r θ = 10 cm x rad = 7.86 cm = r θ = 25 cm x 0.8 rad = 20 cm
SECTORA sector is the part of a circle enclosed by two radii of a circle and their intercepted arc.
AREA OF SECTOR (DEGREE)
= = A = By propotion,
EXAMPLE 1 (AREA OF SECTOR)
Area = = x 3.142 x = x 3.142 x = 14.14 c
AREA OF SECTOR (RADIAN)
= = A = A = θ
By propotion,
EXAMPLE 2 (AREA OF SECTOR)
Area5 cm
O
1.4 rad
22
1r
2
2
5.17
4.152
1
cm
SEGMENTThe segment of a circle is the region bounded by a chord and the arc subtended by the chord.
AREA OF SEGMENT
22
1r sin
2
1 2r
)sin(2
1 2 r
* Where θ is radians
EXAMPLE (AREA OF SEGMENT)
Solution:(i) = 8 cm= r θ 8 = r θ 8 = 6 θ θ = 1.333 radiansÐ AOB = 1.333 radians
The above diagram shows a sector of a circle, with centre O and a radius 6 cm. The length of the arc AB is 8 cm. Find(i) Ð AOB(ii) the area of the shaded segment.(ii) the area of the shaded segment (θ - sin θ) (1.333 - sin 1.333) (36)(1.333 – 0.927) 6.498 c
CHORDChord of a circle is a line segment whose ends lie on the circle.
GIVEN THE RADIUS AND CENTRAL ANGLE
Chord length = 2r sin
EXAMPLE 1
Chord length = 2r sin = 2(6) sin = 12 x sin 45 = 8.49 cm
GIVEN THE RADIUS AND DISTANCE TO CENTER
This is a simple application of Pythagoras' Theorem.
Chord length =
EXAMPLE 2
Find the chord of the circle where the radius measurement is about 8 cm that is 6 units from the middle.
Solution:Chord length = = = = = 10.58 cm
SEMICIRCLE
PERIMETER OF A SEMICIRCLE Remember that the perimeter is the
distance round the outside. A semicircle has two edges. One is half of a circumference and the other is a diameter
So, the formula for the perimeter of a semicircle is: Perimeter = πr + 2r
EXAMPLE (PERIMETER)
Perimeter = πr + 2r = (3.142)+ 8 = 20.56 cm
AREA OF A SEMICIRCLE
A semicircle is just half of a circle. To find the area of a semicircle we just take half of the area of a circle.
So, the formula for the area of a semicircle is: Area =
EXAMPLE (AREA)
Area 25.14 c
SUMMARY
THANK YOU !
