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 radiansРAOB = 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 !