An Arc goes
from one point
on the
circumference
to another.
Circle Properties
Minor
Arc
Major
Arc
An Arc is a fraction
of the circumference
A sector is a fraction of a
circle. Two radii and an arc
Finding the length of an arc
Arc = fraction of the circumference
To get circumference need d
O
3 cm
Write down r= and d= work out values
Part
Fraction
Total
Angle in Sector
360 °
(Complete Turn)
r = 3 cm
A
AOB =50 °
B
Arc AB =
Arc AB =
d = 6 cm
of
50 °
360 °
d
x 3.14 x 6
Area of an Arc
Length
of Arc =
Of Circumference
Area of
Sector =
Area of
Sector =
Of Area of Circle
Angle in
Sector
360°
r=5
of
A=
110°
Area
=
Sector
360°
π r²
x 3.14 x 5 x 5
A = 78.5 ÷ 360 x 110
xπxrxr
B
AOB=110°
Of Complete Turn
To find Area of a sector
110°
O 5 cm
Of Area of Circle
Angle at
centre =
Area=
A
A = 23.986 ….
A= 24.0 cm3 ( 1dp )
O
Calculate Angle of a sector
12 cm
D
Angle =
160.8 cm²
C
Find
of 360°
Need information from
sector and whole circle
COD
Know Area of Sector ……. part
Can find Area of Circle ……. total
Angle =
160.8
3.14 x 12 x 12
for
fraction
of 360°
π r²
Angle = 360 ÷ 452.16 x 160.8 = 128.025….
COD = 128° ( 1dp )
Tangent
A tangent is a line which meets a circle at
exactly one point.
If you draw a diameter from the point of
contact the angle formed is a right angle
A tangent to a circle if perpendicular to
the radius from its point of contact
36°
20°
a
To solve angle problems draw the
diagram a step at a time
The dashed line is a radius.
It meets the tangent a 90°.
Draw tangent and radius.
Complete the RAT. Mark in 20° angle. Angles add to 180°
Repeat for the other RAT.
Extend the right hand triangle. Angles on a straight line add up to 180°
36°
20°
90°
a
20°
20°
36°
90°
90°
70°
70°
54°
20°
36°
54°
90°
70 + 54 +
70°
56°
= 180