the Parts of a Circle and Calculating Arc Length
24 September 2024
Length of arc
LO: To know the formula to calculate the
length of an arc and perform calculations
if the angle is given in radians.
Tuesday, 24 September 2024
Naming the parts of a circle
The distance around the
entire circle boundary is
called the
circumference
.
The
radius
is any line
segment joining its centre
to any point on the
circumference.
radius
circumference
The
diameter
is a line
segment passing through
the centre.
diameter
centre
Note that the
diameter
of
a circle is
twice
its
radius
Naming the parts of a circle
Tuesday, 24 September 2024
Naming the parts of a circle
A
chord
is any line
segment that joins two
points on the circle.
Therefore, a
diameter
is an example of a
chord. It is the longest
possible chord.
tangent
The line that touches the
circumference in exactly
one point is called a
tangent
or a
tangent line.
chord
centre
diameter
The point where the
tangent touches the circle
is called the
point of
contact
or
point of
tangency.
Tuesday, 24 September 2024
Naming the parts of a circle
Any chord encloses two
segments, which have
different areas.
If the segment is enclosed
by the
chord
diameter
segment
Minor
segment
Major
segment
is called
The region of a circle
enclosed by
a chord
and an arc
a
Segment
it is called
diameter
a
semicircle
semicircle
semicircle
Tuesday, 24 September 2024
Arcs and sectors
An
arc
is any continuous
part of the circumference.
arc
Tuesday, 24 September 2024
Arcs
Minor
arc
AB is the
shortest distance between
two points A and B on the
circumference of a circle.
Major arc
AB is the
longer distance around
the circumference from
A to B
Minor arc
Major arc
A
B
a
sector
is
formed.
Tuesday, 24 September 2024
Arcs and sectors
When an arc is bounded
by two
radii
arc
sector
A
sector
is the region
enclosed by two radii and
an arc.
a
sector
is
formed.
Tuesday, 24 September 2024
Arcs and sectors
When an arc is bounded
by two
radii
arc
sector
A
sector
is the region
enclosed by two radii and
an arc.
A
B
The
sector
AOC enclosed
with the smallest angle
is the
minor sector
.
Minor
sector
The
sector
AOC enclosed
with the largest angle
is
the
major sector
.
Major
sector
O
Length of an arc
Any central angle in a circle is a fraction of
2
So, you can calculate the length of the arc
the angle subtends as a fraction of the
circumference.
r
arc
r
A
B
Arc length =
Arc length =
r
Where r is the radius and
is the central angle
measured in radians
Length of an arc
arc
8 cm
A
B
=
r =
Arc length =
r
8 cm
Arc length =
8
⨯
Arc length =
6
A circle has radius 2.5 mm. Find the size of a
central angle subtended by an arc of length 9 mm.
Arc length =
r
9 =
2.5
Another way of writing angles in radians is 3.6
c
where the
c
stands for
circular measure
Area of a sector
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info@mathssupport.org
For more resources visit our website
A circle's components include its center, radius, diameter, circumference, chords, tangents, and segments. Arcs are parts of the circumference, with minor and major arcs distinguished by their lengths. Sectors are regions enclosed by radii and arcs. Learn about these key concepts and how to calculate arc length using radians.
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Presentation Transcript
24 September 2024 Length of arc LO: To know the formula to calculate the length of an arc and perform calculations if the angle is given in radians. www.mathssupport.org www.mathssupport.org
Naming the parts of a circle A circle is a set of points equidistant from a fixed Naming the parts of a circle point called the centre. The distance around the entire circle boundary is called the circumference. The radius is any line segment joining its centre to any point on the circumference. The diameter is a line segment passing through the centre. Note that the diameter of a circle is twice its radius radius centre circumference Tuesday, 24 September 2024 www.mathssupport.org www.mathssupport.org
Naming the parts of a circle A chord is any line segment that joins two points on the circle. Therefore, a diameter is an example of a chord. It is the longest possible chord. The line that touches the circumference in exactly one point is called a tangent or a tangent line. The point where the tangent touches the circle is called the point of contact or point of tangency. centre Tuesday, 24 September 2024 www.mathssupport.org www.mathssupport.org
Naming the parts of a circle The region of a circle enclosed by a chord and an arc a Segment is called Any chord encloses two segments, which have different areas. If the segment is enclosed by the diameter asemicircle semicircle Major segment semicircle it is called Minor segment Tuesday, 24 September 2024 www.mathssupport.org www.mathssupport.org
Arcs and sectors arc An arc is any continuous part of the circumference. Tuesday, 24 September 2024 www.mathssupport.org www.mathssupport.org
Arcs B Minor arc Minorarc AB is the shortest distance between two points A and B on the circumference of a circle. Major arc AB is the longer distance around the circumference from A to B A Major arc Tuesday, 24 September 2024 www.mathssupport.org www.mathssupport.org
Arcs and sectors When an arc is bounded by two radii a sector is formed. arc A sector is the region enclosed by two radii and an arc. sector Tuesday, 24 September 2024 www.mathssupport.org www.mathssupport.org
Arcs and sectors When an arc is bounded by two radii B a sector is formed. arc Minor A sector is the region enclosed by two radii and an arc. The sector AOC enclosed with the smallest angle is the minor sector. The sector AOC enclosed with the largest angle is the major sector. A sector sector O Major sector Tuesday, 24 September 2024 www.mathssupport.org www.mathssupport.org
Length of an arc Any central angle in a circle is a fraction of 2 ? ?? So, you can calculate the length of the arc the angle subtends as a fraction of the circumference. ? Arc length = ??? ?? O Arc length = r r B r Where r is the radius and is the central angle measured in radians arc A www.mathssupport.org www.mathssupport.org
Length of an arc Find the arc length AB if the radius of the circumference is 8 cm and the angle is ?? ? B Arc length = r arc ?? ? 8 cm = 8 cm ?? ? r = O ?? ? Arc length = 8 A Arc length = 6 www.mathssupport.org www.mathssupport.org
Area of a sector A circle has radius 2.5 mm. Find the size of a central angle subtended by an arc of length 9 mm. Arc length = r 9 = 2.5 ? ?.? ? = ? = ?.? ??? Another way of writing angles in radians is 3.6c where the c stands for circular measure www.mathssupport.org www.mathssupport.org
Thank you for using resources from A close up of a cage Description automatically generated For more resources visit our website https://www.mathssupport.org If you have a special request, drop us an email info@mathssupport.org www.mathssupport.org www.mathssupport.org
