Transcript Terminology of a Circle

Circles are all around us. They are products of both our
natural environment and of our artificial environment.
Circles are part of the astronomically big and the infinitesimally small.
Model of an Atom
Whirlpool Galaxy
Throughout history circles have been
considered to have a certain
perfection and harmony to them.
Even today there is a certain mystic
and wonder around the circle.
CIRCLE TERMINOLOGY
To study
circles, it is
important that
we are familiar
with the
terminology of
circles.
A circle is defined by a group of points all being the same
distance from a point identified as the centre, O.
A circle defines three distinct groups of points:
- the points on the circle.
- the points inside the circle (including centre).
- the points outside the circle.
O
Radius – a line segment drawn from the centre to any
point on the circle. OA
Chord – a line segment between any two points on a circle
BC
Note: A line segment is a line
which has a beginning and an end
(the endpoints) and consequently it
has a defined length and can be
measured.
C
B
O
Radius
A
When naming line segments, the
two endpoints are always used in
either order.
Diameter – a chord that passes through the centre of a
circle. DE
E
O
D
Arc – a series of points on the circumference between
two given points on the circumference.
Arcs are classified into two groups:
Minor arcs – arcs that make up less than one half of
the circumference.
Major arcs – arcs that make up one half or more of
the circumference.
When naming arcs,
A
Minors arcs can be named using
E
2 letters representing the
M
endpoints (although the 3 letter
designation can also be used as
with major arcs).
AB
B
F
D
or AMB
3 letters must be used to name a
major arc (two letters to identify
the ends of the arc and a third
letter between them to identify any
other point on the arc).
DFE or EFD not
DE
Line – a series of points along a straight line that
go infinitely in both directions.
To name a line you can use any two points on the line
Secant – a straight line that intersects a circle at
two points. LN
or NL or MN
Tangent – a straight line that intersects a circle at
one point.
AB or BA
or BT
or AT
T
B
Point of Tangency –
A
point of intersection
which is shared by
the tangent line and
the circle. T
N
M
L
DISTINCTION BETWEEN CHORDS AND ARCS
Just as Criminals Steal Apples
so do Chords Subtend Arcs
However it does NOT make sense to say that:
A
Apples Steal Criminals
In the same way it doesn’t make
sense to say that:
Arcs Subtend Chords
therefore AB subtends AB
but AB does not subtend AB
B
When referring to chords, radii, arcs, diameters,
secants and tangents, it is important to use the
correct symbol above the letter names.
- used for line segments (chords, radii or diameters)
- used for lines (tangents or secants)
- used for arcs (minor or major)
AB
AB
AB
B
The 3 geometric items above are all
referring to different sets of points.
AB
- refers to all points on the
circumference between A and B
AB
- refers to all points on a
straight line between A and B
AB
- refers to all points on a straight
line between and beyond A and B
A
Angles are also elements of a circle that are often
referred to. An angle is a rotational separation
between two rays. The angles of a circle are classified
into 4 categories based on the location of their
vertices:
(1) Central angle – vertex at the centre
(2) Interior angle – vertex inside the circle
(3) Exterior angle – vertex outside the circle
(4) Inscribed angle – vertex on the circumference
AOB is a central angle because its vertex, O, is at the
centre of the circle. Incidentally, it is also an interior
angle because its vertex is inside the circle. However, just
as we don’t refer to a square as a rectangle (eventhough it
is) so do we not refer to a central angle as an interior
angle.
A
-formed by two radii
AOB intersects AB
O
B
DEF is an interior angle because its vertex, E, is inside of
the circle.
-formed by two chords
DEF intersects DF and its vertical angle, GEH
intersects GH
D
O
E
H
G
F
IKM, IKN and MKN are all exterior angles because
their vertex, K, is outside of the circle.
-formed by two secants, two tangents or a secant and a tangent
IKM intersects IM and JL
I
IKN intersects IN
and JN
MKN intersects MN
and LN
O
J
K
L
N
M
QPT, QPR and RPT are all inscribed angles because
their vertex, P, is on the circumference of the circle.
-formed by two secants or a secant and a tangent
QPT intersects QRP
QPR intersects QR
RPT intersects RSP
Q
P
T
O
S
R