Circle
Form 4 : Chapter Four
Software, Geometer’s Sketchpad, is required.
Basic Terms
Centre
Circumference
Radius
Diameter
Basic Terms
For any two points
A and B,
Major Arc
arcs be
Can the twointo two parts -------
the circle is divided
equal ? B
A
Minor Arc
Basic Terms
When AB is the diameter,
A two arcs are equal.
Semi-circle
B
Basic Terms
For any two points
the region enclosed
A and B,
Major Sector by radii OA, OB
O
and the arc AB is
called a ……
B
Sector
Minor Sector
A
Basic Terms
For any two points
A and B,
the line joining A, B
is called a ……
CHORD B
A
Basic Terms
A chord also divides
the circle into two
regions ---
Major Segment
CHORD B
Minor Segment
A
Basic Terms
D
P
We can have different
Minimum = 0 chords.
C
Maximum = length of
diameter
B
Minimum length ?
A Q
Maximum length ?
Circumference
Review
Centre
E
Radius
Diameter
D B
O
C Chord
A
Arc
Review
Sector
Chord
O Segment
Chord
P Distance of a point
P from a line
= perpendicular
N distance PN
If P is the centre, the
line is a chord, ……...
Chord If
(1) AB is a chord
(2) ON AB
Then
O
B AN = BN
Nfrom centre chord
A
Reason : line
bisects chord
Chord (example)
If AB = 12,
A OF = 8,
OF AB,
O
F find radius.
B
If AB = 12, AF = 6
OF = 8, (line from centre
OF AB, chord bisects chord)
radius2 = AF2 + OF2
A (Pythagoras thm)
O radius = (62 + 82)
F = 10
B
Chord If
(1) AB is a chord
(2) M is mid-point
Then
O
BOM AB
Mjoining centre to mid-
A
Reason : line
pt of chord chord
Chord (example)
B
If AN = NB = 4,
N radius = 5,
A O find
distance of
centre from
AB
If AN = NB = 4, ANO = 90°
radius = 5, (line joining
B centre to mid-pt
of chord chord)
N
Distance
A O
= ON
= (radius2 - AN2)
= (52 - 42) = 3
Chord
O
B
A
Any perpendicular bisector
of chord passes through the
centre.
Chord C
O
D
Any perpendicular bisector
of chord passes through the
centre.
Chord (example)
B Let A, B and C be 3
points on a circle.
How to find the
A centre and draw
the circle ?
C
Chord (example)
B Joint AB and BC,
their perpendicular
bisectors intersect
O at the centre, O.
A Take OA as radius
to draw the circle.
C C0101
AB,CD are
Chord chords
B OM,ON are
D perpendiculars
M
A If AB CD ,
O N
then
C
OM ON
Chord If AB = CD,
B then …...
M OM = ON
A
O
C
N D
Reason : equal chords, equidistant
from centre
If OM = 3 ,
Chord
B
ON = 2
D then
M
A AB = CD ?
O N
C
Chord If, OM = ON
B then …...
M
AB = CD
A
O
C
N D
Reason : chords equidistant from
centre are equal
line from centre chord bisects
chord
line joining centre to mid-pt of
chord chord
equal chords, equidistant from
centre
chords equidistant from centre
are equal
END