GEOMETRY
Circle Terminology
Component of Geometry
•
•
•
•
•
Point (dot)
Line At least two points given
Angle  If two line intersect in a point
Plane  Something which has area
Space  something which boundary at
least by two plane
Circle
• Set of points which have same distance into
one permanent point
Same distance = radius = r
Permanent point is central point
Radius (or Radii for plural)
A
• The segment joining
the center of a circle to
a point on the circle.
O
• Example: OA
adopted from http://www.worldofteaching.com
Diameter
• A chord that passes
through the center of a
circle.
• Example: AB
• What is AO? Radius
• What is OB? Radius
• What is relation
between radius and
diameter?
d=2r
A
O
B
Chord
B
A
C
• A segment joining two
points on a circle
• Example: AB
Chord
B
C
A
Diameter is the longest chord
• A segment joining two
points on a circle
• Example: AB
• AB= diameter
• So, what is relation
between chord and
diameter?
Secant
A
• A line that intersects
the circle at exactly
two points.
C
O
• Example: AB
D
B
Secant
A
• A line that intersects
the circle at exactly
two points.
C
O
• Example: AB
D
B
Tangent
B
C
• A line that intersects a
circle at exactly one
point.
A
• Example: AB
Central Angle
A
• An angle whose vertex
is at the center of a
circle.
B
• Example: Angle ABC
C
Inscribed Angle
B
A
C
• An angle whose vertex
is on a circle and
whose sides are
determined by two
chords.
• Example: Angle ABC
Arc
• A figure consisting of
two points on a circle
and all the points on
the circle needed to
connect them by a
single path.
B
A
• Example: arc AB
What is the longest arc?
circumference
Intercepted Arc
B
• An arc that lies in the
interior of an inscribed
angle.
A
C
• Example: arc AC
Two Intercepted Arc
D
A
• Example: arc AC
arc DF
B
C
F
• If angle is inside the
circle.
Two Intercepted Arc
B
D
• If angle is outside the
circle.
E
A
• Example: arc DE
arc DC
C
Apothem
• The shortest distance
between center point
and chord
• Example: OA
A
Segment
O
• Area which bordered
by arc and chord
• Shaded area is minor
segment
• Plain area is major
segment
Sector
O
• Area which bordered
by two radii and an arc
• Shaded area is minor
sector
• Plain area is major
sector
Requirements:•
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Compass
Pencils
Eraser
Scale
Set Square
If line touches the circle at one point only that
is called a tangent
If line connect the two point at the circle that is
called a chord
If line intersect the circle at two point that is
called secant
Formation of tangent
Tangent
P
D
Circle
Chord
C
A
B
Secant
APB is called a tangent to the circle
The touching point P is called the point of contact.
A
C
P
B
When two circles do not touch
A
B
E
H
P
Q
G
F
C
We construct four tangents
D
AB,CD, EF & GH
When two circles touches externally
3rd Tangent
1st Tangent
A
.
O
2nd Tangent
C
P
B
.
O’
R
Q
D
We can construct three tangents APB, CQD, PRQ
When two circles intersect each other
1st Tangent
A
B
.
.
O
2nd Tangent
C
O!
D
We can construct two tangents AB, CD
When two circles touches internally
A
P
O
O’
B
We can construct only one tangents APB
When two concurrent circles
O
O’
We can not construct any common tangent
P is a point out side the circle you can construct two tangents
passing through P
Q
P
O
R
Tangent PQ = TangentPR
Constructing Circumcircle
Steps of Construction
C
Construct a Δ ABC
Bisect the side AB
Bisect the side BC
o
The two lines meet at O
From O Join B
A
B
Taking OB as radius draw
a circumcircle.
Constructing of incircle
C
Steps of construction
Construct a Δ ABC
Bisect the
Bisect the
O
BAC
ABC
The two lines meet at O
Taking O draw OP
A
P
B
Taking OP as radius
Draw a circumcircle
AB