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Lesson: Lines and Circles P
Contributed by: Pappal
There are several parts to a circle
There are several parts to a circle
The center of the circle is called
There are several parts to a circle
The center of the circle is called
There are several parts to a circle
the center
The center of the circle is called
There are several parts to a circle
the center
center
A line drawn from the center to the edge is called
There are several parts to a circle
A line drawn from the center to the edge is called
There are several parts to a circle
the radius
A line drawn from the center to the edge is called
There are several parts to a circle
the radius
radius
ANY line drawn from the center to edge can be called
There are several parts to a circle
the radius
radius
ANY line drawn from the center to edge can be called
There are several parts to a circle
the radius
radius
ANY line drawn from the center to edge can be called
radius
There are several parts to a circle
the radius
radius
A line drawn straight across the circle but goes
There are several parts to a circle
through the center is called
A line drawn straight across the circle but goes
There are several parts to a circle
through the center is called
a diameter
A line drawn straight across the circle but goes
There are several parts to a circle
through the center is called
diameter
a diameter
A diameter is really made up of two radii
There are several parts to a circle
diameter
A diameter is really made up of two radii
There are several parts to a circle
radius
diameter
A diameter is really made up of two radii
There are several parts to a circle
radius
diameter
A diameter is really made up of two radii
There are several parts to a circle
so the diameter is twice as big as the radius
radius
diameter
There are several parts to a circle
radius
?
diameter
?
center
?
Any line that goes from edge to edge
Any line that goes from edge to edge
is called a chord
Any line that goes from edge to edge
is called a chord
chord
Any line that goes from edge to edge
is called a chord
chord
chord
The diameter is also a type of chord
Any line that goes from edge to edge
is called a chord
chord
chord
The diameter is also a type of chord
Any line that goes from edge to edge
is called a chord
chord
chord
chord
Any line that goes through the circle
Any line that goes through the circle
Any line that goes through the circle
is called a secant
Any line that goes through the circle
secant
is called a secant
secant
?
chord
?
Any line that only touches the circle once
Any line that only touches the circle once
is called a tangent
Any line that only touches the circle once
is called a tangent
tangent
and the point where
Any line that only touches the circle once
it meets the circle
is called a tangent
tangent
and the point where
Any line that only touches the circle once
it meets the circle
is called a tangent
tangent
point of tangency
is called the
tangency
and the point where
Any line that only touches the circle once
it meets the circle
point of 
is called a tangent
tangent
point of tangency
is called the
radius
?
chord
?
diameter
?
center
?
tangent
?
secant
?
point of tangency
?
If the diameter is 20 ft, how long is the radius?
ft
If the radius is 4 ft, how long is the diameter?
ft
If I draw a radius to the point of tangency
If I draw a radius to the point of tangency
tangency
point of 
If I draw a radius to the point of tangency
tangency
point of 
If I draw a radius to the point of tangency
tangency
point of 
radius
If I draw a radius to the point of tangency
tangency
point of 
the angle formed is a right angle
radius
If I draw a radius to the point of tangency
tangency
point of 
the angle formed is a right angle
radius
If I draw a radius to the point of tangency
tangency
point of 
the angle formed is a right angle
right angle
radius
How many degrees is the
angle ACB?
o
A
C
B
D
Two chords
Two chords
that are equal
Two chords
that are equal
Two chords
cut off equal arcs.
that are equal
Two chords
cut off equal arcs.
that are equal
5
5
7
If a chord
If a chord
If a chord
is perpendicular to a radius
If a chord
is perpendicular to a radius
If a chord
then the radius bisects it.
is perpendicular to a radius
If a chord
then the radius bisects it.
is perpendicular to a radius
If AE = 6 then DE =        and AD =
D
B
E
C
A
If two tangents are drawn to a circle
If two tangents are drawn to a circle
If two tangents are drawn to a circle
If two tangents are drawn to a circle
If two tangents are drawn to a circle
from the same point
If two tangents are drawn to a circle
from the same point
they start at the same
point
If two tangents are drawn to a circle
from the same point
they are equal
If two tangents are drawn to a circle
from the same point
they are equal
8
8
10
If two chords intersect in a circle
If two chords intersect in a circle
If two chords intersect in a circle
If two chords intersect in a circle
If two chords intersect in a circle
the products of the segments of each line are equal
If two chords intersect in a circle
the products of the segments of each line are equal
8
4
x
5
If two chords intersect in a circle
the products of the segments of each line are equal
x and 8 are on on line
8
4
x
5
If two chords intersect in a circle
the products of the segments of each line are equal
x and 8 are on on line
8
4
x
5
8x = 
If two chords intersect in a circle
the products of the segments of each line are equal
x and 8 are on on line
4 and 5 are on one line
8
4
x
5
8x = 
If two chords intersect in a circle
the products of the segments of each line are equal
x and 8 are on on line
4 and 5 are on one line
8
4
x
5
8x = 4(5)
If two chords intersect in a circle
the products of the segments of each line are equal
x and 8 are on on line
4 and 5 are on one line
8
4
x
5
8x = 4(5)
8x = 20
x = 20/8 

If two chords intersect in a circle
the products of the segments of each line are equal
x and 8 are on on line
4 and 5 are on one line
8
4
x
5
8x = 4(5)
8x = 20
x = 20/8 
x = 5/2
x = 4(      )
x =
x
4
2
6
If two secants intersect outside a circle
If two secants intersect outside a circle
the products of the outside segments and the whole line
If two secants intersect outside a circle
are equal
the products of the outside segments and the whole line
If two secants intersect outside a circle
are equal
8
x
6
5
the products of the outside segments and the whole line
On one secant, the outer part is 6 and the whole thing
If two secants intersect outside a circle
are equal
is 14
8
x
6
5
the products of the outside segments and the whole line
On one secant, the outer part is 6 and the whole thing
If two secants intersect outside a circle
are equal
is 14
8
x
6
5
6(14) =
the products of the outside segments and the whole line
and x + 5 is
On one secant, the outer part is 6 and the whole thing
If two secants intersect outside a circle
On the other secant
the whole thing
5 is the outer
are equal
is 14
8
x
6
5
6(14) =
the products of the outside segments and the whole line
and x + 5 is
On one secant, the outer part is 6 and the whole thing
If two secants intersect outside a circle
On the other secant
the whole thing
5 is the outer
are equal
is 14
8
x
6
5
6(14) = 5 (x + 5)
the products of the outside segments and the whole line
and x + 5 is
On one secant, the outer part is 6 and the whole thing
If two secants intersect outside a circle
On the other secant
the whole thing
5 is the outer
are equal
is 14
8
x
6
5
6(14) = 5 (x + 5)
84 = 5x + 25
x = 11.8
Whole line:
Inner part:
Outer part:
8
12
If a circle has both a tangent and a secant
If a circle has both a tangent and a secant
8
5
x
If a circle has both a tangent and a secant
use the outer and whole for the secant
8
5
x
If a circle has both a tangent and a secant
5(x + 5) =
use the outer and whole for the secant
8
5
x
If a circle has both a tangent and a secant
5(x + 5) =
use the outer and whole for the secant
and square the length of the tangent
8
5
x
If a circle has both a tangent and a secant
5(x + 5) = 82
use the outer and whole for the secant
and square the length of the tangent
8
5
x
5x + 25 = 64
If a circle has both a tangent and a secant
5(x + 5) = 82
use the outer and whole for the secant
and square the length of the tangent
8
5
x
5x + 25 = 64

x = 7.8
If a circle has both a tangent and a secant
5(x + 5) = 82
use the outer and whole for the secant
and square the length of the tangent
8
5
x
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