Circle Gaming
arc
-
Vocat
subtends : two
point the circum-
·
on
Secant ference , draw two lines
radius to a third point .
We
say
chard the line subtends
angle
the
at the third point
3
diameter ⑧
W
·
1
2
tangent
cyclic quadrilateral guad
·
: a with
Circle Theorems all four ver tices on the circumferenc
-
Quads
1 O AM MB
Eyclic
-
.
=
T
B
A ·
perp
from centre to chard
M
B
1 A
* + B = 180
B
T
TR + PQ
guad
2
ABET
·
[ opp Ls cyclic
↓
Q
.
line from centre to midpt of chordo H
B E
2 . - B = HFE
F
.
3 S ex t Is Cyclic guad
- - ·
E
[ 11t It B
his of chard BHFE
perp
·
p
Proving
=
.
4
A
B
·
L'at centre = 2XL at circumference converse : Lis In same
~ W
B
E
Segm
[ B
B =T
3
.
5 L's in same
segm * this is a
cyclic
Y
i
A m B S
guad
=
P
P
x
M
3
M 180
-
.
6 N A = 900 R LIS
converse :
Opp
· &
· L's in a semi circle
cydic guad
, 7
. A B
↓
X
* =
-
F Converse : ext L
B
.
1
equal chords Equal Lis
cyclic quad
·
, &
CE
Flangents
1 .
G
GPQ = 90"
·
tan I radius
P &
2 .
A ~ = ABD
Y
E
↑ = EE
Y
DCY 7
x Eo tars-chard thi
B
Proving a
langent
M M (centre)
PS to
tangent
* is
ph converse tan tradius
·
S :
*
LB
DC
tangent
* is to ABC
I [E Converse
·
: Tan-chord thin
B
↑
By = E tan-chord the
(
[
1/
11
A = E
E
- ·: Bi = [l
- AB AC Lis
=
base =
BA AC Tan from same
point
=
arc
-
Vocat
subtends : two
point the circum-
·
on
Secant ference , draw two lines
radius to a third point .
We
say
chard the line subtends
angle
the
at the third point
3
diameter ⑧
W
·
1
2
tangent
cyclic quadrilateral guad
·
: a with
Circle Theorems all four ver tices on the circumferenc
-
Quads
1 O AM MB
Eyclic
-
.
=
T
B
A ·
perp
from centre to chard
M
B
1 A
* + B = 180
B
T
TR + PQ
guad
2
ABET
·
[ opp Ls cyclic
↓
Q
.
line from centre to midpt of chordo H
B E
2 . - B = HFE
F
.
3 S ex t Is Cyclic guad
- - ·
E
[ 11t It B
his of chard BHFE
perp
·
p
Proving
=
.
4
A
B
·
L'at centre = 2XL at circumference converse : Lis In same
~ W
B
E
Segm
[ B
B =T
3
.
5 L's in same
segm * this is a
cyclic
Y
i
A m B S
guad
=
P
P
x
M
3
M 180
-
.
6 N A = 900 R LIS
converse :
Opp
· &
· L's in a semi circle
cydic guad
, 7
. A B
↓
X
* =
-
F Converse : ext L
B
.
1
equal chords Equal Lis
cyclic quad
·
, &
CE
Flangents
1 .
G
GPQ = 90"
·
tan I radius
P &
2 .
A ~ = ABD
Y
E
↑ = EE
Y
DCY 7
x Eo tars-chard thi
B
Proving a
langent
M M (centre)
PS to
tangent
* is
ph converse tan tradius
·
S :
*
LB
DC
tangent
* is to ABC
I [E Converse
·
: Tan-chord thin
B
↑
By = E tan-chord the
(
[
1/
11
A = E
E
- ·: Bi = [l
- AB AC Lis
=
base =
BA AC Tan from same
point
=
