Summary Euclidean Geometry Revision

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
=