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 ()*1G$I(O&+,\'&('(1;4 /BA=>!#$a
( )
A 1;0 ,
( )

B 3; 5 ,- -

( )
C 0;3

1jR+S&+,+$0b&
AE 2BC=
uuur uuur

2jR+S&+,+$0k&
AF CF 5= =

3jZ+$0M&
( )
2 MA MB 3MC MB MC+ - = -
uuur uuur uuur uuur uuur

f51j
( )
E 7;16
2j
( ) ( )
 F 4;0 F 5;3- Ú
3j:+^(_
( )
Tâm I 4; 19
Bk : R 73
ì
ï
- -

ï
ï
í
ï
=
ï
ï
î

 ()*1;4 /BA=>!4
( ) ( ) ( )
A 4;1 ,B 2;4 ,C 2; 2- -

1j!L$(J#&+$0=B>B!H*E7,&$F
2j]
·
cosCBA

3j];1$16$I]A=>!]#H]+^(_,$$a&$
4j+$0M&5
2MA 3MB MC 0+ - =
uuur uuur uuur r

f51j
·
5
cosCBA
5
=
2j

( )
 
ABC
6
Chu vi 6 5 1 ; S
5 1
D
= + =
+
3j
( )
M 1;4-

 *7()-89:23";(8<=(>=1??6@,A31B
()*1G$I(O&+,\'&('(1;4 /B#&+$0
( )
A 2; 3 ,- -

( )
B 2;1 ,
( )
C 2; 1-
&+,+C\+0L$=>!\:#
f5
( )
D 2; 5- -

&'4 =::'P:Q'(P((Q&('$'''HP6&/%%
'()#*+(CN;l],+$0()*&+, /
>G8$:+$0N;l]16g&1$V$a1(J#;,+$;H$I+0N;&

I51G$5L&+$;H$I
>GX3WmI(&+Z$G$7HV7/<&.

)/

mI1+$;
H$I
>GY3a:;5n&4N;l]<&+$0M:
!V+^a;:
M,+^(\a;:
2345
  
 ()*1G$I(O&+,1;4 /B
( )
A 4;3 ,

( )
B 2;7 ,

( )
C 3; 8- -

1j+$0\&=>!\:#
2j$&+$09<&&$+^*-=1>!
3j&+,(@B(g@A=>!
4j@+^(_7$$aA=>!
f51j
( )
D 1; 12- -
2j

4 1
I ;
9 3
æ ö
÷
ç
÷
- -
ç
÷
ç
÷
ç
è ø
3j
( )

2
G 1; , H 13;0
3
æ ö
÷
ç
÷
ç
÷
ç
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ç
è ø

4j
( )
J 5;1-

 ()*1G$I(O&+,1;4 /B
( )
A 1;5 ,

( )
B 4; 5 ,- -

( )
C 4; 1-

@+^(_,$$aA=>!
f5
( )
I 1;0

 '<9,<*9D()E(/<FGH9:<(9I1(>=0JJK
()*1G$I(O&+,\'&('(1;4 /B&+,(g@<&A=>!B
#$a&+,+C
( ) ( ) ( )
 A 1;2 , B 5;7 , C 4; 3- -

f5
1 21
H ;
11 11
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ç
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-
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ç
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ç
è ø

 '<9,L9'=8M93E#FGH9:<(9(>=1??0
()*1G$I(O&+,1;4 /B
( ) ( ) ( )
 A 1;2 , B 2;0 , C 3;1- -

1jR+S@+^(_7$$aA=>!
2j+$0M(+^*>!&6$I]A=>M#J
1
3
6$I]A=>!
f51j
11 13
I ;
14 4
æ ö
÷
ç
÷
- -

ç
÷
ç
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ç
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2j
 
1 1 11 1
M ; M ;
3 3 3 3
æ ö æ ö
÷ ÷
ç ç
÷ ÷
Ú -
ç ç
÷ ÷
ç ç
÷ ÷
ç ç
è ø è ø

 '<9,N+,989*O <(>=1??0
()*1G$I(O&+,\'&('(1;4 /BA=>!4#&+C;,+o
S
( )
C
<&D
1

y
x
=
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( )
C
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\58$
( )
1 1 1
A a; ,B b; ,C c; C
a b c
æ ö æ ö æ ö
÷ ÷ ÷
ç ç ç
÷ ÷ ÷
Î
ç ç ç
÷ ÷ ÷
ç ç ç
÷ ÷ ÷
ç ç ç
è ø è ø è ø
n
( )
AH BC
1
H ; abc H C
abc
BH AC

ì
ï
æ ö
^
ï
÷
ï
ç
÷
Þ - - Þ Î
ç
í
÷
ç
÷
ï
ç
è ø
^
ï
ï
î
uuur uuur
uuur uuur

 *7()L9'=8*=3=(>=1??6
()*1G$I(O&+, /&$+$0
( ) ( )
A 1;2 , B 3;4-
+$0!(

+^*
d : x 2y 1 0- + =
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f5
( )
 
3 4
C 3;2 C ;
5 5
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ç
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
*7()D())9<;F(>=1??6
()*1G$I(O&+,\'&('(1;4 /BA=>!1;7$=1G$
( )
B 3;0 ,-

( )
C 7;0 ,
#H]+^(_,$$a&$:
r 2 10 5= -

&+,@9
<&+^(_7$$aA=>!B#$a+$094;+,6
f5
( ) ( )
   I 2 10; 2 20 5 I 2 10; 2 10 5+ - Ú - -

!"#"$%%%% &' 5
 !3&+,()
*
'<9,PQ9R#(>=1??0@A31B
()*1G$I(O&+,(g;q /B
( ) ( )
A 10;5 , B 15; 5 ,-

( )
C 20;0-
:#&
+C<&,&@=>!\&+,+$0!B#$a(J=>jj!\
f5
( )
C 7; 26- -

'<9,23E#O <(>=0JJS@A31B
()*1G$I(O&+,\'&('(1;4 /B+$0!;,+^*
x y 2 0- + =
&A=>!1;7$!1G$
( ) ( )
A 1; 2 , B 3;3- -

f5

( )
 
7 3
C 1;3 C ;
2 2
æ ö
÷
ç
÷
Ú - -
ç
÷
ç
÷
ç
è ø

'<9,D())9<;FI0(>=0JJC
!+$0
( )
A 1;1
()*&+, /U/+$0>(+^*
y 3=
1+$0
!((O&A=>!:&$+;
f5
   
4 5 4 5
B 1 ;3 , C 1 B 1 ;3 , C 1
3 3 3 3

æ ö æ ö æ ö æ ö
÷ ÷ ÷ ÷
ç ç ç ç
÷ ÷ ÷ ÷
- - Ú + +
ç ç ç ç
÷ ÷ ÷ ÷
ç ç ç ç
÷ ÷ ÷ ÷
ç ç ç ç
è ø è ø è ø è ø

'<9,T()UF(>=0JKV
()*1G$I(O&+,\'&('(1;4 /B
( )
A 1;0 ,-

( )
B 1;0
1:e/
+$06$+,(+^*
d : y 1=
U/]
2
2
MA
MB
1M&
( )


MA
k, k 0
MB
= >

f5
2 2
2 2
MA x 2x 2
MB x 2x 2
+ +
=
- +
1
2 4 2
1;2
2
k 1 k 6k 1
M ;1 d
k 1
æ ö
÷
+ ± - + -
ç
÷
ç
Î
÷
ç
÷

ç
÷
-
÷
ç
è ø

'<9,)*'<9-()(>=0JJ5
()*1G$I(O&+,\'&('(1;4 /B&$+$0
( )
A 3cost; 0
1
( )
B 0; 2sint
Z+$0
( )
o o
M x ;y
&5
2AM 5MB 0+ =
uuur uuur r
H$&/+d$
f5Z+$0M:':$
( )
2 2
x 9y
E : 1
4 100
+ =


'<9,PQ9R#(>=0JJJ
()*1G$I(O&+,\'&('(1;4 /BA=>!1+$0M#eHr
1j!L$(J5
u 3MA 5MB 2MC= - +
r uuur uuur uuur
HO;,11S(]<&+$0M
2jZ+$0M()*&5
3MA 2MB 2MC MB MC+ - = -
uuur uuur uuur uuur uuur

f51j
u 2AC 5AB= -
r uuur uuur
2j^(_@
( )
C
@9B#H]
CB
R
3
=

,<;()A(O()FGH9:<(9(>=1???
()*1G$I(O&+,\'&('(1;4 /BA=>!4+C
( )
C 2; 4- -
1
(@
( )
G 0;4


1j8$VW
( )
M 2;0
:(;+$0<&7>!R+S&+,+C=B>
&'6 =::'P:Q'(P((Q&('$'''HP6&/%%
  
2j8$VWM6$+,(+^*
d : x y 2 0+ + =
U/N;l]+$0>R+S
M+0+,6$7=>:se
f51j
( ) ( )
B 6;4 , A 4;12-
2/ t;l]:
d : x y 2 0+ - =
Xj
1 9
M ;
4 4
æ ö
÷
ç
÷
-
ç
÷
ç
÷
ç

è ø

'<9,)*'<9-()(>=1???
()*1G$I(O&+,\'&('(1;4 /B&(&#:
( )
2
P : y x=
1
+^*
d : y mx 1= +
!L$(JH$&/+d$B+^*:;:;s
&(&#:
( )
P
7$&$+$0@#$I=1>U/N;l]@1_(_7$$aA-=>H$
&/+d$1G$-:D&+,
f5
( ) ( )
  
1 1 2 2
A x ; mx 1 , B x ; mx 1+ +
1N;l]@:&(&#:
( )
2
P ' : y 2x 1= +

'<,D())9<;F(>=0JJK
()*&+, /#&+$0
( ) ( ) ( )
 A 1;1 , B 3;3 , C 2;0


1j]6$I]u=>!
2jU/eV+$0M((O &4
·
AMB
Te
f5
( )
+
ABC
S 2 .v.d.t
D
=
1
M Oº

()* /#&+$0
( ) ( ) ( )
 A 1;3 , B 3;1 , C 2;4

&j]6$I]u=>!
#jeV+$0
M OxÎ
&4
·
AMB
Te
W:,9. I#3"X($<(9'<9,*7()IJK,A3
((O +$0&dHVn+a+$0=1>:T
e

( )
( )

min
hay PA PB+
>$a(J5
1j
( ) ( )
A 1;1 , B 2; 4-

2j
( ) ( )
A 1;2 , B 3;4

f5
j  j
o o
6 5
1 P P ;0 . 2 P P ;0
5 3
æ ö æ ö
÷ ÷
ç ç
÷ ÷
º º
ç ç
÷ ÷
ç ç
÷ ÷
ç ç

è ø è ø

(+^*
d : x y 0+ =
+$0M&dHVnM+a
+$0=1>:Te((^Z&;
1j
( ) ( )
A 1;1 , B 2; 4- -

2j
( ) ( )
A 1;1 , B 3; 2-

!+$0
( )
M 4;1
1&$+$0
( ) ( )
A a;0 , B 0;b
1G$
a,b 0>
&=B>BM*
R+S&+,+$0=B>&
1j\$I]&$-=>:Te
( )
OAB min
S
D


2j
OA OB+
Te
3j
2 2
1 1
OA OB
+
Te
!"#"$%%%% &' 7
 !3&+,()
*
f51j
( ) ( )
A 8;0 , B 0;2
2j
( ) ( )
A 6;0 , B 0;3
3j
( )

17
A ;0 , B 0;17
4
æ ö
÷
ç
÷
ç
÷

ç
÷
ç
è ø

!+$0
( )
M 2;1
1&$+$0
( ) ( )
A a;0 , B 0;b
1G$
a,b 0>
&=B>BM*
R+S&+,+$0=B>&5
1j\$I]&$-=>:Te
( )
OAB min
S
D

2j
OA OB+
Te
3j
2 2
1 1
OA OB
+
Te

f51j
( ) ( )
A 4;0 , B 0;2

()*1G$I(O&+,\'&('(1;4 /B
( ) ( )
A 1; 2 , B 3;4-

1j+$0M((O&dHVnM+a&$+$0=B>:se
2j+$0i((O&
NA NB-
:6$e
3j+$09((O;&
( )
min
IA IB+

4j+$0v((O;&
J A J B+
uur uur
se
f51j
5
M ;0
3
æ ö
÷
ç
÷
ç

÷
ç
÷
ç
è ø
2j
( )
 
max
NA NB 2 2 khi N 1;0- = -

3j
( )
 
min
1
IA IB 2 13 khi I 0;
2
æ ö
÷
ç
÷
+ = -
ç
÷
ç
÷
ç
è ø
 4j

( )
 
min
J A J B 4 khi J 0;1+ =
uur uur

!#&+$0
( ) ( ) ( )
 A 0;6 , B 2;5 , M 2t 2;t-
&+,+$0M&
1j
( )
min
MA MB+
 2j
max
MA MB-

!#&+$0
( ) ( ) ( )
 A 1;2 , B 2;5 , M 2t 2;t+
&+,+$0M&
1j
( )
min
MA MB+
 2j
max
MA MB+
uuur uuur


3j
max
MA MB-
 4j
min
MA MB-

,<;(8M93E#E#Y(>=1???
()*1G$I(O&+,\'&('(1;4 /BN;l]+$0M&
HVnM+a
( )
A 1;2
1HVnM+a :;#J&;
*7()Z9%<[(>=1??5
()* /B&$+$0
( ) ( )
A 1;2 , B 3;4
($& ,+$0&
AP PB+
:Te
f5
5
P ;0
3
æ ö
÷
ç
÷
ç

÷
ç
÷
ç
è ø

'<9,\3%,<FGH9:<(9(>=0JJK@,A30B
()*1G$I(O&+,1;4 /B
( ) ( )
 
2
A 0;2 , Parabol P : y x=
R
+S+$0M(
( )
P
&
min
AM

&'8 =::'P:Q'(P((Q&('$'''HP6&/%%
  
f5
1;2
6 3
M ;
2 2
æ ö
÷
ç

÷
ç
±
÷
ç
÷
ç
÷
ç
è ø

!"#"$%%%% &' 9
 !3&+,()
*

&'10 =::'P:Q'(P((Q&('$'''HP6&/%%
N]^]_
`,#-,9aF9-(),bc()#97()
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("1G$A3]$I;
i.2
ia;:,!<&∆p:,!<&∆
M,+^*+Z.+Sa;#$a,+$01,!
`,#-F9+F#3"f(,bc()#97()
'+Z$:de,#-F9+F#3"f(<&+^*∆a;$<&41;41G$∆3]
$I;
i.2
ia;:,<&∆p:,<&∆
M,+^*+Z.+Sa;#$a,+$01,
ia;:,!1:,<&∆

9-()#Wg(9#9=$%,bc()#97()
!+^*∆+$N;&14(&D<&E:&DF1
i.2
&/
8$H:ID4<&∆
w1G$
w1G$
9-()#Wg(9,9:(9#h,,bc()#97()
!+^*∆+$N;&14(]s<&
A
u
D
r
u
D
r
A
n
D
r
x
=
A
x
y
v
-
x
=
A

x
y
v
-

((^Z)+^*H4(]s
  
!"#"$%%%% &' 11
9-()#Wg(9#T()i3+#,bc()#97()
(51G$E&B#H+o^$F+Z$:F9-()#Wg(9#T()i3+#<&+^
*
i.2
ia;∆4(5∆4
ia;∆+$N;&14(<&∆:
^*∆+$N;&&$+$0(<&U,)<jOF9-()#Wg(9c()#97()
#9`**'(,9h(G
^*∆+$N;&+$014ID4H(<&U,)<jOF9-()#Wg(9
c()#97()#9`*9;$%)k,ZG
M,D(^Z+)#$I5
+,9;$%9-()#Wg(9c()#97()∆:(9,9R#c()#97()∆∆+$N;&D7+,-∆jj 
)∆≡ ∆jj-/)∆≡-/ Q#W:#-()%<,b9<c()#97()
!&$+^*1
7+,$&+$0<&∆

1∆
X
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f3&∩∆
>Ge/=∈6E=≠9FR+S=′+D$.L1G$=N;&∆
>GX$a(+^*6′N;&=′19
d : Ax By C 0+ + =
D
M
Mh

d
D
d'
=
=h

d
D
d'
=


=h
9
  

 (&DB(]sEa;4F1(dN;<&
+^*+$N;&+$0=1412C
u :
r
1j
( ) ( )
A O 0;0 , u 1; 3º = -
r
 2j
( ) ( )
A 2;3 , u 5; 1- = -
r

3j
( ) ( )
A 3; 1 , u 2; 5- = - -
r
 4j
( ) ( )
A 2;0 , u 3;4=
r

5j
( ) ( )
A 1;2 , u 4;6- = -
r

 6j
( ) ( )
A 1;1 , u 1;5=
r

7j
( ) ( )
A 2; 3 , u 4; 1- = -
r
 8j
( ) ( )
A 3;5 , u 0; 2- = -
r

9j
( ) ( )
A 7; 3 , u 0;3- =
r
 10j
( ) ( )
A 1;2 , u 5;0=
r

 (&DB(]sEa;4F1(dN;<&
+^*+$N;&+$0=1412C
n :
r
1j
( ) ( )
A 0;1 , n 1;2=

r
 2j
( ) ( )
A 2;3 , n 5; 1- = -
r

3j
( ) ( )
A 3;4 , n 4; 3= -
r
 4j
( ) ( )
A 1;2 , n 2;3- = -
r

5j
( ) ( )
A 1;3 , n 3; 4= -
r
 6j
( ) ( )
A 3; 1 , n 2; 5- = - -
r

7j
( ) ( )
A 2;0 , n 1; 1= - -
r
 8j
( ) ( )

A 1;2 , n 5;0=
r

9j
( ) ( )
A 7; 3 , n 0;3- =
r
 10j
( ) ( )
A O 0;0 , n 2;5º =
r

 !+^*4(
d : 2x 3y 1 0- + =

1jU/12;/a112C<&+^*6
2j$a(&D1(]s<&+^*6
 (&DB(]sEa;4F1(dN;<&
+^*+$N;&+$0=14ID4H
1j
( )
A 2;4 , k 2=
 2j
( )
A 3;1 , k 2- = -

3j
( )
A 5; 8 , k 3- - = -
 4j

( )
A 3;4 , k 3- =

5j
( )
A 5;2 , k 1=
 6j
( )
A 3; 5 , k 1- - = -

7j
( )
A 2; 4 , k 0- =
 8j
( )
A 4;0 , k 9- = -

9j
( )
A O 0;0 , k 4º =
 10j
( )
A 0;30 , k 7= -

!"#"$%%%% &' 15
`r2EFF9-()#Wg(9c()#97()&′%<!()dn<c()#97()&i3<X=
>Ge/=∈6R+S=′+D$.L1G$=N;&9
>GX$a(+^*6′N;&=′11G$6
 !3&+,()
*

 (&DB(]sEa;4F1(dN;<&
+^*+$N;&&$+$0=1>
1j
( ) ( )
  A 2; 1 , B 4; 5-
 2j
( ) ( )
  A –2; 4 , B 1; 0

3j
( ) ( )
 A 5; 3 , B –2; 7-
 4j
( ) ( )
  A 3; 5 , B 3; 8

5j
( ) ( )
  A 3; 5 , B 6; 2
 6j
( ) ( )
  A 4; 0 , B 3; 0

7j
( ) ( )
 A 0; 3 , B 0; 2-
 8j
( ) ( )
  A 3; 0 , B 0; 5


9j
( ) ( )
  A 0; 4 , B –3; 0
 10j
( ) ( )
 A –2; 0 , B 0; 6-

 (&DB(]sEa;4F1(dN;<&
+^*6+$N;&+$0=11G$+^*A
1j
( )
  A 2; 3 , : 4x 10y 1 0D - + =
 2j
( )
  A 5; 7 , : x 2y 6 0D - + =

3j
( )
  A 1; 2 , : 5x 1 0- D + =
 4j
( )
 A 1; 7 , : y 2 0- - D - =

5j
( )
 
x 1 2t
A 2; 3 , :
y 3 4t
ì

ï
= -
ï
D
í
ï
= +
ï
î
 6j
( )
 
x 1 3t
A 5; 3 , :
y 3 5t
ì
ï
= - -
ï
- D
í
ï
= - +
ï
î

7j
( )
  
x 1 y 4

A 0; 3 , :
3 2
- +
D =
-
 8j
( )
  
x 2 y 2
A 5; 2 , :
1 2
+ -
D =
-

9j
( )
 A 1; 2 , Ox- D º
 10j
( )
 A 4; 3 , OyD º

 (&DB(]sEa;4F1(dN;<&
+^*6+$N;&+$0=11;41G$+^*A
1j
( )
 A 4; 1 , : 3x 5y 2013 0- D - + =
 2j
( )
 A 2; 3 , : x 3y 7 0- D + - =


3j
( )
 A 4;5 , : x 5y 4 0D - + - =
 4j
( )
A 5;5 , OxD º

5j
( )
A 4; 1 , Oy- - D º
 6j
( )
A 7;2012 , : 2012x 3y 11 0- D - + =

7j
( )
 
x 1 y 3
A 1; 4 , :
1 2
- +
- D =
-
 8j
( )
 
x 2 y 3
A 4; 6 , :
3 10

+ -
- D =
-

9j
( )

x 2t
A 1;0 , :
y 1 4t
ì
ï
=
ï
D
í
ï
= -
ï
î
 10j
( )

x 2 t
A 0;7 , :
y t
ì
ï
= - +
ï

D
í
ï
= -
ï
î

 ()*1G$I(O&+,\'&('(1;4 /BA=>!4+C
L&;U/:5
&j(#&7A=>!
#j(+^&n+4;/(&(g@<&A=>!
j(+^(;;/af;/(&(@<&A=>!
6j(+^(;#(A=>!
'j(+^(;(gf;/(&#H]+^(_,$$aA=>!
1j
( ) ( ) ( )
 A 1; 1 , B 2;1 , C 3;5- -
 2j
( ) ( ) ( )
  A 2; 0 , B 2;–3 , C 0;–1

3j
( ) ( ) ( )
 A 4;5 , B 1;1 , C 6; 1- - -
 4j
( ) ( ) ( )
  A 1; 4 , B 3;–1 , C 6;2

5j
( ) ( ) ( )

 A –1;–1 , B 1;9 , C 9;1
 6j
( ) ( ) ( )
 A 4;–1 , B –3;2 , C 1;6

&'16 =::'P:Q'(P((Q&('$'''HP6&/%%
  
 !A=>!B#$a(#&7<&&$$a(+^&
AA ',
BB ',

CC '
<&&$B1G$
1j
 AB : 2x 3y 1 0, BC : x 3y 7 0, CA : 5x 2y 1 0- - = + + = - + =
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2j
  AB : 2x y 2 0, BC : 4x 5y 8 0, CA : 4x y 8 0+ + = + - = - - =

 $a(71(;(g<&&$=>!#$a(;+$0<&7
>!B!=B=>::Z:+$0MBiB1G$
1j
( ) ( ) ( )
 M 1;1 , N 5;7 , P 1;4-
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 M 2;1 , N 5;3 , P 3; 4-
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3j
( )

3 1
M 2; , N 1; , P 1; 2
2 2
æ ö æ ö
÷ ÷
ç ç
÷ ÷
- - -
ç ç
÷ ÷
ç ç
è ø è ø
 4j
( )
3 7
M ;2 , N ;3 , P 1;4
2 2
æ ö æ ö
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ç ç
÷ ÷
ç ç
÷ ÷
ç ç
è ø è ø
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5j
( )
3 5 5 7
M ; , N ; , P 2; 4

2 2 2 2
æ ö æ ö
÷ ÷
ç ç
÷ ÷
- - -
ç ç
÷ ÷
ç ç
è ø è ø
6j
( ) ( ) ( )
 M –1;–1 , N 1;9 , P 9;1
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 $a(+^*+$N;&+$0M1s(&$(O7+,X+7#J&;
E71G$&$(O&+,,&$1;@F1G$
1j
( )
M 4;10-
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M 2;1
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3j
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M 3; 2- -
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M 2; 1-
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 $a(+^*+$N;&+$0M1"1G$&$(O7+,7,&
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1j
( )
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( )
M 2;1 , S 4=
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3j
( )
M –3;–2 , S 3=
 4j
( )
M 2;–1 , S 4=
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 $a;<&+$0M:+^*61+$0M′+D$.L1G$MN;&+^*6
1G$
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( )
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( )
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3j
( )
M 4;1 , d : x 2y 4 0- + =
 4j
( )

M 5;13 , d : 2x 3y 3 0- - - =
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d : 2x 3y 1 0, : 2x 3y 1 0- + = D - - =
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 !(5
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( )
m
d
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m

d
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( )
M 1;0
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+^*
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  


 !&$=>!B#$a(,71&$+^&$a(&$7
1+^&_:7$B1G$
1j
B : 4x y 12 0,+ - =
BB ': 5x 4y 15 0,- - =
CC ': 2x 2y 9 0+ - =

2j
BC : 5x 3y 2 0,- + =
BB ': 4x 3y 1 0,- + =
CC ': 7x 2y 22 0+ - =

3j
BC : x y 2 0,- + =
BB ': 2x 7y 6 0,- - =
CC ': 7x 2y 1 0- - =

4j
BC : 5x 3y 2 0,- + =
BB ': 2x y 1 0,- - =

CC ': x 3y 1 0+ - =

 !&$=>!B#$a7+,,+C1(&$+^&$a(
7<&&$+4B1G$
1j
( )
A 3;0 ,
BB ': 2x 2y 9 0,+ - =
CC ': 3x 12y 1 0- - =

2j
( )
A 1;0 ,
BB ' : x 2y 1 0,- + =
CC ': 3x y 1 0+ - =

 !&$=>!B#$a7+,,+C1(&$+^(;;/a$a
(7<&&$+4B1G$
1j
( )
A 1;3 ,
BM : x 2y 1 0,- + =
CN : y 1 0- =

2j
( )
A 3;9 ,
BM : 3x 4y 9 0,- + =
CN : y 6 0- =


 !&$=>!B#$a(,71&$+^(;;/a$a(
7_:7$<&&$+4B1G$
1j
AB : x 2y 7 0,- + =
AM : x y 5 0,+ - =
BN : 2x y 11 0+ - =

2j
AB : x y 1 0,- + =
AM : 2x 3y 0,+ =
BN : 2x 6y 3 0+ + =

 !&$=>!B#$a(&$717+,(;+$0<&7L#&$a
(<&7L#&B1G$
1j
AB : 2x y 2 0,+ - =
AC : x 3y 3 0,+ - =
( )
M 1;1-

2j
AB : 2x y 2 0,- - =
AC : x y 3 0,+ + =
( )
M 3;0

3j
AB : x y 1 0,- + =
AC : 2x y 1 0,+ - =
( )

M 2;1

4j
AB : x y 2 0,+ - =
AC : 2x 6y 3 0,+ + =
( )
M 1;1-

 !&$=>!B#$a7+,,+CB(,+^&1,(;;/a$a
(7<&&$+4B1G$
1j
( )
A 4; 1 ,-
BH : 2x 3y 12 0,- + =
BM : 2x 3y 0+ =

2j
( )
A 2; 7 ,-
BH : 3x y 11 0,+ + =
CN : x 2y 7 0+ + =

3j
( )
A 0; 2 ,-
BH : x 2y 1 0,- + =
CN : 2x y 2 0- + =

4j
( )

A 1;2 ,-
BH : 5x 2y 4 0,- - =
CN : 5x 7y 20 0+ - =

 !"#$%&'(%#)(*
!"#"$%%%% &' 19
 !3&+,()
*
 R21S(]+D$<&)+^*&;Ba;?s&;7+,$&+$0
<&?
1j
1
d :2x 3y 1 0+ + =
&
2
d : 4x 5y 6 0+ - =

2j
1
d : 4x y 2 0- + =
&
2
d : 8x 2y 1 0- + + =

3j
1
x 5 t
d :
y 3 2t
ì

ï
= +
ï
í
ï
= - +
ï
î
&
2
x 4 2t
d :
y 7 3t
ì
ï
= +
ï
í
ï
= - +
ï
î

4j
1
x 1 t
d :
y 2 2t
ì
ï

= -
ï
í
ï
= - +
ï
î
&
2
x 2 3t
d :
y 4 6t
ì
ï
= +
ï
í
ï
= - -
ï
î

5j
1
x 5 t
d :
y 1
ì
ï
= +

ï
í
ï
= -
ï
î
&
2
d : x y 5 0+ - =

6j
1
d : x 2=
&
2
d : x 2y 4 0+ - =

 !&$+^*61∆+0&$+^*
&j!s&; #jf j("&;
1j
d : mx 5y 1 0- + =
&
: 2x y 3 0D + - =

2j
( )
d : 2mx m 1 y 2 0+ - - =
&
( ) ( ) ( )
: m 2 x 2m 1 y m 2 0D + + + - + =

3j
( ) ( )
d : m 2 x m 6 y m 1 0- + - + - =
&
( ) ( )
: m 4 x 2m 3 y m 5 0D - + - + - =

4j
( )
d : m 3 x 2y 6 0+ + + =
&
: mx y 2 m 0D + + - =

 +0#&+^*&;+oN;$
1j
1
d : y 2x 1= -
2
d : 3x 5y 8+ =
( )
3
d : m 8 x 2my 3m+ - =

2j
1
d : y 2x m= -
2
d : y x 2m= - +
( )
3

d : mx m 1 y 2m 1- - = -

3j
1
d : 5x 11y 8+ =
2
d :10x 7y 74- =
( )
3
d : 4mx 2m 1 y m 2+ - + +

4j
1
d : 3x 4y 15 0- + =
2
d : 5x 2y 1 0+ - =
( )
3
d : mx 2m 1 y 9m 13 0- - + - =

 $a(+^*6+$N;&$&+$0<&&$+^*6

16
X
1
1j
1
d : 3x 2y 10 0- + =
2
d : 4x 3y 7 0+ - =

( )
d qua A 2;1

2j
1
d : 3x 5y 2 0- + =
2
d : 5x 2y 4 0- + =
3
d song song d : 2x y 4 0- + =

3j
1
d : 3x 2y 5 0- + =
2
d : 2x 4y 7 0+ - =
3
d vuông d : 4x 3y 5 0- + =

 +$0+^*&;:;+$N;&1G$$
1j
( )
m 2 x y 3 0- - + =
 2j
( )
mx y 2m 1 0- + + =

3j
mx y 2m 1 0- - - =
 4j

( )
m 2 x y 1 0+ - + =

 !&$=>!1G$
( ) ( ) ( )
 A 0;–1 , B 2;–3 , C 2;0

1j$a(+^(;;/aB(+^&B(
+^(;(g<&&$
&'20 =::'P:Q'(P((Q&('$'''HP6&/%%
  
2j!L$+^(;;/a+oN;$B+^&+oN;$B+^(;
(g+oN;$
 &$7<&#=>!\4(
x 3y 0, 2x 5y 6 0- = + + =
B+C
( )
C 4; 1-
$a(&$7_:7$
 $a(+^*+$N;&+$0M1+;&$+$0Bt1G$
j
( ) ( ) ( )
    M 2; 5 , P –1; 2 , Q 5; 4
 2j
( ) ( ) ( )
    M 1; 5 , P –2; 9 , Q 3; – 2

+(,(-(#$!.(%#)(/
 ]HVn+$0M+a+^*6B1G$
1j

( )
M 4; 5 , d : 3x 4y 8 0- - + =
 Xj
( )
M 3;5 , d : x y 1 0+ + =

3j
( )

x 2t
M 4; 5 , d :
y 2 3t
ì
ï
=
ï
-
í
ï
= +
ï
î
 4j
( )

x 2 y 1
M 3;5 , d :
2 3
- +
=


 ()*1G$I(O&+,\'&('(1;4 /5
1j!+^*
: 2x y 3 0D - + =
]#H]+^(_@
( )
I 5;3-
1$a.?
1G$+^*
D

2j!K=>!\4(X7:5
2x 3y 5 0,- + =

3x 2y 7 0+ - =

1+C
( )
A 2; 3-
]6$I]K+4
3j]6$I]1;4y+CJ(X+^*5
1
d : 3x 4y 6 0- + =
1
2
d : 6x 8y 13 0- - =

 !&$=>!]6$I]&$=>!B1G$
1j
( ) ( ) ( )

 A –1;–1 , B 2;–4 , C 4;3
 2j
( ) ( ) ( )
 A –2;14 , B 4;–2 , C 5;–4

 $a(+^*61+^*∆,HVB1G$
1j
: 2x y 3 0, h 5D - + = =
 2j
x 3t
: , h 3
y 2 4t
ì
ï
=
ï
D =
í
ï
= +
ï
î

3j
: y 3 0, h 5D - = =
 4j
: x 2 0, h 4D - = =

 $a(+^*61G$+^*∆1+$0=,HV
#JB1G$

1j
( )
: 3x 4y 12 0, A 2;3 , h 2D - + = =
 2j
( )
: x 4y 2 0, A 2;3 , h 3D + - = - =

3j
( )
: y 3 0, A 3; 5 , h 5D - = - =
 4j
( )
: x 2 0, A 3;1 , h 4D - = =

 $a(+^*+$N;&=1>,HV#JB1G$
1j
( ) ( )
     A –1; 2 , B 3; 5 , d 3=
 2j
( ) ( )
     A –1; 3 , B 4; 2 , d 5=

3j
( ) ( )
     A 5; 1 , B 2; – 3 , d 5=
 4j
( ) ( )
     A 3; 0 , B 0; 4 , d 4=

 $a(+^*+$N;&+$0M1+;&$+$0BtB1G$

1j
( ) ( ) ( )
    M 2; 5 , P –1; 2 , Q 5; 4
 2j
( ) ( ) ( )
   M 1; 2 , P 2; 3 , Q 4;–5

!"#"$%%%% &' 21
 !3&+,()
*
3j
( ) ( ) ( )
    M 10; 2 , P 3; 0 , Q –5; 4
 4j
( ) ( ) ( )
   M 2; 3 , P 3;–1 , Q 3; 5

 $a(+^*6+$0=,HV#J1+$0>,HV
#JHB1G$
1j
( ) ( )
    A 1; 1 , B 2; 3 , h 2, k 4= =
 2j
( ) ( )
    A 2; 5 , B –1; 2 , h 1, k 3= =

 !+^*
: x y 2 0D - + =
1+$0
( ) ( ) ( )

    O 0; 0 , A 2; 0 , B –2; 2

1j!L$+^*∆s+7*=>
2j!L$(J&$+$0-B=J"1,]&+D$1G$+^*∆
3j+$0-′+D$.L1G$-N;&∆
4j(∆B+$0M&+,6$+^eH?-M=se
 !&$+$0
( ) ( )
  A 2; 2 , B 5; 1
+$0!(+^*
: x 2y 8 0D - + =
&
6$I]&$=>!#JzE+16F
f5
( )
76 18
C 12;10 , C ;
5 5
æ ö
÷
ç
÷
- -
ç
÷
ç
è ø

 Z+$0
1jZ+$0+^*

: 2x 5y 1 0D - + - =
,HV#JY
2jZ+$0+;X+^*
d : 5x 3y 3 0, : 5x 3y 7 0+ - = D + + =

3jZ+$0+;&$+^*
d : 4x 3y 2 0, : y 3 0- + = D - =

4jZ+$04CDHV+a&$+^*&;#J
5
13
5
d : 5x 12y 4 0- + =
1
: 4x 3y 10 0D - - =

 $a(+^@$<&47#m$&$+^*
1j
3x 4y 12 0, 12x 5y 20 0- + = + - =
 2j
3x 4y 9 0, 8x 6y 1 0- - = - + =

Yj
x 3y 6 0, 3x y 2 0+ - = + + =
 4j
x 2y 11 0, 3x 6y 5 0+ - = - - =

 !&$=>!@1#H]+^(_,$$a&$=>!B1G$
1j
( ) ( ) ( )

  A –3;–5 , B 4;–6 , C 3; 1
 2j
( ) ( ) ( )
   A 1; 2 , B 5; 2 , C 1;–3

3j
AB : 2x 3y 21 0, BC : 2x 3y 9 0, CA : 3x 2y 6 0- + = + + = - - =

4j
AB : 4x 3y 12 0, BC : 3x 4y 24 0, CA : 3x 4y 6 0+ + = - - = + - =

0
 ]4$K&&$+^*
1j
x 2y 1 0, x 3y 11 0- - = + - =
 2j
2x y 5 0, 3x y 6 0- + = + - =

3j
3x 7y 26 0, 2x 5y 13 0- + = + - =
 4j
3x 4y 5 0, 4x 3y 11 0+ - = - + =

 ]D+<&4(&$=>!B1G$
1j
( ) ( ) ( )
  A –3;–5 , B 4;–6 , C 3; 1
 2j
( ) ( ) ( )
   A 1; 2 , B 5; 2 , C 1;–3


3j
AB : 2x 3y 21 0, BC : 2x 3y 9 0, CA : 3x 2y 6 0- + = + + = - - =

&'22 =::'P:Q'(P((Q&('$'''HP6&/%%
  
4j
AB : 4x 3y 12 0, BC : 3x 4y 24 0, CA : 3x 4y 6 0+ + = - - = + - =

 !&$+^*61∆+04$K&&$+^*+4#JαB1G$
1j
( ) ( ) ( )
0
d : 2mx m 3 y 4m 1 0, : m 1 x m 2 y m 2 0, 45+ - + - = D - + + + - = a =

2j
( ) ( ) ( ) ( )
0
d : m 3 x m 1 y m 3 0, : m 2 x m 1 y m 1 0, 90+ - - + - = D - + + - - = a =

 $a(+^*6+$N;&+$0=171G$+^*∆,4αB1G$
1j
( )
0
A 6;2 , : 3x 2y 6 0, 45D + - = a =
 2j
( )
0
A 2;0 , : x 3y 3 0, 45- D + - = a =


3j
( )
0
A 2;5 , : x 3y 6 0, 60D + + = a =
 4j
( )
0
A 1;3 , : x y 0, 30D - = a =

 !1;=>!\4@
( )
I 4;–1
1(,7:
3x y 5 0- + =

1j$a(&$+^2<&1;
2j7+,y+C<&1;
12+.(
 *7()L9'=9OWwx3<+*y0(>=1???
()*&+, /B+^*
( )
: 2x 3y 3 0D - + =
$a(
+^*+$N;&
( )
M 5;13-
11;41G$+^*
( )
D


f5
d : 3x 2y 11 0+ - =

 *7()L9'=O <(>=0JJK
()*&+, /BA=>!1G$
( ) ( ) ( )
 A 1; 1 , B 2;1 , C 3;5- -

1j$a(+^1;4=H{n=+a(;;/a>3<&A=>!
2j]6$I]A=>3
f51j
AH : 4x y 3 0+ - =
2j
( )
+
ABK
S 11 vdt
D
=

 *7()8M)9;FGH9:<(9(>=0JJS
()*&+, /B&$+^*5
( )
1
: 4x 3y 12 0D - - =
1
( )
2
: 4x 3y 12 0D + - =


1jR+S+C<&&$4#&7;,
( ) ( )
1 2
,D D
1(O
Oy

2j&+,@1#H]+^(_,$$a&$4$(
f51j
( )
( )
( )
1
2
1 2
A 0; 4 Oy
B 0;4 Oy
C 3;0
ì
ï
- = D Ç
ï
ï
ï
ï
= D Ç
í
ï
ï
ï

= D Ç D
ï
ï
î
2j
( )

4
Tâm I ;0
3
4
Bk : R d I;AB
3
ì
æ ö
ï
÷
ï
ç
÷
ï
ç
÷
ç
ï
÷
ç
ï
è ø
í

ï
ï
ï
= =
ï
ï
î

 *7()L9'=O <Z9%<(>=0JJJ
()*&+, /BA=>!B7>!B+^&>9B!34(:
:Z:
7x 5y 8 0,+ - =

9x 3y 4 0,- - =

x y 2 0+ - =
$a(7=>B
=!1+^&=
f5
 AB : x y 0, AC : x 3y 8 0, AH : 5x 7y 4 0- = + - = - + =

!"#"$%%%% &' 23
 !3&+,()
*
 *7()D())9<;FFGH9:<(9(>=1???
()*&+, /BA=>!4+^&
( )
BH : x y 1 0+ - =
B
( )

CK : 3x y 1 0- + + =
17
( )
BC : 5x y 5 0- - =
$a(<&7_
:7$<&&$1+^&=|
f5
 AB : x 3y 1 0, AC : x y 3 0, AL : x 5y 3 0+ - = - + = + - =

 *7()8<X=L+#9:Nh,(>=1???
()*&+, /BA=>!4
( )
A 1;3
1&$(;;/a:
x 2y 1 0- + =
1
y 1 0- =
$a(7<&&$|
f5
 AB : x y 2 0, AC : x 2y 3 0, BC : x 4y 1 0- + = + - = - + =

 *7()L9'=9OWwx3<+*y(>=1??0
()*&+, /B+$0
( ) ( )
A 1;2 , B 1;2-
1+*64
(
( )
d : x 2y 1 0- + =
U/&+,<&+$0!;,+^*6&#&+$0=B

>B!7&$1T&U,(+$;H$I&;
1j
CA CB=
 2j
AB AC=

f51j
1
C 0;
2
æ ö
÷
ç
÷
ç
÷
ç
÷
ç
è ø
2j
( )
 
1 2
C 3;2 C ;
5 5
æ ö
÷
ç
÷

Ú -
ç
÷
ç
÷
ç
è ø

 *7()L9'=z(99t,Z9%<(>=1??1
()*&+, /BA=>!1+$0
( )
M 1;1-
:(;+$0<&=>&$7
=!1>!'LgJ(&$+^*
2x y 2 0+ - =
1
x 3y 3 0+ - =

1jR+S&+,#&+C=B>B!<&A=>!11$a(+^&!
2j]6$I]A=>!
f51j
( ) ( )
 
3 4
A 1;0 , B 3;2 , C ;
5 5
æ ö
÷
ç
÷

-
ç
÷
ç
÷
ç
è ø
1
CH :10x 5y 2 0- - =
2j
( )
+
ABC
6
S vdt
5
D
=

 *7()D()2A=(>=1??5
()*1G$I(O&+, /B&$+^*
x y 1 0+ - =
1
3x y 5 0- + =
U/6$I]#4&$7J(&$+^*+U
B,+C:$&+$0<&&$+^*+41$&+$0<&&$+^2:
( )
I 3;3

f5

( )
+
ABCD
S 55 vdt=

 *7()L9'=9t9Z9%<(>=1??5
()*1G$I(O&+,& /&$=>!4+C
( )
A 2; 3 ,-

( )
B 3; 2-
16$I]&$=>!#J
3
2
>$a(@8<&A=>!;,+^*
d : 3x y 8 0- - =
&+,+$0!
f5
( ) ( )
 C 1; 1 C 4;8- Ú

 *7()Z9%<[(>=1??6'<9,{()-()
&'24 =::'P:Q'(P((Q&('$'''HP6&/%%
  
()*1G$I(O&+,\'&('(1;4 /BA=>!#$a+C
( )
A 3;9
1
(+^(;;/a>MB!i::Z:

3x 4y 9 0,- + =

y 6 0- =
$a
(+^(;;/a=\<&&$+U
f5
AD : 3x 2y 27 0+ - =

 *7()<I3|(),9:(9i3"(>=1??6'<9,<I3&|()
()*1G$I(O&+,\'&('(1;4 /BA=>!4+C
( )
A 0;1
1
&$+^*L&+^&1}n>1!4(L:
2x y 1 0- - =
1
x 3y 1 0+ - =
]6$I]A=>!
f5
( )
+
ABC
S 14 vdt
D
=

 *7()Z9%<(>=1??6
!&$=>!4
( ) ( ) ( )
 A 6; 3 , B 4;3 , C 9;2- - -


j$a(7<&A=>!
Xj$a(+^@$(<&4=<&&$=>!
Yj+$0M(7=>1+$0i(7=!&Mijj>!1
AM CN=
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AB : 3x y 15 0
AC : x 3y 3 0
BC : x 13y 35 0
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+ - =
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Xj
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d : y x 3= +
Yj
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32 9 33 4

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7 7 7 7
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è ø è ø
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 *7()L9'=/<9}()(>=1??6
()*1G$I(O&+, /B&$+^*
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2
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1+$0
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P 2;1
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j$a(+^*+$N;&+$01$&+$09<&&$+^*A
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1A
X
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Xj$a(+^*+$N;&+$01s&$+^*A

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y 1 0- =
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d AB : 4x y 7 0º - - =
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 *7()L9'=8*=3=(>=1??6
()*1G$I(O&+,\'&('(1;4 /B&$+$0
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d: x 2y 1 0- + =
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5 5
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 *7()8<(9f8M93E#D())9<;FZ9%<N(>=1??6
()*1G$I(O&+, /+^*
d : 2x 3y 1 0+ + =
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$a(<&+^*+$N;&+$0M171G$+^*6,
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0
45
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x 5y 4 0- + =
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 *7()8<(9f8M93E#D())9<;FZ9%<(>=1??6
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