Bài tập hình học lớp 9

A:
1/ AB = 6cm, AC = 8cm.
2/ BC = 10cm, BH = 3,6cm.
3/ AB = 15cm, HB = 9cm.
4/ AC = 40cm, AH = 24cm.
5/ AH = 12cm, HB = 16cm.
6/ BH = 4cm, HC = 9cm.

A:
AB = 6 cm

8/ AB = 6cm, HC = 5cm.
A:
(DE>DF)
cao
2
DE
EK
1/ CM:
2
DF
FK
CM: DA . DE = KE . KF
CM: DA . DE = DB . DF
4/ CM: KE . KF = AD . AE + BD . BF
5/ CM: AB3 = EF . AE . BF
6/ CM:

AE
BF

DE
DF

a)
b)
c)
d)

3

AE . AB = AF . AC.
AB . AE = BH . HC
CA . FA = BH . HC
HB . HC = EA . EB + FA . FC
2
B + cos2C tanB.tanC

D. CM:
FB.FD = KD.KC.
8/ CM: FK . FE = DK . DC
A:

= 8cm;

A:
BC = 10cm.
1/

1/ sin 400 , cos 280 , sin 650 , cos 880 , cos 200

0
0
0
2/ tan 320
3/ sin 240 ; cos 350 ; sin 540 ; cos 700 ; sin 780
4/ sin 150 ; cos 710 ; sin 230 ; cos 230
5/ sin 250 ; cos 350 ; sin 500 ; cos 700
6/ sin320 ; cos290 ; sin510 ; cos650 ; sin450
A:
AC=40cm,BC=50cm

AC ( D AB, E AC).
3

. EC = AC3 . BD

A:

ABC.

2/
3/

, CH
CM: AD . AB = HB . HC.

minh: AH . AK = BH . BC

A:

DE = 6cm,DF = 8cm,EF = 10cm.

2

= HK . HI


cm

A:
AC = 40

3/ CM:

BQ
cosB

CI
cosC

BC .

2

2/ K
CM: AB.AQ = AI.AC.
B:

B:
1/ AC = 12cm, BC = 20cm.

2/ BC = 8cm, CH = 6cm.
3/ AC = 12cm. HC = 7,2cm.
4/ AB = 15cm, AH = 12cm.
5/ AH = 9,6cm, HC = 12,8cm.
6/ BH = 9cm, HC = 25cm.
7/ AH = 12cm, BC = 25cm.
8/ AC = 12cm, HB = 7cm.
AH

B:
.
AB 2
1/ CM:
AC 2

BH
CH

CM: BH . HC = AN . AC
CM: AM . AB = AN . AC
4/ CM: HB . HC = MA . MB + NA . NC
5/ CM: MN3 = BC . BM . CN
6/ CM:

MB
NC

AB
AC

1/ sin 500 , cos 350 , sin 250 , cos 150 , sin 150
0
0
2/ cot 240
21, cot 570
, tan 800
3/ tan 150 ; cot 370 ; tan 340 ; cot 810 ; tan 890
4/ tan 340 ; cot 650 ; cot 120 ; tan 400
5/ tan 250 ; cot 350 ; tan 500 ; cot 700
6/ tan 320 ; cot280 ; tan410 ; cot250 ; tan 750
B:
1
1/ Cho 0 < < 900
=
,
2
tan , cot .
1
2/ Cho 0 < < 900
=
,
2
tan , cot .
B:
1/ sin2110 + sin2150 + sin2320 + sin2790 +
sin2750 + sin2580
2/ sin2150
+ sin2750

3

:

3/ sin2250 + sin2650 + tan120 cot780
0

B:

B:
B:
BH

2 cot 430
tan 470

0

2

0

B:
AB

B:
= 9cm, BC =15cm.

1/ cos2
+ tan2(900

b/
.

B:
DE = 20cm, DF = 24cm.

sin2650

3 tan 54 0
4/ 2cot37 . cot53 + sin 28
+ sin2620
0
cot 36
m,AC =8cm
2 cos 480
5/ cos2640 + cos2260 4cot310.cot590
sin 420
cot 32 0
6/ sin2250 + sin2250
tan350 + cot550
tan 580
0
0
0
0
7/ tan1 . tan2 . tan3

HA . HI = BM . BA
8/ CM: BH . BC = AH . AI

B:
MN = 12cm, MP = 20cm.

sin2250 + sin2350 + sin2550

+ cos(900
1
) + 1
sin 2
) cos + sin2

sin

) + sin2

2/ sin(900
+ sin2 tan2
tan2
3/ (cos
sin )2 + (cos + sin )2
(cos
sin ) 2 (cos
sin ) 2
4/
cos .sin
5/ (tan460 + cot460)2 (tan460 cot460)2
sin 4
cos 4
6/ sinx sinxcos2x
7/

sin
cos
6
6
2
2
8/ sin
+ cos
+ 3sin cos


B: Cho tan

2 sin 2
4 cos 2

=

1
2

=

sin
3 sin

2 cos
4 cos

4/

3

3 cos 2
5 sin 2

. BF = DF3 . AE

B:

14B:
1/ AC = 10cm,
2/ AB = 10cm,
3/ BC = 20cm,
4/ AB = 21cm, AC = 18cm

, CH
, C.
CM: AC . AE = HB . HC.

2/

minh: AH . AI = CH . BC

cm,AC=4,5cm,BC=7,5cm

15B:
1/ CM:

2

= HK . HI

AC=12cm

16B:

B:
AB (E

AH 2
BH 2

AE
BE
B:
= 20cm, AC = 16cm.

(D
AC).
3
CE = BCcos
BD
CE

, DC.
ABC. Suy ra AB2 = BH.BC

3
3

4/ Cho

B;

= BD . CE . BC.
AB
AC

3

= 300

22B:
B:
AC = 3 cm

AC.
AMN
BC, AH.

ACB.

AD=8cm,DC=15cm

23B:
AC. CM:
a) AD . AB = AE . AC.
b) BA . DA = HB . HC
c) EA . CA = BH . HC
2

B + sin2C tanB.tanC
F. CM:
B:
1/

1
2
c
2

= MN . MI

4B:
AB = 9cm, AC = 12cm.
ABC
, BH, CH.
2/
EF=70cm,DF=30cm
a) X = 3sin2B + 2sin2C 5tanB.tanC
.
b) Y = cos2(900 B) + cos2B + 7cotB.cotC
3/
3
DF ( A DE, B DF).
CM: AE.AB = AF.
= BC.BE.CF
4


(AB < AC)

5B:
cao AH.
2

AB
AC 2
2
C.

BH
; BH = BCcos2B
CH

3/ Cho AB = 120cm; AC = 160cm.
.
6B:

MAH MNH .
BC
CH
cot B cotC

=40cm

AH, BH,

AN
CN
3/ CM: AH

ABC.
7B:
, AC = 58cm, BC = 42cm.
1/
sao?

AH 2
CH 2

8B: ABC v

= 5cm,

BC =
BC)

BC tan B
.
tan B tan C

0
0

0

?

3:

0

4:
?
0

5:
0

?
6:
0

bay

7:

?
0

0

.

8:
.

?
0

1000m ?


.
.

e/ C/m: AF // OB.

Cho
2

.

160cm2

CK.CA=CF.CD.

minh: OA

IN.
BD

AMN.
Qu

e/

ID=IM

HM.

inh: ME . MF = MH . MO.

BH.AM.
Cho

9:

b/ C
2

f/ C/m:

2

= 4HO.HM.
MAB.

BC

minh: CH . DM = DH . CM.
= 1200. C/m: SAOBC = SMACB.


2

.

. AD = AH . AO.

(NH 06-07)

AC.
= 900.
theo R

2

(NH 05-06)
=

minh: AM // NK.

a/ C/m:
AFB. Suy
ra: BE.CF = BF.CE.

MNC

DM = DK.
a/

AC.CD = CK.AO.
minh: MH.NA = MA.NH.

2

= AE.AD.


H. C/m

2

MCD.
minh: BD // OK.
2

= KC.KD.
.
KD.

2

= 900.
a/ C/
C/m: BD // OA.

c/ Cho AC = R 3
22: Cho

R
2

b/ C

minh:
Cho n
AB=2
= 900
AC.BD theo R.

hai

64.MN2 + CD2 = 16R2.

B; CA >

= 900

CD = AC + BD.

-R2


:
2

= DK.DC.
= 900. Suy ra AC.BD = R2.

: Cho

ABC

(
minh: AE.AD = AH.AO.
.

:
hai

.
b/

HA.HO = HB.HC.

mi
:
ABC.

:
2

= AC.BC.sinA.sinB.

D). C/m: AE.AD=AH.AO minh: IA.BK = R2.
2

= 2.OC.OF.
(O; R)

:

: Cho

a/ Ch
2

c/ AB

= BD.OA.

.tanEBD d/ Chu vi
N
CH.sinC.


(O,R), KB < KC,

i ti
1200

Cho tam
(O,R), EF < FD,

i ti
0

120

KC

DB

FE
KBD
BD

e/

EDB
DB

Cho

Cho

m:

ABC

.

AB

BD
C/minh: FE OA

C/m: DE OC.
Cho

Cho

b/ C/m: T

EF // IK.

KA // MI.

e/

e/

ABC

ABM

BCK

.EB = CB.AB.

.BF = CB.AB.

CA

BA
minh: DE//MN.

ABIC theo R.
AB

ABMC theo R.
(O;

CH

b/

DE


MH

CH

i K.
KI.

minh: SE.SF = SI.SA.
ABC

2R.

2R.
c/

?

?

a/
b/

(O).

minh: I

(O).
,

N, H, Q

a/ C/m

Cho
AC.
a/ C/m: T
.
DE.
:
1200.

e/ Cho
Cho
b/
c/ KB2 = KA.KE
:

MN. C/minh: MB
2

= AE.AF


:

a/
b/

a/
b/

Il
minh:

c/

c/
ng minh: AE.AF = AI.AK.

ABC.
:

d/
: Cho

KCD.

a/
b/
c/
.
:

d/
1
e/ Cho DE =
2

.

:

a/

.

minh: EH . BD = ED . HF

c/

CE (H

AQ . AM = 3R2
C.
: Cho

ABC (AB < AC) n i ti
ng cao AH c

:

ng

(O) theo th t t
t nhau t i K.

ng th ng

a/ Ch ng minh: t
b/ Ch ng minh: AB.AD = AE.AC
c/ Ch ng minh: t
i ti p

nh t.

0: Cho

2

MAB

= MC.MD.

minh
g
:
.
m

MH.

minh:
b/ AB2 = AD.AE = OA2 R2.
c/ AH.AO = AD.AE.
e/ AE.MD = AD.ME


:

qua O).
b/
KF.KE = KB.KC

C/m: EF // BC.

.
: Cho

AE
: Cho

a/
b/ KB2 = KA.KE

.

AME.
: Cho
A
C
tuy

A
AB, AC

T
(B,

NHD.
(
a/

:

.
.

.
2

b/

= AN.AM
: Cho

: Cho

.

.
b/
.

2

= IA.IB
: Cho

:
R).

.

n

b/
DEF.

.
AB2 = AD.AE = OA2 R2.


d/ Tia AO

6:

ABC

ABC (AB <
.

S

2S

AHG

AOG

.

: Cho

; R).
AB,

.
b/
ABC.
7:

2

= AH.AO

ABC (AB <

R)

:

.

ABC (AB <

.
b/
.

a/ C

minh:

b/
d/ Cho BC

= OB2

3
AK
4

theo R.
8:

ABC (AB <

a/ C/minh:

:

BC.

ABC (AB <
minh:

ADB.

e/ C/minh : AH.BC + BH.AC + CH.AB = 4S
: Cho

ABC

.

; R).
MA,
:

b/
c/ C/minh:

:
G
a/

.
IA2 = ID.IB.

ABC (AB <
h AF.
minh:
AMN.

ABC (AB <
A
CH.CN theo R.


:

n

ABC (AB <

a/
: Cho

; R).

KE.KF = KB.KC

a/ C/m:
b/ Ch
c/ C/minh: AC2

3

: Cho
sao cho OA = 2R.

; R)
AB, AC
ABC

1
AD

.

1
AE

.

2
AS

: Cho

ABC.

; R).

OH.AH = BH.CH.
.
2

2

ID .
OI.OM theo R.

ES
AS
: Cho
sao cho OS > 2R.

EK
AK

EQ
1
CQ

; R)
SA, SB

/m:
:

ABC (AB <

.
DC.DA = DO.DM.

a/

minh

:

a/

42:

a/

AMCB
2

AHC.

= AB.AC DB.DC
= AI2 + AI.AB

2


: Cho

S

FBE

: Cho

.
b/

minh: CN

CB.CM = CF.CD

DA
DR

DB
DS

DE
.
DK

:

:

ABC (AB <
BC).
a/
.
.

R 2

S

: Cho

ABC

2S

:
ADE

; R).

S sao cho
.
a/
minh: MA.MB = MS.MN
2

.

MB2 = MC.MD.
b/
: Qua

; R)

hai

.
: Cho
sao cho OM = 2R.

; R)
MA, MB

AB
DK
.
b/

2

MC.MD = 3R .

AB
DK

BC
DH

AC
DI

AC
DI

BC
DH


: Cho

:
.
.

suy ra: OA EF.
:

ABC (AB < AC)
.
: Cho
2

; R).

.

(

.
.
,F
2

.

= ID.IB

c/

CDE.
O

CHK.
sao cho

:
R).

.
:

ABDE
b/

minh:

R 3.
AHE theo R

: MN = MD.

ABC.

R 2
AQT.

: Cho

.
:
a/ Ch

minh: MB2 = MD.MA
.
.


: Cho

:

.

AI .MB
MA
minh:
:

0

:

a

BF song

minh: AB2 + AC2

: Cho

4AH.AM

ABC (AB < AC)

.

R
.