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- 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. A:
6/ BH = 4cm, HC = 9cm. 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 a) AE . AB = AF . AC.
5/ CM: AB3 = EF . AE . BF b) AB . AE = BH . HC
3 c) CA . FA = BH . HC
AE DE d) HB . HC = EA . EB + FA . FC
6/ CM: 2
BF DF 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
2/ tan 320 0 0 0
AC ( D AB, E AC).
3/ sin 240 ; cos 350 ; sin 540 ; cos 700 ; sin 780
4/ sin 150 ; cos 710 ; sin 230 ; cos 230
3
5/ sin 250 ; cos 350 ; sin 500 ; cos 700 . EC = AC3 . BD
6/ sin320 ; cos290 ; sin510 ; cos650 ; sin450
A: AC=40cm,BC=50cm
A:
, CH
ABC. 2/ CM: AD . AB = HB . HC.
3/
minh: AH . AK = BH . BC
2
A: DE = 6cm,DF = 8cm,EF = 10cm. = HK . HI
- A: cm BQ CI
AC = 40 3/ CM: BC .
cosB cosC
2
2/ K
CM: AB.AQ = AI.AC.
B:
B:
1/ sin 500 , cos 350 , sin 250 , cos 150 , sin 150
1/ AC = 12cm, BC = 20cm.
2/ BC = 8cm, CH = 6cm. 2/ cot 240 0
21, cot 570 0
, tan 800
3/ tan 150 ; cot 370 ; tan 340 ; cot 810 ; tan 890
3/ AC = 12cm. HC = 7,2cm.
4/ tan 340 ; cot 650 ; cot 120 ; tan 400
4/ AB = 15cm, AH = 12cm.
5/ tan 250 ; cot 350 ; tan 500 ; cot 700
5/ AH = 9,6cm, HC = 12,8cm.
6/ tan 320 ; cot280 ; tan410 ; cot250 ; tan 750
6/ BH = 9cm, HC = 25cm.
7/ AH = 12cm, BC = 25cm. B:
1
8/ AC = 12cm, HB = 7cm. 1/ Cho 0 < < 900 = ,
2
B: AH tan , cot .
.
1
AB 2 BH 2/ Cho 0 < < 900 = ,
1/ CM: 2
AC 2 CH tan , cot .
CM: BH . HC = AN . AC B:
CM: AM . AB = AN . AC
4/ CM: HB . HC = MA . MB + NA . NC 1/ sin2110 + sin2150 + sin2320 + sin2790 +
5/ CM: MN3 = BC . BM . CN sin2750 + sin2580
MB AB
3
2/ sin2150 sin2250 + sin2350 + sin2550 sin2650
6/ CM: + sin2750
NC AC
2 cot 430
3/ sin2250 + sin2650 + tan120 cot780
: tan 470
HA . HI = BM . BA 0 03 tan 54 02 0
8/ CM: BH . BC = AH . AI 4/ 2cot37 . cot53 + sin 28 0
+ sin2620
cot 36
B: m,AC =8cm 2 cos 480
5/ cos2640 + cos2260 4cot310.cot590
sin 420
cot 32 0
B: 6/ sin2250 + sin2250 tan350 + cot550
tan 580
0 0 0 0
B: 7/ tan1 . tan2 . tan3
BH B:
B: AB 1/ cos2 sin + cos(900 ) + sin2
= 9cm, BC =15cm. 1
+ tan2(900 ) + 1
sin 2
b/ 2/ sin(900 ) cos + sin2 + sin2 tan2
. tan2
B:
3/ (cos sin )2 + (cos + sin )2
MN = 12cm, MP = 20cm.
(cos sin ) 2 (cos sin ) 2
4/
cos .sin
B: 5/ (tan460 + cot460)2 (tan460 cot460)2
DE = 20cm, DF = 24cm. sin 4 cos 4
6/ sinx sinxcos2x 7/
sin cos
6 6 2 2
8/ sin + cos + 3sin cos
- 4/
1 sin 2 cos 3
B: Cho tan = = . BF = DF3 . AE
2 3 sin 4 cos
2 sin 2 3 cos 2
4 cos 2 5 sin 2 B:
14B:
, CH , C.
1/ AC = 10cm, 2/ CM: AC . AE = HB . HC.
2/ AB = 10cm,
3/ BC = 20cm,
4/ AB = 21cm, AC = 18cm minh: AH . AI = CH . BC
15B: cm,AC=4,5cm,BC=7,5cm
1/ CM: 2
= HK . HI
16B: AC=12cm
B:
AB (E
AE AH 2
BE BH 2
B:
3
= 20cm, AC = 16cm. (D AC). B;
3 3
CE = BCcos = BD . CE . BC.
3
BD AB
CE AC
, DC.
ABC. Suy ra AB2 = BH.BC
4/ Cho = 300
22B:
B: AC.
AC = 3 cm AMN
BC, AH. ACB.
23B: AD=8cm,DC=15cm
AC. CM: 1
2
a) AD . AB = AE . AC. c
2
b) BA . DA = HB . HC = MN . MI
c) EA . CA = BH . HC
2
B + sin2C tanB.tanC 4B:
AB = 9cm, AC = 12cm.
F. CM: ABC , BH, CH.
2/
B: EF=70cm,DF=30cm a) X = 3sin2B + 2sin2C 5tanB.tanC
1/ . b) Y = cos2(900 B) + cos2B + 7cotB.cotC
3/
3
DF ( A DE, B DF). CM: AE.AB = AF. = BC.BE.CF
4
- 5B: (AB < AC)
cao AH. ABC.
AB 2
BH 7B: =40cm
; BH = BCcos2B , AC = 58cm, BC = 42cm.
AC 2 CH
2
C. 1/
sao?
3/ Cho AB = 120cm; AC = 160cm. AH, BH,
.
6B:
AN AH 2 8B: ABC v = 5cm,
CN CH 2 BC =
MAH MNH . BC)
BC BC tan B
3/ CM: AH CH .
cot B cotC tan B tan C
0
0
0
3: ?
0
4:
?
0
5:
0
?
6:
0
7: bay
?
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:
2
b/ C = 4HO.HM.
2
MAB.
minh: CH . DM = DH . CM.
f/ C/m: BC = 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.
2
= AE.AD.
minh: MH.NA = MA.NH.
- H. C/m
2
-R2
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
hai = 900 CD = AC + BD.
AC.BD theo R.
64.MN2 + CD2 = 16R2.
B; CA > = 900
- :
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. : Cho
: (O; R)
a/ Ch
2
= BD.OA.
c/ AB .tanEBD d/ Chu vi
N CH.sinC.
- i ti Cho tam i ti
0
(O,R), KB < KC, 1200 (O,R), EF < FD, 120 DB
KC FE
KBD e/ EDB
BD DB
Cho Cho ABC
m: .
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. ABMC theo R.
AB (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.
:
e/ Cho 1200.
Cho
b/
c/ KB2 = KA.KE
:
MN. C/minh: MB
2
= AE.AF
- :
a/
b/
a/
Il
b/
minh:
c/
c/ ABC.
ng minh: AE.AF = AI.AK. :
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
ng cao AH c
(O) theo th t t ng th ng 2
t nhau t i K. = MC.MD.
a/ Ch ng minh: t nh t.
b/ Ch ng minh: AB.AD = AE.AC
c/ Ch ng minh: t i ti p
0: Cho MAB minh
g
:
.
m
minh:
MH. 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 T
A AB, AC (B,
C
tuy NHD.
: ( .
a/
.
. b/
2
= AN.AM
: Cho
: Cho
. .
b/
.
2
= IA.IB
: : Cho
R). .
n
.
b/ AB2 = AD.AE = OA2 R2.
DEF.
- d/ Tia AO
6: ABC (AB < ABC
. S AHG 2S AOG .
: Cho ; R).
AB,
.
b/
ABC. 2
= AH.AO
7: ABC (AB <
R) : ABC (AB <
.
.
b/
. a/ C minh:
b/
d/ Cho BC
3
AK = OB2
4
theo R.
8: ABC (AB <
a/ C/minh: BC. : ABC (AB <
minh:
ADB.
e/ C/minh : AH.BC + BH.AC + CH.AB = 4S ABC .
: Cho ; R).
MA,
: ABC (AB <
. h AF.
b/ IA2 = ID.IB. minh:
c/ C/minh: AMN.
: ABC (AB <
A
G CH.CN theo R.
a/
- : ABC (AB < n
a/
: Cho ; R).
KE.KF = KB.KC
3 a/ C/m: .
b/ Ch
c/ C/minh: AC2
: Cho ; R)
sao cho OA = 2R. AB, AC 1 1 2
AD AE AS
ABC .
ABC. : Cho ; R).
OH.AH = BH.CH.
.
2 2
ID .
OI.OM theo R.
ES EK EQ
1
AS AK CQ
: Cho ; R) /m:
sao cho OS > 2R. SA, SB
: ABC (AB <
.
DC.DA = DO.DM. a/
minh
:
a/ 42:
a/
AMCB
2
= AB.AC DB.DC
2
AHC. = AI2 + AI.AB
- : Cho S FBE
: Cho
.
minh: CN b/ CB.CM = CF.CD
DA DB DE
.
DR DS DK
:
: ABC (AB <
BC).
a/
.
.
:
R 2 S ABC 2S ADE
: Cho ; R).
S sao cho .
a/ minh: MA.MB = MS.MN
2
.
MB2 = MC.MD.
b/
: Qua ; R)
hai
.
: Cho ; R)
sao cho OM = 2R. MA, MB
AB AC BC
DK DI DH
.
2
b/ MC.MD = 3R . AB BC AC
DK DH DI
- : Cho :
.
.
suy ra: OA EF.
: ABC (AB < AC)
.
: Cho ; R).
2
. (
.
.
,F
2
. = ID.IB
CDE. c/
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
. minh: AB2 + AC2 4AH.AM
: Cho ABC (AB < AC) .
AI .MB
R
MA .
minh:
:
0
:
a
BF song
nguon tai.lieu . vn
