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
2
8/ AB = 6cm, HC = 5cm. A: (DE>DF) cao
2
1/ CM: DE DF EK FK
CM: DA . DE = KE . KF CM: DA . DE = DB . DF
3
4/ CM: KE . KF = AD . AE + BD . BF 5/ CM: AB3 = EF . AE . BF
6/ CM: AE BF DE DF a) AE . AB = AF . AC. b) AB . AE = BH . HC c) CA . FA = BH . HC d) HB . HC = EA . EB + FA . FC 2B + cos2C tanB.tanC
D. CM:
0
= 8cm; FB.FD = KD.KC. 8/ CM: FK . FE = DK . DC A: A: BC = 10cm. 1/
3 . EC = AC3 . BD
AC ( D AB, E AC).
1/ sin 400 , cos 280 , sin 650 , cos 880 , cos 200 2/ tan 320 0 0 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 A:
, CH CM: AD . AB = HB . HC. ABC. 2/ 3/
2 = HK . HI
minh: AH . AK = BH . BC
A: DE = 6cm,DF = 8cm,EF = 10cm.
cm CI 3/ CM: BC . A: AC = 40 BQ cosB cosC
2
2/ K CM: AB.AQ = AI.AC.
021, cot 570
0, tan 800
B: B:
1/ sin 500 , cos 350 , sin 250 , cos 150 , sin 150 2/ cot 240 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 2
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. 1/ Cho 0 < < 900 = ,
2
B: AH tan , cot .
1 2
2
2/ Cho 0 < < 900 = , 1/ CM: . AB AC BH CH . tan , cot B: CM: BH . HC = AN . AC CM: AM . AB = AN . AC
3
4/ CM: HB . HC = MA . MB + NA . NC 5/ CM: MN3 = BC . BM . CN
MB NC
AB AC
sin2250 + sin2350 + sin2550 sin2650 6/ CM: 1/ sin2110 + sin2150 + sin2320 + sin2790 + sin2750 + sin2580 2/ sin2150 + sin2750
0 2 cot 43 0 tan 47
0
3/ sin2250 + sin2650 + tan120 cot780 :
4/ 2cot370 . cot530 + sin2280 + sin2620 HA . HI = BM . BA 8/ CM: BH . BC = AH . AI tan3 cot 54 0 36
0
B: m,AC =8cm 5/ cos2640 + cos2260 4cot310.cot590
0
0 2 cos 48 0 sin 42 cot 32 tan 58
0
B: 6/ sin2250 + sin2250 tan350 + cot550
7/ tan10 . tan20 . tan30 B: BH B: B: AB 1/ cos2 sin ) + sin2 = 9cm, BC =15cm. + tan2(900 ) + 1
2
2
b/ + cos(900 1 2 sin + sin2 ) cos + sin2 tan2 . B: )2 MN = 12cm, MP = 20cm. 2/ sin(900 tan2 3/ (cos (cos sin )2 + (cos sin (cos + sin sin
)
4/
) cos
sin.
4
4
5/ (tan460 + cot460)2 (tan460 B: DE = 20cm, DF = 24cm. 6/ sinx sinxcos2x 7/ cot460)2 sin sin cos cos 8/ sin6 + cos6 + 3sin2 cos2
3 . BF = DF3 . AE
1 2 2
2
2
2
4/ B: Cho tan = = sin sin3 cos2 cos4
B:
sin2 cos 4
cos3 sin5
, CH , C. CM: AC . AE = HB . HC. 2/
14B: 1/ AC = 10cm, 2/ AB = 10cm, 3/ BC = 20cm, 4/ AB = 21cm, AC = 18cm minh: AH . AI = CH . BC
2 = HK . HI
15B: cm,AC=4,5cm,BC=7,5cm 1/ CM:
16B: AC=12cm
2
2
B: AB (E
3B;
3 = BD . CE . BC.
3
EA BE AH BH B: AC). = 20cm, AC = 16cm. (D CE = BCcos3
DB CE AB AC , DC.
ABC. Suy ra AB2 = BH.BC 4/ Cho = 300
22B: B: AC = 3 cm AC. AMN BC, AH. ACB.
23B: AD=8cm,DC=15cm AC. CM:
2 = MN . MI
1 2 c
a) AD . AB = AE . AC. b) BA . DA = HB . HC c) EA . CA = BH . HC 2B + sin2C tanB.tanC 4B:
3 = BC.BE.CF
F. CM: AB = 9cm, AC = 12cm. ABC , BH, CH. 2/ B: 1/ EF=70cm,DF=30cm . a) X = 3sin2B + 2sin2C 5tanB.tanC b) Y = cos2(900 B) + cos2B + 7cotB.cotC 3/ DF ( A DE, B DF). CM: AE.AB = AF. 4
2
2
(AB < AC) 5B: cao AH. ABC. 7B: =40cm ; BH = BCcos2B BH CH AB AC 2C. , AC = 58cm, BC = 42cm. 1/ sao?
2
3/ Cho AB = 120cm; AC = 160cm. AH, BH, . 6B:
2
8B: ABC v = 5cm, AN AH CN CH BC = BC)
MAH MNH .
tan
3/ CM: AH .
CH
BC B cot cotC
BC B
B tan
tan
C
0
0
0
0
3: ?
0
4: ?
0
5:
0
? 6:
0
7: bay ?
0.
8:
.
0
?
1000m ?
.
.
2.
e/ C/m: AF // OB. Cho
160cm2 CK.CA=CF.CD.
minh: OA
IN. BD
AMN. e/ Qu ID=IM
HM.
inh: ME . MF = MH . MO.
BH.AM. Cho 9:
2 = 4HO.HM.
2
b/ C
MAB.
minh: CH . DM = DH . CM. f/ C/m: BC = 1200. C/m: SAOBC = SMACB.
2.
. AD = AH . AO.
(NH 06-07)
AC. = 900.
2
theo R
(NH 05-06) minh: AM // NK. =
a/ C/m:
AFB. Suy ra: BE.CF = BF.CE.
MNC
DM = DK. a/
2 = AE.AD.
AC.CD = CK.AO.
minh: MH.NA = MA.NH.
2-R2
H. C/m
MCD.
2 = KC.KD.
minh: BD // OK.
2
. KD.
= 900. a/ C/ C/m: BD // OA.
c/ Cho AC = R 3 22: Cho R 2
b/ C
minh:
Cho n AB=2
CD = AC + BD. hai = 900 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 :
2 = AC.BC.sinA.sinB.
ABC. :
2 = 2.OC.OF.
D). C/m: AE.AD=AH.AO minh: IA.BK = R2.
: Cho : (O; R)
2 = BD.OA.
a/ Ch
c/ AB .tanEBD N d/ Chu vi CH.sinC.
i ti Cho tam i ti
(O,R), EF < FD, 1200 DB (O,R), KB < KC, 1200
KC FE KBD e/ EDB BD DB Cho ABC Cho
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.
ABMC theo R. ABIC 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
:
2 = AE.AF
MN. C/minh: MB
:
a/ b/ I l a/ b/ minh:
c/ ABC. c/
ng minh: AE.AF = AI.AK. : d/
: Cho KCD.
a/ b/
c/ . : d/
1 2
e/ Cho DE = .
: 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 = MC.MD.
t nhau t i K.
nh t.
a/ Ch ng minh: 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 AB, AC T (B, A C
tuy NHD.
2 = AN.AM
: . ( a/ . . b/
: Cho
: Cho
. . b/
2 = IA.IB
.
: : Cho R). .
n . b/ AB2 = AD.AE = OA2 R2.
DEF.
d/ Tia AO
ABC 6: ABC (AB < .
S
2
S
AHG
AOG
.
: Cho ; R). AB, .
b/
2 = AH.AO
ABC.
7: ABC (AB < R) : ABC (AB < . . b/ . a/ C minh:
b/ = OB2 d/ Cho BC AK 3 4 theo R.
8: ABC (AB <
: ABC (AB < a/ C/minh: BC.
minh: ADB.
.
S
e/ C/minh : AH.BC + BH.AC + CH.AB = 4 ABC
: Cho ; R). MA,
: ABC (AB <
h AF. . minh: IA2 = ID.IB. AMN. b/ c/ C/minh:
: ABC (AB <
A CH.CN theo R. G a/
n : ABC (AB <
a/ : Cho ; R).
KE.KF = KB.KC
3
.
a/ C/m: b/ Ch c/ C/minh: AC2
: Cho sao cho OA = 2R. ; R) AB, AC
1 1 AD AE 2 AS ABC . : Cho ; R). ABC.
OH.AH = BH.CH.
2
. ID2. OI.OM theo R.
1
ES EK EQ AS AK CQ
/m: : Cho sao cho OS > 2R. ; R) SA, SB
: ABC (AB <
.
DC.DA = DO.DM. a/
minh
:
a/ 42:
a/
AMCB
2 = AB.AC DB.DC 2 = AI2 + AI.AB
AHC.
FBE
: Cho S
: Cho
. b/ CB.CM = CF.CD minh: CN
. DA DB DE DR DS DK
:
: ABC (AB < BC). a/ . .
:
2R
S
2
S
ABC
ADE
2.
: Cho ; R). . S sao cho a/ minh: MA.MB = MS.MN
MB2 = MC.MD. b/ ; R) : Qua hai
.
; R) : Cho sao cho OM = 2R. MA, MB
AB AC BC DK DI DH
. b/ MC.MD = 3R2.
AB BC AC DK DH DI
: Cho :
. .
suy ra: OA EF.
2.
: ABC (AB < AC) . ; R). : Cho ( . .
2 = ID.IB
, F
.
c/ CDE.
O
CHK. sao cho : . R). : ABDE
minh: b/
3R
. AHE theo R : MN = MD. ABC.
2R
AQT. : Cho .
: a/ Ch
minh: MB2 = MD.MA
. .
: Cho :
. minh: AB2 + AC2 4AH.AM
: Cho ABC (AB < AC) .
R .AI MB MA . minh:
0
:
:
a
BF song
