Tài liệu 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 .