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 = cm 8/ AB = 6cm, HC = 5cm A: (DE>DF) cao DE EK 1/ CM: 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) AE AB = AF AC AB AE = BH HC CA FA = BH HC HB HC = EA EB + FA FC B + cos2C tanB.tanC D CM: FB.FD = KD.KC 8/ CM: FK FE = DK DC A: 1/ sin 400 , cos 280 , sin 650 , cos 880 , cos 200 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 ABC A: BC = 10cm 1/ = 8cm; AC ( D AB, E AC) EC = AC3 BD A: 2/ 3/ , CH CM: AD AB = HB HC minh: AH AK = BH BC A: DE = 6cm,DF = 8cm,EF = 10cm = HK HI A: AC = 40 cm 3/ CM: CI cosC BC 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 B: AB 1/ CM: AC AH 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 : HA HI = BM BA 8/ CM: BH BC = AH AI B: B: = 9cm, BC =15cm B: MN = 12cm, MP = 20cm B: DE = 20cm, DF = 24cm 1/ sin2110 + sin2150 + sin2320 + sin2790 + sin2750 + sin2580 2/ sin2150 + sin2750 sin2250 + sin2350 + sin2550 3/ sin2250 + sin2650 + tan120 cot780 sin2650 cot 430 tan 470 tan 54 4/ 2cot37 cot53 + sin 28 + sin2620 cot 36 m,AC =8cm cos 480 5/ cos2640 + cos2260 4cot310.cot590 sin 420 cot 32 6/ sin2250 + sin2250 tan350 + cot550 tan 580 0 0 7/ tan1 tan2 tan3 B: b/ 1/ sin 500 , cos 350 , sin 250 , cos 150 , sin 150 0 21, cot 570 , tan 800 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/ Cho < < 900 = , tan , cot = , 2/ Cho < < 900 tan , cot B: B: BH BQ cosB AB 1/ cos2 B: + tan2(900 + cos(900 ) + sin ) cos + sin2 sin ) + sin2 2/ sin(900 + sin2 tan2 tan2 3/ (cos sin )2 + (cos + sin )2 (cos sin ) (cos sin ) 4/ cos sin 5/ (tan460 + cot460)2 (tan460 cot460)2 sin cos 7/ 6/ sinx sinxcos2x sin cos 6 2 8/ sin + cos + 3sin cos B: Cho tan sin cos = = cos sin sin 3sin cos cos 4/ 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/ 15B: 1/ CM: cm,AC=4,5cm,BC=7,5cm 16B: AC=12cm minh: AH AI = CH BC = HK HI B: (D AC) CE = BCcos ABC Suy AB2 = BH.BC BC, AH a) AD AB = AE AC b) BA DA = HB HC c) EA CA = BH HC B + sin2C tanB.tanC B: 4/ Cho = BD CE BC AB AC = 300 AC AMN ACB c B; 22B: AC CM: 1/ 3 BD CE , DC F CM: AH BH AE BE B: = 20cm, AC = 16cm B: AC = cm AB (E 23B: AD=8cm,DC=15cm = 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/ DF ( A DE, B DF) = BC.BE.CF CM: AE.AB = AF 5B: cao AH (AB < AC) AB AC 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 CH BC = 8B: ABC v = 5cm, BC) BC tan B tan B tan C 0 3: ? 4: ? 5: ? 6: 7: bay ? 0 8: ? 1000m ? e/ C/m: AF // OB Cho 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 f/ C/m: = 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 (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 = AE.AD H C/m MCD minh: BD // OK = KC.KD KD = 900 a/ C/ C/m: BD // OA c/ Cho AC = R 22: Cho R b/ C minh: AB=2 Cho n = 900 AC.BD theo R hai 64.MN2 + CD2 = 16R2 B; CA > = 900 CD = AC + BD -R2 : = DK.DC = 900 Suy AC.BD = R2 : Cho ( minh: AE.AD = AH.AO ABC : hai b/ HA.HO = HB.HC mi : ABC : = AC.BC.sinA.sinB D) C/m: AE.AD=AH.AO minh: IA.BK = R2 : Cho = 2.OC.OF (O; R) : a/ Ch c/ AB = BD.OA .tanEBD d/ Chu vi N CH.sinC (O,R), KB < KC, i ti 1200 Cho tam (O,R), EF < FD, KC Cho KBD BD m: AB Cho i ti 120 DB FE e/ Cho DB ABC BD C/minh: FE OA Cho C/m: DE OC b/ C/m: T EF // IK KA // MI e/ e/ ABC ABM EB = CB.AB BCK BF = CB.AB CA BA minh: DE//MN ABIC theo R AB (O; CH EDB ABMC theo R 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 = AE.AF : a/ b/ a/ b/ Il minh: c/ c/ ng minh: AE.AF = AI.AK d/ ABC : : Cho KCD a/ b/ c/ d/ : e/ Cho DE = : a/ minh: EH BD = ED HF CE (H c/ AQ AM = 3R2 C : Cho ABC (AB < AC) n i ti ng cao AH c (O) theo th t t t t i K ng th ng a/ Ch ng minh: t b/ Ch ng minh: AB.AD = AE.AC i ti p c/ Ch ng minh: t 0: Cho : ng = MC.MD nh t MAB g minh : MH m 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 A C : Cho A AB, AC T (B, NHD : ( a/ b/ = AN.AM : Cho : Cho b/ R) = IA.IB : : Cho n b/ DEF AB2 = AD.AE = OA2 R2 d/ Tia AO 6: ABC (AB < S 2S AHG AOG : Cho ABC ; R) AB, b/ ABC R) 7: ABC (AB < b/ : d/ Cho BC theo R 8: a/ C minh: = OB2 ABC (AB < a/ C/minh: : BC e/ C/minh : AH.BC + BH.AC + CH.AB = 4S : Cho MA, ABC ; R) : : G a/ IA2 = ID.IB ABC (AB < minh: ADB b/ c/ C/minh: ABC (AB < b/ AK = AH.AO ABC (AB < minh: ABC (AB < A CH.CN theo R h AF AMN : n ABC (AB < a/ : Cho ; R) KE.KF = KB.KC a/ C/m: b/ Ch c/ C/minh: AC2 : Cho cho OA = 2R ; R) AB, AC ABC ABC AD AE AS : Cho ; R) OH.AH = BH.CH ES AS : Cho cho OS > 2R EK AK ID EQ CQ OI.OM theo R ; R) SA, SB /m: : ABC (AB < DC.DA = DO.DM a/ minh : a/ 42: a/ AMCB AHC = AB.AC DB.DC = AI2 + AI.AB : Cho S FBE : Cho b/ minh: CN CB.CM = CF.CD DA DR DB DS DE DK : : ABC (AB < BC) a/ R S : Cho b/ ABC 2S : ADE ; R) S cho minh: MA.MB = MS.MN a/ MB2 = MC.MD hai : Qua ; R) : Cho cho OM = 2R b/ ; R) MA, MB MC.MD = 3R AB DK AB DK BC DH AC DI AC DI BC DH : Cho : suy ra: OA EF : ABC (AB < AC) : Cho ( ; R) ,F c/ CDE O R) = ID.IB CHK cho : ABDE b/ : minh: R AHE theo R : MN = MD ABC R : AQT : Cho a/ Ch minh: MB2 = MD.MA : : Cho AI MB MA minh: : : a BF song R minh: AB2 + AC2 : Cho 4AH.AM ABC (AB < AC) ... // OK = KC.KD KD = 90 0 a/ C/ C/m: BD // OA c/ Cho AC = R 22: Cho R b/ C minh: AB=2 Cho n = 90 0 AC.BD theo R hai 64.MN2 + CD2 = 16R2 B; CA > = 90 0 CD = AC + BD -R2 : = DK.DC = 90 0 Suy AC.BD = R2... = , 2/ Cho < < 90 0 tan , cot B: B: BH BQ cosB AB 1/ cos2 B: + tan2 (90 0 + cos (90 0 ) + sin ) cos + sin2 sin ) + sin2 2/ sin (90 0 + sin2 tan2 tan2 3/ (cos sin )2 + (cos + sin )2 (cos sin ) (cos... 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/ Cho < < 90 0 = , tan , cot = , 2/ Cho < < 90 0 tan