Hunh Minh Khai: Trng THCS Th Trn Cu K, Tr Vinh NHNG KIN THC TRNG TM MN TON 9, A. I S 1.Chng I: CN BC HAI. CN BC BA. * NI DUNG CHNG TRNH: - Cn bc hai: nh ngha, k hiu, iu kin tn ti. Hng ng thcA A =2. - Khai phng mt tch. Nhn cc cn thc bc hai. Khai phng mt thng. Chia hai cn thc bc hai. - Khai phng bng my tnh b ti. - Bin i n gin biu thc cha cn thc bc hai. - Khi nim cn bc ba. * MC , YU CU: Hcsinhnmcnhnghacnbchai,khiucnbchaishc, iu kin tn ti cn bc hai, cc tnh cht, quy tc tnh v bin i trn cc cn bc hai. Hiu c nh ngha cn bc ba. C k nng tnh nhanh, ng cc php tnh trn cc cn bc hai, k nng thc hin cc php bin i n gin, rt gn cc biu thc cha cn thc bc hai (ch xt cc trng hp n gin). Bit khai phng bng my tnh b ti.I. Cn bc hai. Hng ng thcA A =2. * CC DNG BI TP C BN (yu cu hc sinh phi lm c). BI 6. SGK tr10: Vi gi tr no ca a th mi cn thc sau c ngha: a) 3a ; b) a 5 ; c) a 4; d) 7 3 + a BI 8. SGK tr10: Rt gn cc biu thc sau a)( )23 2 ; b) ( )211 3 ;c) 22avi a> 0;d) 32( 2) a vi a < 2. * CC DNG BI TP NNG CAO.BI 15. SBT tr 4: Chng minh b)9 4 5 5 = - 2c) 2(4 7) 23 8 7 =

BI 21. SBT tr 6 :Rt gn biu thc d) x 4 216 8x x +vi x >4 BI 11. TP I Tc gi: V HU BNH, NXB GIO DC. Rt gn cc biu thc:

a)10 2 11;b)3 2 4 3 2 4 +; c)7 4 7 4 + + ; d) 10 2 7 5 2 6 26 2 5 2 6 11 3+ + ++ + +; Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.Hunh Minh Khai: Trng THCS Th Trn Cu K, Tr Vinh e)3 4 7 10 48 5 3 5 + + ;g) 5 2 10 4 5 2 10 4 + + + +; II. Lin h gia php nhn, chia, php khai phng. * CC DNG BI TP C BN (yu cu hc sinh phi lm c). BI 17. SGK tr14: Tnh a)0, 09.64b) 4 22 .( 7) c)12,1.360 BI 18. SGK tr14: Tnh a)7. 63 b)2, 5. 30. 48 c)0, 4 6, 4 BI 19, 20. SGK tr15:Rt gn biu thc 19a) 20, 36avi a < 019c) 227.48(1 ) a vi a > 1 20a) 2 3.3 8a a vi a> 020b) 5213 . aa vi a > 0 * CC DNG BI TP NNG CAO. BI 30. SBT tr7:Cho biu thc A =2. 3 x x + v B =( 2)( 3) x x + . a)Tm x A c ngha.Tm x B c ngha. b)Vi gi tr no ca x th A = B. III. Bin i n gin, rt gn biu thc cha cn bc hai. * CC DNG BI TP C BN (yu cu hc sinh phi lm c). BI 51. SGK tr30: Trc cn thc mu vi gi thit cc biu thc ch iu c ngha: a) 1 33+ ; c) 3 23 2+;d) bb+ 3 BI54.SGKtr30:Rtgn biuthcvigithitccbiuthcch iuc ngha a)2 21 2++b) 15 51 3c) 1a aa BI 58. SGK tr32:Rt gn cc biu thc sau a)5 2021515 + + ; b)5 , 12 5 , 421+ + c)72 18 3 45 20 + + ; d) 50 . 4 , 0 08 , 0 . 2 200 . 1 , 0 + +Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.Hunh Minh Khai: Trng THCS Th Trn Cu K, Tr Vinh BI 60. SGK tr33: Cho biu thc 1 4 4 9 9 16 16 + + + + + + = x x x x B ,vi x> -1.a)Rt gn biu thc B;b)Tm x sao cho B c gi tr l 16. BI 71. SGK tr40: Rt gn a)( ) 5 2 10 2 3 8 + ; b)( ) ( )225 3 2 3 . 10 2 , 0 + BI 74. SGK tr40: Tm x, bit:a)( ) 3 1 22= xb)x x x 15312 15 1553= BI 84. SBT tr16: Tm x, bit: a) 44 20 3 5 9 5 63x x x + + + + =b) 15 125 25 6 12 9xx x = + * CC DNG BI TP NNG CAO. BI 64. SBT tr12:a)Chng minh ( )22 2 4 2 2 + = + x x x vix> 2 ;b)Rt gn biu thc 4 2 2 4 2 2 + + x x x xvix> 2 . BI 66. SBT tr13: Tm x, bit: 0 3 3 92= x x BI 86. SBT tr16:Cho biu thc ||.|

\|++ |.|

\|=1221 111aaaaa aQa)Rt gn Q via > 0, a=4 v a=1 b)Tm gi tr ca a Q dng. BI 103. SBT tr19:Chng minh 432112+|.|

\| = + x x xvi x > 0.T , cho bit biu thc11+ x x c gi tr ln nht l bao nhiu? Gi tr t c khi x bng bao nhiu? Chng II: HM S BC NHT. * NI DUNG CHNG TRNH:Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.Hunh Minh Khai: Trng THCS Th Trn Cu K, Tr Vinh - Nhc li v hm s. Hm s bc nht. - th cu hm sy = ax + b (a=0). - H s gc ca ng thng. Hai ng thng song song, hai ng thng ct nhau. *MC , YU CU:Hc sinh nm c cc kin thc c bn v hm s bc nhty = ax + b (a =0)(tpxcnh, tnhbinthin,th),ngha cch savb,cc iu kin song song, ct nhau ca hai ng thng, c v v thnh tho th hm s y = ax + b (vi cc h s a, b ch yu l cc s hu t). * DNG BI TP C BN:(yu cu hc sinh phi lm c). BI 9. SGK tr48: Cho hm s bc nhty = (m-2)x + 3. Tm cc gi tr ca m hm s:a)ng bin ;b) Nghch bin. BI 14. SGK tr48:Cho hm s bc nht y = (1 -5 )x 1 a)Hm s ny ng bin hay nghch bin trn R ? v sao ? b)Tnh gi tr a y khi x = 1 +5c)Tnh gi tr ca x khi y =5

BI 16. SGK tr51:a) V th cc hm s y = xvy = 2x + 2 trn cng mt mt phng to .b) Gi A l giao im ca hai th ni trn, tm to im A.c)VquaimB(0;2)mtngthngsongsongvitrcOx,ctng thng y = x ti im C. Tm to im C ri tnh din tch tam gic ABC (n v o trn cc trc to l xentimt).

BI 23. SGK tr55:Cho hm s y = 2x + b. Hy xc nh h s b trong mi trng hp sau:a) th ct trc tung ti im c tung bng -3;b) th ca hm s cho i qua im A(1:5). BI 33. SGK tr61:Vi nhng gi tr no ca m th th cc hm sy = 2x+(3+m) v y = 3x+(5-m) ct nhau ti mt im trn trc tung?

BI 34. SGK tr61:Tm gi tr caa hai ng thng y = (a-1)x+2(a = 1)v y = (3-a)x+1 (a = 3) song song vi nhau. * CC DNG BI TP NNG CAO. Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.Hunh Minh Khai: Trng THCS Th Trn Cu K, Tr Vinh BI 35. SGK tr61:Xc nhkv m hai ng thng sau y trng nhau: y = kx+(m-2)(k= 0) ; y = (5-k)x+(4-m) (k= 5).

BI 38. SGK tr62:a)V th cc hm s sau trn cng mt mt phng to : y = 2x(1);y = 0,5x (2);y = -x + 6(3). b) Gi cc giao im ca cc ng thng c phng trnh (3) vi hai ng thng c phng trnh (1) v (2) theo th t l A v B. Tm to ca hai im A v B.c) Tnh cc gc ca tam gic AOB. Hng dn cu c) Tnh OA, OB ri chng t tam gic OAB l tam gic cn.Tnh x O B x O A B O A = . Chng III: H HAI PHNG TRNH BC NHT HAI N. * NI DUNG CHNG TRNH: - Phng trnh bc nht hai n. - H hai phng trnh bc nht hai n. H phng trnh tng ng. - Gii h phng trnh bng phng php th, phng php cng i s. - Gii bi ton bng cch lp h phng trnh bc nht hai n.*MC , YU CU: Hcsinhnmvngcchgiihphngtrnhbcnhthainbngphng php cng v phng php th; gii thnh tho cc h phng trnh bc nht hai nkhngchathamsv bitcchgiiccbi ton thct bngcchlph phng trnh. I. H hai phng trnh bc nht hai n * DNG BI TP C BN:(yu cu hc sinh phi lm c). BI 12. SGK tr15:Gii cc h phng trnh sau bng phng php th:a)x y = 3b) 7x 3y = 5c) x + 3y = -23x 4y = 24x +y = 25x 4y = 11 BI20. SGKtr19:Giicchphngtrnhsaubngphngphpcngi s: a) 3x + y = 3 b) 2x +5y = 8c) 4x + 3y = 6 2x y = 7 2x 3y = 0 2x + y = 4 BI 24. SGK tr19:Gii cc h phng trnh :a)2(x+y) + 3(x-y) = 42(x-2) + 3(1+y) = -2 (x+y) + 2(x-y) = 3.3(x-2) 2(1+y) = -3 Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.Hunh Minh Khai: Trng THCS Th Trn Cu K, Tr Vinh * CC DNG BI TP NNG CAO. BI 24. SBT tr7: Gii cc h phng trnh sau bng cch t n s ph: a) 54 1 1= +y xb) 51 1 1= +y x 85 1 1=++ y x y x

83 1 1 =+ y x y x BI 34. SBT tr9: Gii h phng trnh:3x + 5y = 34 4x 5y = - 13 5x 2y = 5 BI 33. SBT tr9: Tm gi tr ca m ng thng (d): y = (2m 5)x 5m i qua giao im ca hai ng thng (d1); 2x + 3y = 7 v (d2): 3x + 2y = 13 Bi tp b sung Cho h phng trnh(m 1)x y = 2 mx + y = m a) Gii hpt vi m =2b)Xcnhgitrcamhphngtrnhcnghimduynhtthamn iu kin x + y >0. Bi tp b sung( 210/12 V Hu Bnh ) Tm gi tr ca m nghim ca h phng trnh sau l cc s dng: x y = 2 mx + y = 3 II. Gii bi ton bng cch lp h phng trnh

BI 35. SBT tr9: Tng ca hai s bng59. Hai ln ca s ny b hn ba ln ca s kia l 7. Tm hai s . BI 40. SBT tr10: Mtsntrnghnhchnhtcchuvi340m.Balnchiudihnbnln chiu rng l 20m. Tnh chiu di v chiu rng sn trng. BI 42. SBT tr10:Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.Hunh Minh Khai: Trng THCS Th Trn Cu K, Tr Vinh Trong phng hc c mt s gh di. Nu xp mi gh 3 hc sinh th 6 hc sinh khngcch.Nuxpmigh4hcsinhththamtgh.Hilpcbao nhiu gh v bao nhiu hc sinh? BI 44. SBT tr10: Hai ngi th cng xy mt bc tng trong 7 gi 12 pht th xong (vi va v gchccngnhnkhcvnchuyn).Nungithnhtlmtrong5giv ngi th hai lm trong 6 gi th c hai xy c bc tng. Hi mi ngi lm mt mnh th bao lu xy xong bc tng? 2.Chng IV: HM S y = ax2 (a=0). PHNG TRNH BC HAI MT N. * NI DUNG CHNG TRNH: - Hm sy = ax2 (a=0). th. -Phngtrnhbchaimtn.Cngthcnghim.HthcVi-tvpdng (tnh nhm nghim, tm hai s bit tng v tch ca chng). - Phng trnh quy v phng trnh bc hai mt n. - Gii ton bng cch lp phng trnh bc hai mt n. *MC , YU CU: Hc sinh nm c cc kin thc c bn v hm sy = ax2(a=0) (tp xc nh, tnh cht bin thin, th), v c th ca hm s y = ax2. Nm vngcngthcnghimvgii thnh thocc phngtrnhbchai mt n. Bit s dng h thc Vi-t tnh nhm nghim v tm hai s bit tng v tch ca chng. Bit gii cc phng trnh quy v phng trnh bc hai (ch xt cc trng hp n gin: bin i v tri v dng tch cc nh thc bc nhtv tamthcbchai(vphi bng 0); phngtrnhc nmu(mu lnhthc bc nht) v cha khng qu hai phn thc; phng trnh trng phng). Bit gii cc bi ton bng cch lp phng trnh bc hai mt n (ch n cc bi ton c ni dung thc t v ni dung gn vi cc mn hc khc). I.HM S y = ax2 (a=0) *CC DNG BI TP C BN (yu cu hc sinh phi lm c).

Bi tp b sung . Cho hm s y = ax2, bit th ca n i qua im A( 1; - 1) a) Tm h s ab) V th vi gi tr a va tm c cu a) c) Tm im thuc parabol c tung bng 3. Bi 9. SGKtr39 Cho hm s y = 13x2 v y = - x + 6. a) V th ca cc hm s ny trn cng mt mt phng ta . b) Tm ta cc giao im ca hai th ( bng phng php i s ) * CC DNG BI TP NNG CAO.Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.Hunh Minh Khai: Trng THCS Th Trn Cu K, Tr Vinh Bi 11 tr 38 SBT. Cho hm s y = ax2 a) Xcnh hsa,bitrngthcan ctngthngy=-2x+3ti im A c honh bng 1. b)V ng thng (d): y = - 2x + 3 v parabol (P): y = ax2 vi gi tr ca a va tm c cu a) trn cng mt mt phng ta . c) Da vo th hy xc nh ta ca giao im th hai ca hai th va v. II. PHNG TRNH BC HAI MT N. PHNG TRNH QUI V PT BC HAI * CC DNG BI TP C BN (yu cu hc sinh phi lm c). Bi tp b sung. Gii cc phng trnh vi n s x sau y a) x2-4x+3=0b)-8x2+7x+15=0c) 2x2-6x+1=0 d) x2+6x-16=0 e)7x2+12x+5=0g) x2-6x-7=0 h)3 x2+(1- 3 )x-1=0 i) 4321x2 + 21x 4300 = 0. BI 34. SGK tr56: Gii cc phng trnh trng phng: a)x4 5x2 + 4 = 0;b) 2x4 3x2 2 = 0;c) 3x4 + 10x2 + 3 = 0. BI 35 SGK tr56: Gii cc phng trnh:a)( )( )( ) x xx x = + +1 233 3 ;b) x xx= ++26352;c) ( )( ) 2 12142+ ++ =+ x xx xx. BI 36. SGK tr56: Gii cc phng trnh:a)(3x2 5x + 1)(x2 4) = 0 ;b) (2x2 + x 4)2 (2x 1)2 = 0. BI 24. SGK tr50: Cho phng trnh (n x):x2 -2(m 1) + m2 = 0 a)TnhA b)Vi gi tr no ca m th phng trnh c hai nghim phn bit? c nghim kp? V nghim? * CC DNG BI TP NNG CAO. BI 50. SBT tr46: Gii cc phng trnh sau bng cch t n ph:Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.Hunh Minh Khai: Trng THCS Th Trn Cu K, Tr Vinh b)( ) ( ) 0 8 1 3 2 1 3222= + + + x x x x ;e) ( )0 3151222= +++ xxxx; f) 0 3 1 = x x .

III. Phng trnh bc hai, h thc Vi-t. * CC DNG BI TP C BN (yu cu hc sinh phi lm c). BI 28. SGK tr53: Tm hai suvvtrong mi trng hp sau: a)u + v = 32,uv = 231 b)u + v = 8 ,uv = 105c)u + v = 2 ,uv = 9. BI 30. SGK tr54: Tm gi tr cam phng trnh c nghim, ri tnh tng v tch cc nghim theom.a)x2 2x + m = 0; x2 + 2(m1)x + m2 = 0. BI 40. SBT tr44: Dng h thc Vi-t tm nghim x2 ca PT ri tm gi tr ca m trong cc trng hp sau: a) PT x2 + mx 35 = 0, bit nghim x1 = 7 c) PT 4x2 + 3x m2 + 3m = 0, bit nghim x1 = -2 * CC DNG BI TP NNG CAO. BI 62. SGK tr64: Cho phng trnh7x2 + 2(m 1)x m2 = 0.a)Vi gi tr no camth phng trnh c nghim?b)Trong trng hp phng trnh c nghim, dng h thc Vi-t, hy tnh tng cc bnh phng hai nghim ca phng trnh. BI 44. SBT tr44: Cho phng trnh x2 6x + m = 0. Tnh gi tr ca m, bit rng phng trnh c hai nghim x1; x2 tho mn iu kinx1 x2 = 4. BI 71. SBT tr49: Cho phng trnhx2 2(m+1)x + m2 + m 1= 0.a)Tm cc gi tr cam phng trnh c nghim.b)Trong trng hp phng trnh c nghim lx1;x2hy tnh theom :x1 + x2;x1x2 ;x12 + x22 . IV. Gii bi ton bng cch lp phng trnh BI 45. SGK tr59: Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.Hunh Minh Khai: Trng THCS Th Trn Cu K, Tr Vinh Tch ca hai s t nhin lin tip ln hn tng ca chng l109. Tm hai s . BI 46. SGK tr59: Mt mnh t hnh ch nht c din tch240m2. Nu tng chiu rng3m v gim chiu di4m th din tch mnh t khng i. Tnh kch thc Ca mnh t. BI 49. SGK tr59: Hai i qut sn mt ngi nh. Nu h cng lm th trong 4 ngy xong vic. Nu h lm ring th i I hon thnh cng vic nhanh hn i II l 6 ngy. Hi nu lm ring th mi i phi lm trong bao nhiu ngy xong vic? BI 52. SGK tr60: Khong cch gia hai bn sng A v B l 30km. Mt can i t bn A n bn B, ngh 40 pht bn B ri quay li bn A. K t lc khi hnh n khi v ti bn A ht tt c 6 gi. Hy tm vn tc ca can trong nc yn lng, bit rng vn tc nc chy l 3km/h. B. HNH HC CHNG I. H THC TRONG TAM GIC VUNG: I. H THNG KIN THC H thc gia cnh v ng cao trong tam gic vung: *, 2 , 2. ; . c a c b a b = = *2 2 2c b a + =* , , 2.c b h =*, ,c b a + =*c b h a . .=* , , 21 1 1c b h+ =*,,22,,22.;bcbccbcb= = H thc gia cnh v gc trong tam gic vung: T s lng gic ca gc nhn: Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.Hunh Minh Khai: Trng THCS Th Trn Cu K, Tr Vinh ; ; ;D K D KSin Cos Tan CotH H K D= = = = Tnh cht ca t s lng gic: 1/ Nu 090 = + | oTh: | o| oSin CosCos Sin== Tan CotCot Tano |o |== 2/Vi onhn th 0 < sino< 1, 0 < coso< 1 *sin2 o+ cos2 o= 1 ; *tano= sinocoso; *coto = cososino ;*tano . coto =1 H thc gia cnh v gc trong tam gic vung: + Cnh gc vung bng cnh huyn nhn Sin gc i:SinC a c SinB a b . .; . = = + Cnh gc vung bng cnh huyn nhn Cos gc k: CosB a c CosC a b . .; . = =+ Cnh gc vung ny bng cnh gc vung kia nhn Tan gc i: b = c. tanB; c = b.tanC+ Cnh gc vung ny bng cnh gc vung kia nhn Cot gc k: b = c. cotC; c = b. cotB II. H THNG BI TP: Bi 6 Trang 69 SGK ng cao ca mt tam gic vung chia cnh huyn thnh hai on c di l 1 v 2. Hy tnh cc cnh gc vung ca tam gic vung ny. Bi 8 Trang 70 SGK : Tm di x, y trong hnh sau: Bi37 SGK tr 94: Cho tam gic ABC c AB = 6cm, AC = 4,5cm, B = 7,5cm. a) C/m tam gic ABC vung ti A. Tnh cc gc B, C v ng cao AH ca tam gic . b) Hi rng im M m din tch tam gic MBC bng din tch tam gic ABC nm trn ng no?Bi 96 SBT tr 105: Cho tam gic AB vung ti A, ng cao AH chia cnh huyn BC thnh hai on BH, HC c di ln lt l 4m, 9cm. Gi D v E ln lt l hnh chiu ca H trn AB v AC. a) Tnh di on thng DE. x94xy1612Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.Hunh Minh Khai: Trng THCS Th Trn Cu K, Tr Vinh b) Cc ng thng vung gc vi DE ti D v ti E ln lt ct BC ti M v N. Chng minh M l trung im ca BH v N l trung im ca CH c) Tnh din tch t gic DENM. CHNG II. NG TRN I. H THNG KIN THC S xc dnh ng trn: -Tm ng trn bit tm v bn knh -Tm ng trn bit bn knh -Tm ng trn qua 3 im khng thng hng * Ch : a ni dung bi 3 tr 100 SGK vo cui bi hc. Cc mi lien h: - Quan h gia ng knh v dy - ng knh vung gc vi dy - ng knh i qua trung im dy khng qua tm - Quan h gia dy v khong cch n tm * Cn lu : Mi lin h gia ng knh v dy dy v khong cch n tm V tr tng i ca ng thng v ng trn: - Ba v tr tng i H thc lin h gia d v R Tip tuyn ca ng trn: - nh ngha tip tuyn - Du hiu nhn bit tip tuyn -Tnh cht 2 tip tuyn ct nhau V tr tng di ng trn: - Ba v tr tng i H thc lin h gia d v R - Quan h gia dy cung v ng ni tm cu hai ng trn ct nhau. II. H THNG BI TP: Bi 12 SGK tr 106: Cho ng trn (O) bn knh 5cm, dy AB = 8cm. a)Tnh khong cch t tm O n dy AB. b)GiIlimthucdyABsaochoAI1cm.KdyCDi quaIv vung gc vi AB. C/m rng CD = AB. Bi 12 SBT tr 130: Cho tam gic ABC cn ti A, ni tip ng trn (O). ng cao AH ct ng trn ti D. a)V sao AD l ng knh ca ng trn (O)? b)Tnh s o gc ACD. Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.Hunh Minh Khai: Trng THCS Th Trn Cu K, Tr Vinh c)ChoBC=24cm,AC=20cm.TnhngcaoAHvbnknhca ng trn (O). Bi 40 SBT tr 133: Cho ng trn (O), bn knh OA, dy CD l ng trung trc ca OA. a)T gic OCAD l hnh g? V sao? b) K tip tuyn ca ng trn ti C, tip tuyn ny ct ng thng OA ti I. tnh di CI bit OA = R Bi 48 SBT tr 134: Cho ng trn (O), im A nm bn ngoi ng trn. K cc tip tuyn AN, AM vi ng trn (M, N l cc tip im). a)C/m OA vung gc vi MN. b)V ng knh NOC. C/m rng MN// OA. c)Tnh di cc cnh ca tam gic AMN bit OM = 3cm,m OA = 5cm. Bi 85 SBT tr 141: Cho ng trn (O), ng knh AB, im M thuc ng trn. V im N i xng vi A qua M, BN ct iong trn ti C. Gi E l giao im ca AC v BM. a)C/m rng NE vung gc vi AB. b) GiF l im i xngvi E quaM. C/mrngFAl tiptuynca ng trn (O). c) C/m rng FN l tip tuyn ca ng trn (B; BA).Bi 88 SBT tr 142: Cho na ng trn O c ng knh AB. Gi M l im bt k thuc na ng trn, H l chn ng vung gc k t M n AB. V ng trn (M; MH). K cc tip tuyn AC, BD vi ng trn tm M (C v D l cc tip im khc H) a)C/m ba im C, M, D thng hng v CD l tip tuyn ca ng trn (O). b) C/m rng khi im M di chuyn trn ng trn (O) th tng AC + BD khng i. c) Gi s CD v AB ct nhau ti I. C/m rng tch OH.OI khng i. CHNG III : GOC VI NG TRON I. H THNG KIN THC 1: Gc tm. S o cung * Lin h gia gc tm v cung b chn. 2: Lin h gia cung & dy *Cc nh l v lin h gia cung v dy. * Ch : a ni dung cc nh l bi 13, 14 SGK tr 72 vo cui bi hc 3: Gc ni tip Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.Hunh Minh Khai: Trng THCS Th Trn Cu K, Tr Vinh * nh ngha* nh l v h qu4: Gc to bi tia tip tuyn v dy cung * nh l v gc to bi tip tuyn v dy cung . * Lin h vgc to bi tip tuyn v dy cung, gc ni tip, gc tm cng chn 1 cung. 5:Gccnh bntrong ngtrnv gccnhbnngoing trn. * Cc nh l6: T gic ni tip. *nh nghat gic ni tip *nh l thun, nh l o. * Du hiu nhn bit mt t gic ni tip.7: ng trn ngoi tip, ng trn ni tip. * nh ngha8: di ng trn, cung trn. * Cng thc tnh di C ng trn c bn knh R: C= 2tR Cng thc tnh di C ng trn c ng knh d:C= td * Cng thc tnh di cung trn :- di cung n0 : l = 180Rn t ( l : di cung n0) 9: Din tch hnh trn, hnh qut trn. *Cng thc tnh din tch hnh trn bn knh R:S = tR2 Cng thc tnh din tch hnh trn c ng knh d: S = t.24d *CngthctnhdintchhnhquttrnbnknhR:S= 2R . lS hay360n R2=t ( l: di cung hnh qut n0 ) II. H THNG BI TP: Bi 42 Trang 83 SGK Cho tam gic ABC ni tip mt ng trn. P, Q, R theo th t l im chnh gia ca cc cung b chn BC, CA, AB bi cc gc A, B, C. a/ Chng minh AP QR . b/ AP ct CR ti I. Chng minh rng CPI l tam gic cn. Bi 58 trang 90 SGK Cho tam gic u ABC. Trn na mt phng b BC khng cha nh A, ly im D sao cho DB =DC v = 1DCB ACB2 a/ Chng minh ABCD l t gic ni tip b/ Xc nh tm cu ng trn i qua bn im A, B, C, D Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.Hunh Minh Khai: Trng THCS Th Trn Cu K, Tr Vinh Bi 40 Trang 106 SBT Cho tam gic ABC. Cc ng phn gic trong ca B vaC ct nhau ti S, cc ng phn gic ngoi ca B vaC ct nhau ti E. Chng minh t gic BSCE l t gic ni tip. Bi64 Trang 92 SGK Trn ng trn bn knh R ln lt t theo cng mt chiu, k t im A ba cung AB, BC, CD sao cho = = =0 0 0sAB 60,sBC 90,sCD 120a/ T gic ABCD l hnh g? b/ Chng minh rng hai ng cho ca t gic ABCD vung gc vi nhau. c/ Tnh di cc cnh t gic ABCD theo R. Bi 97 Trang105 SGK Chotamgic ABvung tiA.TrnACly im Mvv ngtrnng knhMC.KBM ct ng trntiD. ngthng DA ct ngtrntiS. Chng minh rng:a)ABCD l t gic ni tip. b) ABD ACD =c)CA l tia phn gic ca gc SCB. Bi 14 Trang 152 SBT ChotgicABCDnitipna ngtrn ng knhAD.Hai ngcho AC vBDctnhau tiE. K EF vunggc viAD. GiMl trungimca DE. Chng minh rng: a)Cc t gic ABEF, DCEF ni tip c. b)Tia CA l tia phn gi ca gc BCF; c)T gic BCMF ni tip * Bi tp b sung: Cho ng trn (O:R) c ng knhAB. K 2 tip Ax v By vi ng trn. ng thng qua O ct Ax v By ti M v P .T O v ng vung gc vi MP ct By ti N. Chng minh:a)OM=OP ; ANMP cn. b)K OI MN .Chng minh OI=R;MN l tip tuyn ca (O)c)AM.BN=R2 * Bi tp b sung: Cho tam gic ABC ni tip ng trn tm O (AB