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Con ng dn n thnh cng l s ti luyn Page 0

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Con ng dn n thnh cng l s ti luyn Page 1

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LI NI U Trong chng trnh ton THPT, Bt ng Thc l mt phn mn kh nhng li thng bt gp trong nhng k thi quan trng nh tuyn sinh i hc, thi hc sinh gii cc cp, cc k thi Olympic trong v ngoi nc Nht l i vi phn Bt ng Thc Trong Tam gic, n l mt dng ton logic, ngi lm cc bi ton ny cn c nhng hiu bit su v hnh hc, lng gic v c i s.Chnh v th, tc gi tp hp, phn loi, bin son nn cun Chuyn Bt ng Thc Trong Tam Gic. Cun sch trn tay cc bn l tm huyt ca chng ti cng vi s gip ca cc thy c, n l mt h thng kin thc t c bn n chuyn su, tp hp nhiu bi ton khc nhau thuc nhiu chuyn . Quyn sch gm 3 phn: I.BT NG THC I S II.BT NG THC HNH HC III.BT NG THC LNG GIC Trong , m u bng phn kin thc c bn v nng cao, sau l phn bi tp tham kho, sau cng l phn bi tp ngh c km hng dn gii. Do l ln u tin bin son chuyn , d c gng ht si c gng cng khng trnh khi nhng thiu st. Rt mong cc bn thng cm.Mi gp xin gi v a ch ngohoangtoan1994@gmail.com. Cui li, tc gi chc tt c cc bn mt ma thi 2013 thnh cng v thng li.Thn i! Thnh Ph Cn Th, ngy 25 thng 09 nm 2012 Ng Hong Ton

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MC LC Chng Trang I.BT NG THC HNH HC 4 II.BT NG THC I S 30 III.BT NG THC LNG GIC 51

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CHNG 1:

CNG THC H THC LNG TRONG TAM GIC THNG

1. nh l hm s Cosin. a2 = b2 + c2 - 2bc cosA b2 = a2 + c2 2ac cosB c2 = a2 + b2 2ab cosC 2. nh l hm s Sin R

Cc

Bb

Aa 2

sinsinsin(vi R l bn knh ng trn ngoi tip tam gic ABC)

3. nh l trung tuyn. 2

22

222 BCAMACAB

4. Cng thc v din tch

cba

cba

rcprbprapScpbpappS

cbapprS

RabcS

CabBacAbcS

chbhahS

)()()())()((

)2

(

2

sin21sin

21sin

21

21

21

21

knh ng trn bng tip cc gc A, B, C ). ( vi r l bn knh ng trn ni tip tam gic ABC; ra, rb, rc ln lt l bn 5. Cng thc bn knh ng trn ni tip

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VT 331 xyz M xyz=CBA sinsinsin

1 Ta c:sinAsinBsinC8

33 suy ra: xyz33

8 Vy : VT 333

321

3381

Du = xy ra khi tam gic ABC u.

Bi 38: BA sin

1sin

1

2

tan2

tan2

tan21

233

sin1 CBA

C Gii Ta c: tan

BBB

sin2

2cot

2 (1) tan

CCC

sin2

2cot

2 (2) tan

AAA

sin2

2cot

2 (3) Cng v theo v ta c

2

tan A

CBA

CBACBsin

1sin

1sin

122

cot2

cot2

cot2

tan2

tan

)(2

tan2

tan2

tan21

233

sin1

sin1

sin1

233

2tan

2tan

2tan

21

sin1

sin1

sin1

332

cot2

cot2

cot2

cot2

cot2

cot

2cot

2cot

2cot

21

2tan

2tan

2tan

21

sin1

sin1

sin1

pcmCBA

CBA

CBACBA

CBACBAn

CBACBACBA

Bi 39:

2cot

2cot

2cot

21

23

sin1

sin1

sin1 CBA

CBA

Gii

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Con ng dn n thnh cng l s ti luyn Page 91

Trong mi tam gic ta lun c tan

CBA

CBACBAsin

1sin

1sin

122

cot2

cot2

cot2

tan2

tan2

cpcmCBACBA

CBAm

CBACBACBA

2cot

2cot

2cot

21

23

sin1

sin1

sin1

32

tan2

tan2

tan:

2tan

2tan

2tan

21

2cot

2cot

2cot

21

sin1

sin1

sin1

Bi 40:

183

sinsinsinsinsinsin

2 CBACBA

Gii Ta c: sinAsinBsinC=8sin2

cos2

sin2

cos2

sin2

cos2

CCBBAA Ta li c; sinA+sinB+sinC = 4cos2

cos2

cos2

CBA Vy 2

tan2

tan2

tan21

sinsinsinsinsinsin

2

CBACBCBA

M theo BT c bn VT

183

361

331.

21