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Duong ChtmgminhrangCDf ME' F AB < AC' cdrcduongcaoBD virCE'Gqi ABC gi6c tam Cho 2.0 didm... PHONGGD&DTHUYENAN DUONG DAP AN DE THI CHQN HQC SINH GIOI.[r]
(1)PHONGGD&DTHIYEN-AN DUONG KV rHI cHoN HQC sINHGIoI t'6P a Nam hoc 2011'20L2 oEcsiNHTHuc MON:TOAN Bhi 1: (2.0ttidm) 111 t I a.ChO-+-t v' t -n Tinh gi6 tri cuabi6u thuc xyz y' x' x - + / ' Y Z Y 2+ Z z x 11 = =-=- z' z' +ZxY rll - *nU * ; = t h o a m d n d i d u k i Q + c r a + b v A a , b , c * b.Cho - Chtmgminh.anBm I * ' Uzotl a+b+c I *-rb20ll I C20l Bdi2: (2.0tliim) Giaiphuongtrinh (x-2)',(!:] l'-,,(+l =o \;'-t)-" to[-.t,1 tx-I) cuaphuongtrinh Biri 3: (r.0 tli6m).Tim nghiQmnguyOn l+x+x2+*':Y' = di€mc?nhBC,bi€tAB 5cm' trung ld M co ABC gi6c tam Cho (2.0 dicm) Bii 4: va vudnggoc voi Bc cit duong B qua = thing Duong l3cm = AM 6cm va Ac voi BC cit duongthangAB o E' goc vuong vd C qua thing thangAM o D Duong ChtmgminhrangCDf ME' F (AB < AC)' cdrcduongcaoBD virCE'Gqi ABC gi6c tam Cho (2.0 didm) Bhi 5: minhrdng:AB'AE + F D F E : A F ' ld giaodi6mcuaBC vir DE' Chrmg co c6cc4nhthoam d na < b S c ' Bhi6: (1.0didm).Chotamgi6cABC a 9bc' Chimgminhrang(a + b + c)" < Hdt - Gidm thi so l: ' Ho vdtOn: r""r"'r"i"'r""' (2) A\1 PHONGGD&DTHUYENAN DUONG DAP AN DE THI CHQN HQC SINH GIOI NNON: TOANL6P S Nnm hoc 2011- 2012 Bdi 1:(2.0didm) a Tir gi6thi6tta c6: xy * xz + yz: T ac o : x 2+ y z : x 2+ y z - x y - x z - y z = ( x - y ) ( x - z ) -x) (x- vXy-zXz- x) _, _ _ x ' ( z y ) + y ' ( x z ) + z ' ( y V' Y vJA " (* vXy z)(z* x) (x yXv z)(z- x) b Ta c6: 1 I I I -I+ - +1- - I <+-+-+ abca+b+cabca+b+cabc(a+b+c) / ,rc(a+b+c)+ab ^ / r\,r e ( a\ + b ) ' /# = < + ( a + b ) ( c + b ) ( a\+ c ) =/6\ abc(a+b+c) [u*b=0 0'5d '.sd +b - U^< + a + b * - - - ; a -==U r\/ /\ / 0'25d [a=-b olu+c=o<+lb=-c lt lc+a=0 Khi d6 ta c6: 1l lc=-a 0.5d ffi=ry= 111111 J a20t3 I J-=-I-I- a2013 b2013' c2013 a20t3' (_a)t0,, =C a20t3 111 Suyra 0.25d -_-I-l a +3 3* a a2013 62013 C2013 Bii 2: (2.0didm) DiK: x * +l ') ., r vx L , u ^ (l) = " D [' t u x+l' x-l l <+ u:v hoflcl0u:v T a c : 0.u 2+ vt -l l u v: e (u- v) ( Ou-v;:g *N6uu:v -x+2 g1= x+1 x-l "6*-2 [x=3 * N6ulou: v c6I o.*-z =**2 o (x -:)(ex - 6)= s *"1 lX=x+l x-1 L3 0.75al 0.75d 0.5d Biri3: (1.0ili6m) T a c :* ' + * l : ('x * l ) t * t o v d i m q ix 2' " 5x2+lIx+7: 5(x+*lt*9to 10' 20 vdi msi x 0.25d 0.25d (3) NOn(1 * x * x2 + r ' ) - ( l + x + x t ) I * x * x t + x ' < ( + x + x + x3) + (5x2+11x+7) 0.25d t + *' < (x+2)2hay x3 y' (x + 2)3 €*'<i+x*x d6 tr: 1x+1)3 = o, 0.25d : + + x 2+ x e [ * (x+1)3 x S u yr a lx l N6ux:0thiy:1 N ux : - t h i y : Bhi 4: (2.0tliim) Ggi K li giaodi€m cuaAM vd EC, tr€ndo4nMK l6y di6m I s a oc h oM I : M A : c m Tri gi6cABIC ld hinh binh hinh =)AB = IC = 5cm,AI= 2AM =l}cm,AC = l3cm vu6ng tai I = AI2 + IC2- ACz= AAIC = fr =900 B L4icoBm = diM = 900 ABEK co BC, KM la c6cdulng cao (I) + M ld tryc tdm+ EMIBK AMBD= AMCK(c.g.c)+ MD = MK Me MB : MC vi DMC = BMK :+ ADMC = AKMB(c.g.c) (II) +ffi=ffi=DCttBK " _ 0.5t1 0.5d 0.5d 0.5d Tt (I) vd (II) suyra EMI DC Bhi 5: (2.0tli6m) Tr€n do4n thing AF laY di€m M cho D FME=Fil AADB.,,AAEC-> -49 AE AC :t ^ffiE=.ffib AADE ,oAABC ^ ^ Do FME = ABC = AME = ABF AAME , AABF AM AE AB AF ^F ^I FM = p=+fD.FE = AF.FM FD AF Vfly AB.AE + FD.FE: AF(AI'A+ FM) : AF.AF = AFz Bhi 6: (1,0didm) Tu gidthi6tbaira ta c6: zb>b+ a > c =+4b - c > = (b -c).(ab- c) < l.0iI AFME.- AFDA :t (l) = 4b2+ c' < 5bc=+(ZA+c)t < 9bc (2) M d :( a + b + c ) 2< ( b + c ) z Tu (l) va(2)suyra: (arb+ )) SdA + c)2<9bc.Tac6diAuph6ichungminh l.0tl 0,5d 0,5d (4)