dadng thdng AB vit CE ,dt nhru tqi di€m N. Chilmg minh riing:
a) B6n di€m A, E, M, N cilng nim tAn mQt
dudng trdn.
b) PC.PM: PD.PN.
Einh hufng khai th6c bdi to6n gdc: Tim thAm
cdc h€ thac gi*a cdc doan thdng md hai ddu mut cila chung ld cdc di€m dd cho.
@tYc,t'cttt /''/A Hinh 4 A Hinh 4 2 ,2 Ttd6 vd (2) "U +: g e d : b2 + ac. Ta c6
Biri tofn 4. N€u tam gidc ABC vdi di€m D tuan cqnh BC sao cho IBa AD vd
- 1^
Eni : eoo+ 1 Zpe tni pC : Ae + BC.AB.
2
5) Nriu 6k : goo + FEd thi o: 9oo+ B, suy ra
tamgitc ABDvuOng va 6tri : 90o. Tu,cl6 theo
dinh li Pythagoras c6 Bd : Afr + BA2 (h.5).
E"ii fdp 6di:
Mor c[cH BEN odr nflr oflne rufc
@Aiao7 fiAn Ddc san Todn hoc vd Tudi trd Sd 12, trang 44)
@rrnfgio bdi tfp, thAy gi6o gqi bqn Ddng
16n gi6i hQ phuong trinh
lf =3y2 -3x (1)
)
lf =3*2 -3t, (2)Vd sau ddy ld loi gi6i ciaEdng: Vd sau ddy ld loi gi6i ciaEdng:
Tru theo v6 c5c PT (1) vi PT (2) suy ra
*' - y' = 3(y2 - x2) +z(y - x1
e (x- y)(r' + *y * y' +3x+3y +3)=g (3)
* V6i x = y thay vdo PT (1), ta c6:
*3-3*'+3x=0<>x=0.
Do d6 hQ c6 nghiQm(x;y) ld (0; 0).
* N6u x2 + *y * y' *3x+3y+3 = 0
HN PIrUONG TRiNII Co IIAI NGIIIftnne
e *2 +(y +3)x * y' *3y +3= 0, ta c6
A, = (y+3)' -4(y' +3y+3)= -3(/+1)2 < 0
n6nPT inxc6nghiQmkhi
A, = o € ! = -1. Khi d6 PT trd thenh x2 +2x+1=0€x=-1.
Do d6 hQ c6 nghiQm(x;y) h (-1; -1).
K€t luQn: NgtriQm cuahQ PT ld: (0; 0) ve (-1; -1). Tri du6i lop bpn Bdc xinph6t biiSu:
"Thua they (-1; -1) kh6ng phii ld nghiQm cria he PT, vi thay vio hQ PT k*r6ng thoi mdn". ThAy trd dang bdn kholn vC tOi gi6i !!!!
Bpn gd rOi nhu th6 ndo trong tinh hu6ng tr€n?
vO nuU nn
(GV THPT Cdm XuyAn, Hd TTnh)
A? xuir BAIr rLr 1e61 Ddc san 56'14
Toa soAn:1878, [h0'Gienq ui, Hil NQi
DI BiCn lap: 04.35121607
0I - Fax Phfl hanh, rri su: 04.35121606 Email: l0anh0Glu0ilreyietnam@gmail.c0m
Iqp thi I0All H9( uo IUil mt
Muthemutis und Youth Muguzine
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GS. T SKH. NGUYEN CANH TOAN
GS. T SKH. TRAN VAN NHTING
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cs. ooaNquirvn
PGS S. TRANVANHAO
cHlu raAcn xntqur xuir atNCht tich HQi d6ng Thinh viOn Cht tich HQi d6ng Thinh viOn
NXB Girlo dgc ViQt Nam NGU?.NC,OTRANAI
Tdng Girim ddc ki6m Tdng bicn tQp
NXB GiSo duc Vi6t Nam
cs.rs.vuvANntxc
ttot odt'tc arutt r,qe
Tdng biin tQp : TS. fnAf'{ HUU NA.Iu ThukiTda soan : ThS. ffd QUaNC VINH
rs. rn-AN oiNu cHAu, rts. NcuyEN eNs nfiNc, rs. rnAN uav oONc, zs. NcuvEN tr,,nNn o[c, rs. NcuveN
rrarNH uA,rs.NcuyEN vrEr HAr,pcs.rs. lr qudc gAN,zts.rHAM vAN HuNG, PGS.TS.w rHANH rruf,r,
GS.TSKH.T.ICUY6N VAN MAU,6NgNGITYEN TUAC UTNU,TS.PHAM THI BA,CH NGQC,PGS S.NCUTEN PANC
pHAr, rcs. zs. TA DI-ry pHlx]t\c, rfts. NGlryEN rr$ urecH, cs. zsKI1. DANG mnvc rsiNc, PGs. rs. PHAN DoAN
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TRONG SO NAY
Gifp ban 6n tAp
Thdi Nhil Phuong - Vfln d+ng dang
(A+B)" = AC + Bn vito giAi to6n ...1
Pham Phuong Li€n - Sir drlng di6n tich dd
giii to6n.. ...3
Trudng Quang An - Ung dgng cria dinh libdn didm ...7 bdn didm ...7
Phuong ph6p girii torln
Trdn Xudn Uy - Nhi6:u c6ch giAi phrrong
tr\nh axz + bx +, = kJ it*i ...11 Pham Trong Thr - MQt sd phrrong ph6p
thrrdng dring tim gi6 tri ldn rirt't, gi6 tri
nh6 nhdt cria bidu thrlc ... ...-...L4 Thi tuydn sinh vio lop 10 THPT
NguydnThanh Giang - H6 phrrong trinh ba
dn ... ...19
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chrlng minh c6c drrdng di qua didm cd
dinh ... ...24
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Nhi6u crich gidi cho mot bii to6n
Vi€t Hdi - Bii to6n v6' gi6 tri 16n nhdt cria
tdng d0 ddi hai doan th8,ng...3s
Pham Hing - Hqc giii to6n qua chidc d6ng h6... ...38
Philrug Kim Dung - Gi6i thi6u cu6c thi to6n hsc tr6 Qudc td IMC 20L4 (The
International Mathematics CompetitionIMC 2014) ...40 IMC 2014) ...40
Khai th6c biri to6n th6 nio?
Hodng Minh - Tinh ti sd dO dai do4n th&ng
theo c6c canh cria tam gi6c ...45 Don vudn To6n... ...47
Anh bia 1. Cd,u Thd.p (Tower Bridge) &
ffi TAP cH[]rcAN Hoc vA TUdl TR#
t-' :
Wl,,*i' *rar* #pw,ff girii rhusu a**g'{,bu #rrii
Gfy -^) fi-drl ruvir\cHoNrHEo cnuynx,Df J "
EHUASI B! CHO KI THI VAO THUI{G HOC PHO THONG MON TSANqO o sach gdm hai t6p tuydn chon qO o sach gdm hai t6p tuydn chon
/,Fin.o rnr"yOn dd nhtrng naiuidff'ry ti6n Tap chf TH&TT va mot so bai vidt
them c&a c6c nha gi6ro c6 kinh nghiem
nhlm gi0p cac ban HS THCS on tAp vd
thi c6 hi6u qu6 vdo l6p 10 c5c trrlong
THPT va THPT chuyen. Bo sach c0ng li
tai li6u tham kh6o hfru ich cho cac thdy co gi6o va cac bdc phu huynh HS.
200 trang, Kh6 1l*24cm
Gi6 bia: 35.000 ddng
200trang, Kndn"z+cm
Gi6 bia: IS.OOO ddng
4ttLri r.*fiN I HE0 f riL,Yif+ *r
Itiiiiii, ii iiiil ti i-i
lii i iiiiiiil iiliiiii: :1ri Ijilii rij,i;itii iitl 1l:; rjt;i liii: ili!it i:il:t tirilI
,
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i\i#i'; : :-';i'4
1Ap r"1qr
u*lt8 Lljgt*ti!{ ft*1Isi
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TUYTH cHou IHEG cHUYEt{ M I ililiJ,t'i ,11 Iriir it: 1iil
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lfiuilc l8r plit ,illlalll
ul3 lul til]r s8l |1{r. li1{} i}*li$
z A ir-;l-.';'*:';il1,. a;
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r1.&l: ,tA!
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n,".. "d,
260trang, Kh61l"24cm 240trang,Kh61l"24cm
Gi6 bia: +0.OOO ddng Gi6 bia: ++.OOO ddng
Moi chi tidt xin'li6n h6: TAp cHi TOAN HQc vA rudr rnE
1878, Giing V6, Ha Noi
o CIT"Fax Phdt hinh, Trisuf: {04}35121606 r Email: toanhoctuoitrevietnam@grnail.com
(T? triuilc ;191 P;irij 1i14;l
lt Hun
ToRn 'i:,Tg'
GCL firl/L ruYiN cHoN rHEo cHUvEx oi
CHUAN" BI CHO Ki THI T6T NGHIEP THPT VA THI VAo DAI HQc,
J
CAO DANG MON TOAN
qO o s6ch co hait&p gdnr '10 ehufdmg
llicti nhidu ctruyen-*6 dlrda tul,drlcYon trt c6c bii vi6t erla e*e th$y eo cYon trt c6c bii vi6t erla e*e th$y eo gi6o gi6i chuy6n mon v& eo kimh *gfrle* giing day trong c6 nrfdc, dl,fde s&p xdp theo dfing thrf td tnong 6Su true dd th, tuydn sinh Oai hoe, Gao d*ng e&a Bo Gi6o duc y& E&o tao"
Fhdn cudi m6i eudn gidi tlri6ur mst sS0d tr luy6n v& eo [r#6mg d&n gi&!" 0d tr luy6n v& eo [r#6mg d&n gi&!"
t,\t \t [N v l:i:r::r t:.r. N
{ ?:,;"ii:::l::::i. llir:l r"i l'
' r' H PH9 HA!.PH0NG PHAT,'T I$N /r\\ irJ)\r: r/J \@-2l- {0 NAnt {!.,rt1 8ie!4- I
NGUT Nguyen Phan Long Hi6u trudng nha truong
-Flr.Poc thdnh l6p ndm 1974, trong
Y H oo nem qua, truong THCS.Hon!
t-,.Bdng luon hodn thdnh xuAt sdc htreng nhiQm vu duoc giao. TQp th6 nha
truong d6 vinh du nhAn cluoc nhi6u phAn
thu&ng cao quli c0a Ddng vd Nhd nuoc: Bdng khen cia HQi d6ng BO trudng ndm
1988; HuAn chuong Lao dQng hqng Ba
ndm1992, Bdrng khen cria Thi tuong Chinh phti nim 2002, HuAn chvong Lao dQng hqng Nhi ndm 2004, HuAn chuong
Lao dOng hqng NhAt ndm 2009. Truong
cUng nhQn ilucyc nhi6u Bdng khen, Co thi
dua xuAt sdtc crla BO Gi5o duc vd Ddo tao,
cia UBND thanh ph6 Hdi Phong. Nhd
trucrng li6n tUc dat danh hieu lap th) Lao
dQng XuAt sdc; Li6n dQi thi6u ni6n nhi6u
ndm li6n tqc duoc cdng nhAn Li6n DQi
mqnh, dwoc Trung uong Dodn, Thdnh Doirn H6i Phdng iSng Bang khen-
Truong dA c6 4 gi6o vi6n dugc Nhdr
nu0c phong t{ng danh hiQu A/hd gi6o Uu
fu, 1 giiro vi6n duoc t{ng thu&ng Hu6n
chuong Lao dong hang Ba. Hdng ndm,
nhi6u gi5o vi6n dqt danh hieu Chi6n sithi
dua, Gido vien dqy gi6i cdc c6p. HQc sinh cria truong lu6n dat k6t qu6 cao trong c6c
ky thi chqn hgc sinh gidi c5p thdnh ph6 vdr
. .:
qu6c gia, nhi6u em dd ph6t huy ndng luc vir dat k6t qud cao trong cAp hqc kO ti6p,
nhu c6c em Nguy1n The Trung - Huy chuong Bac IMO tai Canada ('1995); Ddo Th! Thu Hd - Huy chucrng DOng IMO tai
Ddri Loan (1 998); /Vguye n Anh Qu€rn - Huy chucrng Bac IMO tai MV (2001); NguySn
Huy Ting - Huy chucrng DOng IMO tqi
Nam Phi(2014),...
Ndm hoc 2013-2014 vua qua, hoc sinh
nhd truong gidnh dugc 333 gidi trong c5c cu6c thi, trong d6 c6 96 gidi vd huy
chuong c5p th2rnh ph6, 11 giai qu6c gia.
Nhir truong dugc UBND thanh ph6 Hai
Phong t{ng Co TQp thO hodn thdnh xuAt
sdtc, toitn dien nhiem vu cong titc giiro duc vd ddo tao, d1n dAu phong trdo thi dua; Cdng clodn trucrng duEc T6ng Lien
dodn Lao dOng ViQt Nam t{ng Cd Cong
dodn co sd vhng manh co phong trito thi
dua xuAt sitc. Chi bO nhd truong d5 duoc
QuQn iy H6ng Bdng phe chuAn trd thdnh D6ng bQ truc thu6c QuQn Liy.
Ket qu6 dat clucvc trong nhirng ndm vira qua ld nhirng d2ru 6n dQm net tr6n con
duong xAy dung vdr phdrt tri6n nhd trucrng.
D6 c0ng chinh ld ccr sd v0ng cnic de tQp
th6 truong THCS H6ng Bdng v0ng vdng,
tu tin trong trong nh[rng ch{ng Cfuong
fe ti6p, lu6n phSn dAu d6 xung ddrng voi ni6m tin y6u cia nh6n d6n thanh phO Hdi Phong.
Le khai gldng ndm hoc moi
r ! ill, Y&Y
rlgg
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