) NhQn xit Da s6 c6c ban gi6i PT nny blng c6ch binh
Hdm s6lx ): x, Yxe R th6amdn bdi to6n vita
c6 hing <ting thric
xt + yt = (x + y)(xa - xt y + x' y' - *y' + yo).
Ydy flx) : x, Yx e R. ld him sO duy nh6t th6a
min bdi to6n. E
YNhQn xA.Dey ld bdi to6n phuong trinh hdm dpng
ccr bin, kh6ng qu6 kh6 vd hay. Hoan nghdnh c6c b4n
hqc sinh l6p l0 sau d5 tham gia vd c6 loi gi6i tlfng:
BIc Giang: NghiAm Vdn Nghia,10A1, THPT L4ng Giang s6 3; Hir NQi: Tq Khdnh Ha, Vfi Dtic Vdn,
10T1, THPT chuyCn DHSP Hd NQi; Hung YOn:
Truong Quang Khdnh, 10T1, THPT chuy6n Hrmg Y6n; Nam Dinh: Dodn Thi Nhdi, 10T1, THPT chuyCn LO H6ng Phong; Th6i Binh: Trdn Quang Minh, l0Al, THPT D6ng Thuy Anh, Th6i Thpy;
Thanh H6a: Nguydn Dinh Luong, l0T, THPT chuy6n Lam Son; NghQ An: Nguy€n H6ng Qu6c Khdnh,l0Al, THPT chuydn Phan B6i Chdu; Quing Nam: Zd Tdn Ddng Tdm, l0Tl, THPT chuy6n LC
Th6nh T6ng; Phrri YGnz H6 Minh Hodng, Ng6 LA Phucrng Trinh, Phan Xudn Thdnh Ldm,l0T,THPT
chuy6n Luong Vdn Ch6nh.
NGUYENMINHDI.IC
Bni T121456. Cho tam giac ABC vq didm M
nirn trong tam giac kh6ng trilng voi trong tdm
C . wAi AM, BM, CM ldn lu'ot cit BC, CA, AB
tgi Ao,Br,Co. KA A0A1// CA, AoA,// AB vdi
A,,ArthuQc BoCn. Tu'ctng ttr, ta c6 Bt,82, Ct,C2. Goi G,,G. ldn lu'ot ld trong tdm tam giu<' A,B,C,. A2B.C,. Chu'ng minh rang
a) A,B.// Bp,// C4..
b) MG di qua trung di€m crta G,Gr.
rrn.ooo-roru, T?[l#tE
Loi gi,rti.
B1
a) Ggi H = BoB, oAAo;K=CoC, aA,4o;
D=MB r-tAoAr;E=MC a,4o,4r;F =DE oM,\.
o6 ttrSy ,4b(BocoMB)=-1. Ktit hqp v6i BoB2llBC,
suy ra,FIld trung didm ctr- BoBr. Tucrng t.u c6 K ld trung di€m cira CoC,.
V4y, chri f ring BoB2llCoCp theo b6 OC frintr thang thi BoCo,B2Ct,@ tl6ng quy (tai 4.
Yi ABo I lAoD; AC o I lAoE ndn
MD MA" ME ,
:=:=:=..