Ldi gidịDIL| BC: a, CA: b, AC: c.
86 dẠ NCu di6m P ni- trong tam grdc ABC tln
(PA + PB + PC)2 > J1@P,q, + bPB + cPC).
^
Chung minh. Y\ BPC + CPA+ APB : 2n nln
.ọ,6FE *"orfi)*"orlFa>-l ftct qua2 2
quen thuQc).
Theo dinh li c6sin, BDT Bunyakovsky, ta c6
a2PA+b2PB+czPC = PĂPP + PC) + PB(PC) + P,4) + N(P.4 + PE) - 2 PẠP B.P C (cos6Fi * "rrdFA * "orFFEl < PĂPB2 + PC2)+ PB(PCZ + PA2) + PC (.PA2 + PBz) + 3PẠPB.PC = (PA+ PB + PC)(PB.PC + PC.PA+ PẠPB) 1 <l-t p,q+ PB + PC)r. 1\ J
Tt il6, 14i theo BDT Bunyakovsky, ta c6
(PA+ PB + PC)4
> 3(a2PA+ b2PB + czPC)(PA+ PB + PC) >3(aPA+ bPB + cPC)z. }J.ay
(PA+ FB + PC)z > Ji@P,q+ bPB + cPC). Ding thric xiry rakhi vd chi khi tam gr6c ABC
d6u vd P ld1'2,m cua tam gi6c clOu cl6.
Tro lai giai bdi tohnT72. Ggi Á, B', C' theo
thri tu ld hinh chi6u gia P fiAn BC, CA, ,48 (hinh v0). Ta co PÁ.a =25orc
: PB.PC.sinBPC.
Gqi R ld b5n kinh cluong trdn ngoai ti6p tam
grhc ABC, tt dinh ii sin ta c6
B'C'.PÁ : PAsinẠPÁ= P1 a .P1' 2R PẠSPBC : ' l^PẠPB.PCsLIPBC 2R = J-p,l2ạpg q :Lr,q,.pụr,,sinA 2R 2R, 2 Tucrng V C'Á.PB' : !eọrạec,+q 2 Rr, ÁB'.PC' : LPl.Pn.PC tTq 2R,
Theo b6 dO tren, chf y rdng do:PÁ, dr,: PB',
d, : PC'ta c6
(d, + d6 + d,)' - J:f sinA , sinB sinC)
'PAP,;;=7[ u .T.
& ]o
FNfr4" x6t. Nhi6u b4n t6 ra lung tung trong viQc trinh
bny ldi gidị Xin n6u t6n mQt vAi bpn c6 lcri gi6i fucrng d6i rot.
Bic Ninh: Chu Vdn Trang, L€ Thi Hai Linh, 9A,
THCS YCrr Phong; Nghg An: Hoang Anh Taị Nguy€n
Xudn Tudn Trung,9A, Tran Ngpc Duy,9C, THCS Li
Nhgt Quang' Do Luong'
NGÚEN MINH HA *Bni Lll4ll" h,{ot ing rhilv tinh hinh rn.r
thartg rlii 20cm. l;in hoi diu, c{uq'c dcir ci dinh:'u nghi0ng.gdr'-10" ío t'r'ti phrong ngan$ tai nói c:d gia toc' trortg lt'ffót'tg bdng 9,8:.n,s-. Ben lt"rmg ong t'i ntot elLrtt t'ciu nhd ndng 0.lg