THCS YOn Lpc; Ninh Binh: Vli Thi Minh Phrottg,
12T, THPT Luong Vin Tuy; Hir Nam: Trrin Minh IIai,
10A2, THPT A Phu L!; H6i Ducrng: Bili Hu1- Hoiing,
10A. THPT Kim Thinh I; Thanh }Ioi- LA Vdn Tudtt,
Tru'nns, Vil Li€u, l0T, THPT chuy0n Lam Son; Eh
Nine:-gii Dans Khoa. 1lAl, THPT chuy€n Le Quf OOnl Stin Tre. Khong Hrtu Hi€p, I I Torin, THPT
chuY€n B€n Tre'
NGUYEN MINH HA
*Bei Lll3gs. Mot so'i dAy dong chat chiiu
CA
(4) ... zR J ^
doi '-" ndm tr?n ntot ltinlt
2
R c6 truc .ndm ,go,rg.
ddy tai di€ru A (xdc dinh boi gdc anhu hinh vd) ngay saLt
khi tha, Cho khoi
Itrqng sqi (tAy bing
t't'i, gia (C trong trud'ng bdng g.
tru nhdn bdn kinh
Irc cdng cua so'i
v vho ding thric
EB FC
KA CA
Tu (l) vh (4), suy ra
BC= FC.
l{oin tohn ch[mg minh tuong tg nhu t€n, suy ra KC LBF (5)
'fu (3) vn (5) suy ra H ld tryc tdm ctra tam
gi6c KRC. Do d6 KH LBC mh KA L BC(cdch v0), suy ra ba <1i6m K, A, H thdng hbng, (cdch v0), suy ra ba <1i6m K, A, H thdng hbng,
c16n d6n AII L rBC (clpcm).
'fro lai gi6i bhi todn (h. 2).
B
Hinh 2
Y\ AC ll l--D n€n AE = CD. Do d6
MEA= F-EA= DEC = NEC (6)
V) /iI1 lI duong kfnh cua cludng trdn (O) ndn
cdc g6c BAE, BCE ld g6c vudng. Do cl6 c6c
g6c MAIi, NCE cfrng lh g6c vu6ng . (7) 'It (6) vI (7) suy ra hai tam gi6c EAM vit ECM clong dang v<i'i nhau vd theo thu tu vu6ng t4i
A vir C. Ap dung b6 d€ tr6n ta c6 EI L AC. A
(Nhan x6t. l) Bii to6n niry thuQc d4ng co brin nOn
khri nhieu ban tharn gia girii, tuy nhi€n v6n c6 b4n
giai sai.
Ldi giAi. O thoi di6m ngay sau khi tha d6y, gia
toc cua cric phin tLr c6 phucrng ti0p tuyOn vh
bing nhau ve 00 ton. ta kf hiqu gia t6c ndy ld a.
Xdt trong khoring thoi gian t rdtngin sao cho
gia t6c lh kh6ng cl6i, sgi dAy dich chuy€n duoc
mOt do4n nho / = +vh cl4t vdn t6c v = at.
Ta sd su dUng ilinh luflt bdro tohn n[ng luong
cle tim gia t6c a cira ddy. Xcm nhtr ilop_n ddy
dg dAi / chuy€n xu6ng ddu dudi, do 116 dQ cao c.u1 nhAn dAy bi giam- mQt. do_an.R. P0 giam
th€ nang cua doan dAy d6 sE chuy6n thhnh
dQng nang cua tohn b0 sqi dAY, ta c6
ml - mv2
-_ aR
R6" 2
It-'
2
Thay c6c biriu thric cua / vh )o
tr6n ta duoc a =:q.
fi
Bdy gio ta x6t phAn dAy phia dudi di€m A c6
kh5i luqng t9.
|rEnt ndng cua phAn dAy
TI
,
nhy c6 duoc bing t6ng c6ng do trgng lgc cua
or rr,,r-roro, T?Eil.HS
n6 vh c6ng cua lgc cdng T cira d0y t4i A. Ap
dung dinh lu6t brio,tohn ning lugng ta c6
*!
.pRsina -Tl - md .vz
R" Tc 2
IL
22
Thay l, v cr trOn vho ding thuc nhy ta dugc
( za\ 2mp
T =l sina. -'- 1.'"'6
[ ,r,/ ,,
Tu ktit qua nhy ta thAy luc clng 6 hai dAu d6y
lb bang kh6ng (do a= 0). D
(Nnfl, x6t. C6c b4n c6 loi giai dring: Thdi Nguy€n: Vfi Quang.Minh I I Lf THPT ChuyOn; Quiing Ngii:
Phqm Qu6c D6,, ll Bl, Bili Et?c Khdnh, l1 Li, THPT
chuyOn L€ Khi6t.
NGUYEN XUAN QUANG
*Iiari 1,21395. Cho N clien rith tlieln tlro'ng q
nhtr nhcttt, nim t'dt'h din nhoLr trAn motcltrong tritn tLm O btin kinh R. Cin ddr t(ti cltrong tritn tLm O btin kinh R. Cin ddr t(ti tdnt clLrong tritn mol diAn fic'h bing bao nhi|u
d0 he c'An bdng? Khao srit th?m vcti c'dc'
trLrr)ttg hoTt riAngN = 3 r,d N = 4.
Loi gidi. Ta kh6o s6t bhi to6n trong haitruong trqp N chin vh N 16. truong trqp N chin vh N 16.
t6c dr,rng l6n cli6n tich duong d[t o C hai luc
'' -+
ts nhau F, = kQ' . uoi day 4 c6 dO lon bar _
rz
= 4Rzsin23.
N
T6ng hai luc ctra hai cli€n tich duong thu I t6c
dr,rng 16n iliQn tfch duong d4t tpi C c6 phuong
cira cluong kfnh C'C (cung lh phuong O,r,
hinh v€), vh c6 d0 l6n bing
' i.O;
2F,cosb,=.-It39b-=
*n't'nT
, - @' ,
ZR2sin2nt 2Rzsinzfit 2R2 sin9
NNN( 2ni n -a,\ ( 2ni n -a,\
ldo a, =-' b. - l.
( N' z )
V) vfy,hqp luc mi (N - 1) diqn tfch duongkh6c t6c dpng l€n tli6n tich duong cl6t tai C sE