mo +7 (o ddy a td sd nguyAn kh6ng dm).
Ldi gi,rti. (theo ila si5 c6c ban). Ta c6 2^-1 n+l n 1 m -m +m -l Df;t n+l=2's, trong d6 r,se m-l N, s 16vdr<n. X6t cla thric P(m)=*2'-1 -*n+1 +m'-l _ mn (mz'(z*'-') +l)_(mr', + 1). Do s vir (2' ' - s) ld c5c sO 16 n€n P(m) chia hi5tcho m2' +1. Suyra P(m)=(m'z' +l)Q@) Q)
trong d6 Q@) ldcla thric v6i hQ s6 nguy6n. Vi
P(1)=g n6n Q(1)=0 vd Q(m)=(m-l)T(m)(2)
trong d6 T(m) litda thric v6i hO sti nguy6n.
Tt (1) vd (2) suy ra ), _l
*
, t -*' =\2' +l)T(m)
m-l
hav s6 ' 1u6n c6 mdt u6c s6 c6
" m-l
dqng m'+ 1 voi a ld s5 nguy€n kh6ng Am. tr
YNhQn xdt.Tr€nddy ld c5ch ghi ctnhai bqn Trdn Bd Khdi,llT2, TIIPT chuyCn DHSP HA NQi vd Trdn Nhdt
Quang, 11T, TIIPT chuyCn KHTN, DHQG Hn NQi.
^
NGUYEN VAN MA,U
B,diTl2l463. Cho tam gidc nhqn ABC vdi O h
tdm dudng trdn ngoqi t!€p tam gidc. Gei D, E,.F theo tha hS la trung"di€m cua BC, CA, AB. Di€m
M thudc dadng thdng BC. N ld giao di€m c{ta
AM vd EF. P ld gigo di€m thu hai cuct ON vddudng trdn ngogi ti6p tam gidc ODM. Q ld diem dudng trdn ngogi ti6p tam gidc ODM. Q ld diem
2, -|m -l n m -l n __m = m-1 ^ U TORN HOC Z+ -clirdiff@
dAi xung vcti M qua trung didm ctia DP. Qhtimg minh rdng Q thu6c drong tron ngoai ti€p tam giac DEF.
Ldi gi,rti.
A
Trong loi giai nay, kf hiQu,Srchi phep AOI xrmg t6mf. Gqi (O') ld duong trdn ngoai tidp LDEF; H lir
di6m dOi ximg cua D quia O'; I ld giao di6m cria
ADvitEF: R:S/(N).
Vi O h t6m clucmg trdn ngoai ti(:p LABC vd D, E, F theo tht tU ld trung itii5m cria BC, CA, AB n6n O ld truc t6m cira LDFE (1).
Vi O'e DH vitD,E,Ftheothf t.uldtrungdiilm
cl;;a BC, CA, AB nln EH LEDIIAB=AF:
FH L FD llAC = AE. (adsbygoogle = window.adsbygoogle || []).push({});
Do d6 H ld truc trim cria LAEF t2).
Tri (1) vd (2), chri f ring MEF:5,(A,DFE),
suy ra H = Sr(O) (3).
Vi O ld diOm dOi ximg cira M qtatrung dii5m cira
DP n)n FA = M6.
Vi R=Sr(N) vd E, F theo thri t.rr ld trung di6m cin CA, AB n)n wF.:Zwi = UD G).
Ydy FA=NR.
Di6u d6 c6 nghTa ld RQIINP = NO.
Tt (3) vd (a) h co HNOR ld hinh binh hdnh
=HRllNO, suy ra HeRQ. Chri f ring
HQ=RQllNP =OP LMPIIDQ, suy ra QthtQc
cluong trdn iludng kinhDH.
N6i c6ch thdc Q thuQc (O') (dpcm). tr
YNhQn xd1
1) IG6 nhi6u bpn tham gia gihibdi torin ndy, da s6 di:u
sri dqng phdp d6i ximg t6mL
2) Xin n6u t6n m6t sr5 b4n c6 loi gi6i t6t: fnri tng:
Nguydn Ti€n Long,10T, THPT chuy6n Hirng Vuong, TP. ViCt Tri; Bic Ninh: Nguydn Thanh HiAu, 1lT,
TIIPT chuy6n.Bic Ninh, TP. Bic Ninh; Hn NQi: Vfr Dilrc Vdn, Trdn Ba Kh6i, Phqm Nggc Khdnh, llT,
THPT chuy6n DHSP Hd NQi; Thanh lJoil Vil Duy Manh, D6 Thu) Anh, 11T, TIIPT chuy6n. Lam Scrn, TP. Thanh Ho5; NghQ An: Vd ViQt Anh, Phqm Trdn Anh,10Al, THPT chuyCn Phan B6i Ch6u, TP. Vinh; Long An: Pham Hodng NguyAn,1141, TIIPT Hflu Nghia' Dric Hod'
NGTTYEN MINH HA
BdiLll463. Bdn mfit phiing v6 hqn tlch di€n diu
vcti mdt d0 di€n mdt ld -o, giao nhau, tqo thdnh
m\t hinh chdp diu cd canh ddy ld a, canh b€n ld
b. Tqi mQt di€m ndm tr€n dudng cao cila hinhchdp cdch ddy mQt doan h ngrdi ta ddt m6t qud chdp cdch ddy mQt doan h ngrdi ta ddt m6t qud c,iu khiii laqng nhd m, diQn tich +q. Budng qud cdu kh6ng vQn tdc ban diu.
^:
Tim vdn l6c cua qua cdu khi nd tcti va chgm vdo hinh ch6p. Xet cdc tinh huiing co th€ xdy ra. Gid thid diAn tich tr€n mdt hinh chop kh6ng dich chuy€n.
Ldi gidi.
^t
Hinh 1 Hinh 2 (adsbygoogle = window.adsbygoogle || []).push({});
Gi6 sir SABCD ld hinh ch6p <16u (ld giao cuab6n mflt phing tich cli6n t16u), Sl1ld dudng cao, b6n mflt phing tich cli6n t16u), Sl1ld dudng cao, ,SD ld ttuong cao qia m{t b6n CSB (h.1). MAi
m[t phing tich iliQn t4o ra mQt diQn trucrng tl6u c6 phucrng vudng g6C v6i mdt d6 vd c6 cl6 l6n
bing E =+. Vi hinh ch6p ld ddu n6n trongzto zto
re n.r,u-ror., T?[]#EE
hinh ch6p, t6ng c5c hinh chi6u 16n mdt d|y ABC ctra b6n vecto cudng d0 diQn trudng bing 0, cdn tdng c5c hinh chi6u 16n <luong cao SIl cin cbc
vecto cudng dQ diQn trudng bing E. : E -
3,Ecoscr (1), trong d6 cr ld g6c giira tludng cao
SIl vd tlucmg cao cira mQt mflt b6n b6t ki cira hinh ch6p (h.2). Xdt trvc Ox hu6ng dgc theo 51L Tr6n h.2 c6 tam gi6c ASD;E ld vecto cucrng dQ diQn trucrng t4o boi mpt phing BCS; O ld di6m d{t dien tich+q. Ta c6:
+ = -qE,(SH - ir). Tri d6 :
oqh (
,". t,
y=
YNhQn xet Chic mring hai bpn c6 lcri gi6i ding: LA
Cao Anh, l0F, THPT chuy6n Lam Son, Thanh Ho6; Trdn Htru Hodng, 11A1Li, TI{PT chuy6n KHTN, DHQGHnNoi.
DINH THI THAI Qt].iNH
Bdi L21463. MAt khai bp phrumg dqc. d6n7chdt, canh 2a. Traql diu kh6ng ma sdt, vQn t6c chdt, canh 2a. Traql diu kh6ng ma sdt, vQn t6c vs ffAn mdt bdn nhdn - nd* ngorg, o cqnh bdn co mQt cd nho. Vcti diiu ki€n ndo ctia vs d€ vqt
co thd rcti khdi ban. Gia sa kich thadc gd rdtnh6, kh6ng ldm sai Mch dang kd chuydn dQng nh6, kh6ng ldm sai Mch dang kd chuydn dQng
M6men qu6n tinh cira kh6i AOi voi truc A nim
ngang <Ii qua gd: 1o = Io+*(oJ|)' =\*o'1t1
Ngay sau va chpm, ttrOi sC 4ray quanh t1lc A voi t5c d0 g6cro. Ap dung dinh lu4t b6o toan m6men
dQng lugng AOi voi truc A i mavo = I o{D (2) DQng nlng cira khOi ngay sau va cham:
nn =lt o.;' (3)
Khi khdi quay quanh truc A mQt g6c a00, th6 ndng ctra kh6i da tdng mQt lugng:
n, = mga(J, -l)
OC tnOi roi khoi bdn dugc th\ Ek> E,
Thay Ep, E d (3) ve (a) vdo (5), t6t hqrp vtri (1)
t6-M
vd (2) ta tim dugc: v6 > -\l 4.1#. 3 tr
YNhQn xet. C6 3 ban gur lcri gi6i toi tda soan, trong d6 chi c6 b4n Trin H{tu Hodng, 11Al Li' THPT
chuy6n KHTN, EHQG He NQi c6 ldi gi6i <lttng. NGUYEN XUAN QUANG (adsbygoogle = window.adsbygoogle || []).push({});
I;
- J3a
I-@7 .tr
Tu (1) vd (2) ta c6 :
/-\
E,: E- 3Ecosct : tl t- Jza 1
t' 1+*--)
C6 ba trucrng hqp sau:
l.E,> 0, tuc ld khi b > a. Khi dugc budng ra,qu6 cAu chuy6n dQng theo hu6ng va ch4m mflt qu6 cAu chuy6n dQng theo hu6ng va ch4m mflt d5y hinh ch6p.
Vi dien trucrng ld cldiu, n6n lpc t6c dung l6n qu6
ciu ld F, : QE,.Ap dpng dinh lupt b6o todn
' mv'=Fh=aEh ndng lugng tac6: 1 r r . t- {zo L - ,,14b' - a'
2. E*:0, tric liL b : a. Khi d6, b6n trong hinhch6p, cudng dO diQn truong bing 0 vd qui cdu ch6p, cudng dO diQn truong bing 0 vd qui cdu khdng chuy6n dQng.
3. E* < 0, tuc lir b < a. Khi d6 qui cAu chuy'5nclgng vC phia dinh hinh ch6p vd va chpm vdo dinh. clgng vC phia dinh hinh ch6p vd va chpm vdo dinh.
visr: F=n6nb> VJa
(h.2).
Nhu v{y phdi c6 ,
ft'U'u
Ap dirng dinh 1u0t b6o todn ndng lugng ta c6: