+
"l +yl',ll *oro .
. Khoing cdch d dat cuc tidu khi
JlGo.,6-y, )
\2)
t - tm - 4..
Lvl
soil!: so!i9,,
Ldi giii. 1) Khi dich
chuydn AB dgc theo
truc chinh ctra quang
he, thi tia t6i tt B song
song v6i truc chinh t6i
qqang hO lu6n ktd+g vd, kr= fz-@-Ld) AnB" ArB, 1.2 ,,t"t _,-)*) _-)- (5) AB AB AB Tir (2) vi (5) ta c6 : lArl 0,9 l_fz-1d+Ldt_3 lkzl 1,2 4 fz-d 4 ) fz= d - 4Ld (6) TU (i), (4) vd (5), nit ra : (Ld)'-13(Ld)+12=0.
(Xem tidP trang 7)
(vi v, = * t. rni d6 vat A vi vat b c6,ch O lit:
J3
xn, = x,t -v{r,Yb' lm = lo - vzt* (3)' Theo dd bei
x* = dt = 30"v8 (m). Do d6 tir (2) vh (3) tim
dvgc y*= *nrJ3 = 90(m) : vAt B c6.cho ti 90m' NhAn x6t. C6c ban c6 ldi giii gon vh dring :
Kh6nh Hda: Nguy€n Ngqc K) Nam,l0 Li, THPT ch.
I-c Qui Don, NhiTrane ; Quing Nam t Nguyd-nThd Tdi Ldm,11/2, THPT Qud Son ; Phti Y6n t Ngtty€n Hfiu
Di?n, 12C1, THPT l-c Hdng Phong, Tuy Hda ; hi TAy :
Le Ddc H(ii,l1L2, THPT ch. Nguyen Huc, Hi Dong ;
Hda Binh : DdoTudnTil, LICJ-I,TIIPT ch. Hoing Van
Thu ; Ninh Binh : Vfr Thi Ngoc Anh, 12A3, TFIPT Y€n Khenh A ; Binh Dinh z Trdn Qudc Thdnh, i 1 Li, THPT chuyon I-e Quf Ddn, Quy Nhon ; Thanh H6a: Nguydn
uuy aieu, fuF, Tfil'I Lam Son ; Quing Ngai : Ini)r
Anh D[rc,11Bl, T]{PT chuy€n lJ Khidt : Quang Binh :
PhamVfi Dxc,Tl.-lYT chuy€n QuAng Binh : Hii Phdng :
PhamTudln Hi€p, l0 Li, THPT NK Trdn Phri ; Hi finh :
Nguy€nVdn Dfing,10 Li, THPT chuyOn He Tinh ; Hung
Yin : Nguydn Hodng Duy, l1 Li, TFIPT chuy0n Hrrng YOn ; Bdc Giang : DtongTrung Hi|u, Hd NangTdtt,
118, THPT NK NgO Si Licn I Bdc Ninh : Nguydnl/dn
Nsoc, l0 Li, k Minh Huy, 12 Li, Vn Van Tho. 12 Li, TFffrI chuyOn Bic Ninh ; Tp. Ho Chi Minh: L€ Qu6'c
Khdnh, 11 Li, PINK, DHQG Tp. HCM ; Dnk Lak :
Nguydn Chi Linh,11A1, 1TIPT Phan BOi ChAu, KrOng Nang ;\tnh Long : Tntong Huynh Qudc Khdnh, ll L|
THPT chuyen Nguyen Binh Khiem ; Ngh6 An :
Plnifhanh Hidn, 10 Li,K32, T[{PT PhanBoi ChAu,
Vinh; Hi Nam : LrrongTudn t ong, l0 Li, THPT chuyOn
Hi Nam ; Phri Tho : Ngu1,6n Quang Huy, 10 Li, THPT chuyon Hung Vudng ; Vurh Phric t Nguy€n Ngoc Hiing, 10A3, Cao Vi1r Trutng, 11A3, THPT chuyen Vinh Phtic; Hii Duong : Iz Hoiing Dnns, 10Li, *.ilIi;ffi*
Bni L2l317. Dat ntdt t'dt sdng AR vttdng .Edr:
yoi truc clinh ct?a tlrut kfith L irui O 1) t'd gttrt4q
ciiu l1m G (tai 02) (h. vd). L cd riiu c$ ft =
20cm vd G cd ti€rr cU fz = l2cm.
1) ){ac dinh gid tri a = OtO2 dd dnh ctia AB
tao boi h€ cd chi€u cao khbng ddi khi dich chuydn,q,fj doc theo truc chlnh cia lt€.
z4
ddi. Do d6, dd inh c[ra
A-n tao b6i quang h0 c6 chidu cao khong ddi thi
tia 16 kh6i quang h0 cira tia t6i n5i tron phi-i song song u,ii t lid
"lrinh. Nhu vay c6 thd cd 2 truong hgp :
- Dinh gucmg O2tring vdi tieu didm Fy cira
t. Khi d6 a=fi = 20(cm) ;
- Quang am C iria guong G trr)ng vdi tiOu didm F1 cila L. Khi d6 : a = ft + 2f2= 44 (cm)'
2) Khi chua dit bAn mat song song, so dd tao
hnh: ABffe'n'' Tacd a'= ll2- tt);
k, = fz : rft,r= A'B' -o'9 e).
' "fz-d AB Ats
Khi dat bAn mat song song, so dO tao Anh :
s-!\ trst 1f*7,+2a2 1ffi7 t3n3
Ydi Ld lh do dich chuydn so v6i vAt cira inh
/ r\
tao boi b6n mat song song Ld = el 1-: I (3)
" ( n)
Tac6: d'+b-6a= 9-Ld,lfz G)
(d - Ld)- I)
W *Ss *na(Ti€p bia 3) (Ti€p bia 3)
tglBA.dy) = tg(d1.BC) co !+ = !-,n', ra tim duoc 12 vd tuong ,ilff.ri. f3tu ru.
,t, cfia duong thdng CA. O day c6 didu gi dd hoi
ia ! ThAt vAy thAy ngay bii toiin cd v0 songhiOm hinh vi rlng vdi m6i giri tri tiry chon cta nghiOm hinh vi rlng vdi m6i giri tri tiry chon cta
k, sO c5 mOt tam gir{c th6a m6n dd bdi. Ldn nhy
ban thAt su hhi ldng.
Nh*g neu giA rhidr vd d,, d, lai rha1, d6ii,
chang han th hai dulng cao, hai dudng trung tuydn, hai dudng trung truc cira hai canh thi
sao ? Chfng tdi tin l) ban se giAi quydt duoc,
tuy nhien cflng xin gidi thieu de ciic ban tu ddi chidu vdi cric[ thiet l+p PT duong thing chfa
c6c canh cia LABC tr6n mat phing toa d6 Ory
trong m6t sd trudng hqp dudi day.
Trudng h-o. p 1. Bi€lr toa d6 A vd PT hai dudng cao khdng qua A.
- L4p PT dudng thi,ng AC qua A vi vuOng gdc voi d r.
- L4p PT dudng thang AB qua A vi vuOng g5c
v6i dr.
- Tirn toa d0 B, C suy ra PT dudng thing BC.
Trudng hW 2. Bi€1 roa dO B, PT drdng cao
d, qtra B vd PT dttdng cao d, (qua C ).
- L4p PT dudng thing A chfa canh BA (A qua
B vd vnOng g6c vdi dr).
- Chon didm A bdt ki rren A (A + B), l4p pT duong thhng AC vu6ng g6c vdi d1, cho duong ndy cat d dd tim toa do C.
BlLi to6n c5 vO sd nghiOm hinh vi rmg vdi m6i
A e L sd c6 mOt tam gidc rh6a m6n.
Trudng hqp 3. Bi€lr rca dO A, PT ltai trung
ruyAh d,, d, (ldn laot qua B, qwa C) (h.2).
- Tim toa dO trong
mm G cia MBC (d, cdt d2tai G).
- Tim toa d0 didm D ddi xung vdi A qua G.
- L4p PT dudng thing
d', qua D vd song song
vdi d,.
- Tim toa dd C ld siao
didm cfia' d','vir dr."Toa
dd B cflng duoc xdcdinh tuong tu. dinh tuong tu.
Trudng hqp 6. Bi6lt toa d6 B vd pT hai dadng
trung trltc (cila AB vd cia AC).
Ta chi cdn lim toa d0 didm A doi xung vdi Il
qua d,, rdi tim toa d0 C doi xung vdi A qta clr. C5 v6 nhu qic vdn dd d5 duoc giAi quydt boi vi hinh nhu chring ta dE x6t dii ciic trudng hqp
c5 li€n quan den c6c dudng dac bi0r trong ram gir{c. Nhtmg chua !
1) Chfng ta chua xdt bii toi{n v6i gid rhi€| cho
biei PT hai durtng phdn gidc ngodi (chic ld li
thri ldm day l)
2) Khi x6t bdi toi{n bidt roa do B, pI dudng
phAn giric trong d, qua B, PT phdn gi6c trong d,
chfng ta dd goi tr lA hO sd g5c cira dudng thing 84, tit d6 tim duoc ldi gi6i. Nhung xdt dubng
thing c6 h0 sd g5c ld dd duong nhiOn coi n6 ld
do"*g ngang hoic xi0n. Ndu n6 lai ld duong thang dritig c5 dang x = ru thi sao ?
Mong duoc tiep tuc trao drii vdi ciic ban.
CIlinh 3 Ilinh 3 A LL=u i I- H, g t\ ,ir, *-_.A( Hinh 4 t#{,{€, }-{,,41,t Trudng hgp 4. Bi€i roa dd B vd PT hai dLtdng trung ruy€h d,, d2 (ldn luot qua B, qua C) (h.3)
-Tim toa dO trong tt t6m G cia LABC
- Tini toa dO didm Br ddi xring vdi B qtaG.
- LQp PT dudng thing A, qua B, vh song song
vdi d2.
- Tim toa d61, trung didm cria GB,
- Chon mOt didm A thich ho.p tr6n Ar, rirn roa dO C (C doi xung v6i A qua 1)
Bii todn c6 v0 sd nghi0m hinh.
Trudng hqp 5. Bii'r toa do A , PT hai dudng
trwtg trtc d,, d" (cila AB vd cLia AC) (h.4)