n6ng dugc.
'/?ta4rV T
"rrfu* a/"AL
Nnieu nguoi cld bi6t bdi to6n sau :
Tr6n mOt bin dd c6 ba dia di6m (kho, tr4m buu
cliQn, ...) A, B, C kh6ng thdng hdng. CAn ph6i
xdy dqng c5c do4n tludng tir mOt vi tri M ndo d6 t6i A, B, C sao cho d0 dei cta mang cludng
MA + MB + MC ld ngf,n nhAt. Nhd to6n hoc
Italia ld Torricelli dd giAi bii to6n nay vdokhoing ndm 1640. KOt lu6n nhu sau: NOu tam khoing ndm 1640. KOt lu6n nhu sau: NOu tam gi6c A-BC c6 m6t g6c bing hopc l6n hon 120o
thi <liOm M phei trr)ng vdi clinh g6c ti cria tam
gi6c, cdn n6u ba 96- cria tam gi6c ABC d€'t
nh6 hon 120" thi di6m M phii th6a min
1fr8 = BMa=cfr : 120". Di€m M nhu th6
... -.;
gQt la dtem I orrtcellt.
Ta x6t bdi toSn tuong tU aOl v6i tir gi6c.
Dinh cho bln tlgc
l) Cho ttr gi6c l6i ABCD. Hdy x6c dinh vi tri
didm M sao cho rlQ ddi crha MA + MB + MC + MD
ld nho nhAt.
2) Cho hinh chfr' nhAt ABCD voi AB < AD. Hdy x6c <linh vi tri hai didm M vd N sao cho d0 ddi .cia MA + MB + MN + NC + ND le nh6 nhAt.
ciai d6p bii: l-llNH HCA NAI'I CANH
1) Hinh trdn l6n tAmO (h. 1) c6 b6n kinh O (h. 1) c6 b6n kinh R: OAI: AHr sin36" - sin36" n6n c6 di€n tich ld S: zrR2 : ttAHz rr2
sin2 36o sin2 36o
Ding thfc xiy ra e> ArH = 7' Q A1A2: 2r,
nghTa ld 44u ld cludng kinh cria dudng tron
tAm O,*r (i : 1, 2, 3, 4) vd ArAs : 2r. .,.)
Lric116S mil = sin2 36olrr- =9-09312.
2) Kf hiQu Sz ld dien tich tam gi6c, Sr ld diQn
tich hinh quat. Ta tinh dugc (h.2): AO 12 trr7?9 5o,u,1,4,=f'orc=ff " _o.O4 _ /rr2 oqto{h.t- fO - 41so'r1;rc lo(sa@Ao2r + s+rr2,1,, -s0,,,^,r,) : 12.cos2 7V' + 70Sq<ct,\ttzl
I 0 cos 72o.sin 72o ll)rii l 108.rr2 3rr2 Sq(h4r:) i0 360 E- s - 1= 1,081. ISSN : 0866-8035 Chi sd ;12884 Ma so :88T50M6 7f
Bqn Trinh Vdn Nam, llAl, THPT chuydn Phan BQi ChAu, Vinh, NghQ An c6 ldi gi6i tdt, dugc nhfln tflng ph6m.
PHI PHI
Gidy ph6p XB sd67/GP-BVHTT cdp ngiy 15.6.2004
In tai Cdng ty CP in Di6n Hdng, 1878 Giing V6, Ha NQi Gir{ : 4000 tldng In xong vd nQp luu chidu th6ng 6 nam 2006 Bdn nghin ddng