- 4HA l 4HB l 4HCl
PQ cit EMtqitdm vi ty ngodi Tcta hai tludng trdn (Oz) vd (O:).
hai tludng trdn (Oz) vd (O:).
Suy ra TM.TE =TP.TQ, nghia ld M, E, P, Q cingthuQc mQt dulng hon. Nhu vfy 6 di6m M, N, E, F, P, Q
cr)ng thuQc mQt dudng tron.
Suy ra tfi gi6c MNFE nQi tii5p.
Gii sir ntrcit dudng trdn (Y, YD tqt F' . Do hai
ttucrng trdn (Y, YA[) i
vd(Y,ỈV) d6ng tdm
vd hai tlucrng thlng ME, NF'giao nhau t4i I
n6n tu gi6c MNF'E h hinh thang cdn, suy ra
MNF'E ld tu gi6c nQi ti6p.
Lai c6 F vir F'ctng nim trdn (I, Iltr) n6nF = F',hay Y, N, F thinghdng. Ta c6 dpcm. F = F',hay Y, N, F thinghdng. Ta c6 dpcm. C6ch 4. Trudc ti6n ta ph6t bi6u hai b6 đ saụ gO ai 4. Cho hai dtdng trdn (O) vd (O2) kh6ng chaa nhaụ Gei Cu Cz ld hai dadng
.:
trdn ti€p xilc ngodi voi (O), (Oz) ldn luqt tqi A, B vd C, D. Khi d6 A, B, C, D cilng thuQc
mQt &rdng trdn. Chirng minh. Ap dung dinh li Monge- D'Alembert Hhh 5
BO dA 5. Qhudi dudng trdn Apollonius - Bdi todng
dudng trdn). Cho ba drdng trdn (O), (Oz), (Oz)
ffAn mQt phdng. Ta xay dwng m\t chudi itudng trdn xoay vdng nha sau: Ggi Cn ld dudng trdn tiiip xuc v6i (O) vd (O); Czz ld iladng trdn fidp nic vbi Cn, (O), (O); Ctq ld iluong trdn tidp xuc voi Cy, (O), (O); Cr,s ld duong trdn tiiip xtic voi C3a, (O), (O); Csa ld &rdng trdn tidp xilc vhi Ca5, (O), (O); Cer ld dudng trdn
tidp xilc vhi Cse, (Q), (O). Khi d6 Cn, Czz, ...,
Car ld mAt chudi d6ng, hay Cer fidp nic voi Cn Chftng minh. Ta chimg minh bdi to6n trong trudng hqrp ba tluong trdn (Or), (O2), (q) dii
mQt ngoii nhau (ft.7). Cbc trudng hqp kh6c chimg minh tucrng t.ụ
Gei Pr, Pzl6,n luqt ld
titip di6m ola Cp v1r (O1) vd (O); Pt lit
ti6p di6m c:iura Czt vbi (O); Pc ld ti€p tti6m cria C3av1i (O1), tucrng
t.u v6i Ps, Pe,&.Nhu v$y ta cAn chimg minh
D _Dt7:11. t7:11.
Ap dl,mg AA ae 4 cho hai dudng trdn Crz vi
C3a cirng hai tlulng trdn titip x'itc Czt vi (O1)
suy raP1, Pz, Pz,Pa ctrng thuQc mQt tludng frdn.
Ap dune na ai 4 cho hai dulng trdn (O2) vd (O:) v6i hai dudng tron ti6p x:6c Czt vi Go
suy ra Pz, Pt, Ps, Pecirng thuQc mQt dudmg trdn.
cho ba tluong trdn (O),(Oz), C1 su! ra