2) M I AB I Nkhivd chi khi LI4I4B|J, tu,qs. C6c bd dd L, 2, 3, 4 ld cbc k6t qud co bin v6
sU dinh hufng trOn m[t phing. Tuy nhiOn, v6i
c6ch hi6u vd s1r dinh huone trOn m[t phing
don giAn nhu chring ta dang hi6u (dfnh hufng
bing c5i d6ng h6)," chring ta chi c6 thii thria nhfln chir khdng tht chimg minh tlugc c6c bd
d6 tr6n.
BO dA 5. Cho tu gi6c l6i ABCD kh6ng nQi
ti6p. X, Y, Z, T theo thri tu le tam ducrng tron ngopi ti6p ci,r' cbc tam gi6c BCD, CDA, DAB,
Chwng minh
Gqi ,Y, Y, Z, T theo thri tU le tam c6c duong tron (BCD), (CDA), (DAB), (ABQ; M, N theo
thir t.u ld trung tli6m cria CB, CD; P, Q theo thri t.u ld giao cliiim cria MN voiAB, AD1\.L).
Oe thAy XY, YZ, ZT, TX, XZ, YT theo thri tu
vu6ng g6c v6i CD, DA, AB, BC, BD, AC. Di6u t16 c6 nghia ld, XY, YZ, ZX theo thrl ru vu6ng g6c v6i CD, DA, BD vir XT, TZ, ZX
theo thrl t.u wOng g6c v6i CB, BA, BD. K6t hqrp vbi QN ll BD vd PM ll BD,ta c6 XY, YZ, ZX theo thrt t.u vu6ng g6c v6i ND, DQ, QN vd XT, TZ, ZX theo thi t.u vu6ng g6c vdi
MB, BP, PM.
Do d6, theo BO tl6 1, c6c c{p tam gi6c (XYZ,
NDQ) vd (XTZ, IWP\ tl6ng dang ctng
huong.
YQy LYYZTI LNDA vd LXrZ tf tuar g1
M[t kh6c, theo c6c 86 d.i 1,2, chu f ring
D I NQ / C; Q t CN / MN t CMt P; C I MP I B; theo 86 dA 4, ta c6 luvef{ towgttr, tCWg
tI tgct'tt|. tttcttll Lt{MCfJ, MMC
tl tcpu f{ tnpu It tunp e)
A
a
Hinh I
Tri (1) vi (2), theo BO de 3, suy ra
LXYZIl. nXrZ.
Vdy, theo gO aC 4,Y IXZ /T
TucrngWYlXZlT
Tt (3) ve (a) suy TaXYZT ld tu gi6c l6i.
C.ni i,.C6 the chimg minh kh6ng kh6 khln
rdng cdc t& gi6c ABCD, XYZT nguoc hu6ng.
aa ai 6. cho bt5n di6m A, B, c,D kh6ng c6 ba <ti6m ndo cing thudc m6t ducrng ,t8rg.
Khi d6 ducrng trdn Euler cua cilc tam gi6c
BCD, CDA, DAB, ABC ctng di qua mQt
tli€m.
eO AC 6 r6t quen thuQc, c6 th6 tim thAy
ph6p chimg minh cria n6 0 bei T9/280,
TH&TT s5 280, th6ng l0 nam 2000.
AA ai 7. Cho ttr giac titi ABCD vi b6n ttiiSm
X, Y, 2,7. Nt5u cfuc tam gi6c XYT, ZYT theo
thf t.u tl6ng dang ctng hudng (ngugc huong)
vbi cic tam gi6c ABD, CBD thi tu gi6c XYZT
tOi va d6ng dpng cirng hu6ng (ngugc hucrng)
v6i tu gi6c ABCD.
Chilmg minh
Trudng hW 1. Cic tam gi6c XYT, ZW theo
thf t.u d6ng dpng ctng hufng v6i chc tam gi6c ABD, CBD. Vl cic tam gi6c ABD, XYT tl6ng dpng cing hudng n6n t6n tpi (duy nh6t) phdp <t6ng dpng thufn f theo thf t.E bi6n A, B,