- Thuat giai 4.4:
1/ t~p cae d6i tu<;fng :
0 ={01> O2, 03, 04, Os}.
2/ t~p cae quail h<$(giua cae d6i tu<;fng): F ={ fI. f2, . . . , f2I. f22}.
3/ t~p cae bie'n dU<;fCxem xet : .
f3 : 02.e =Ol.a f4 : 02.GoeA =OI.GA f5 : 03.a =OI.BD f6 : 03.b =Ol.e f7 : °3.e =Ol.b fs : 03.GoeA =OI.GC f9 : 04.a =OI.AC flO : 04.b =Ol.b f11: 04.e =Ol.a f12: 04.GoeA =OI.GB f13: °5.a =OI.AC fl4 : Os.b =Ol.e fls: Os.e =Ol.d fl6 : Os.GocA =OI.GD
f17 : OI.GA =04.GoeB + Os.GoeB fls : OI.GB =02.GoeB + 03.GoeB fl9 : OI.GC =04.GoeC + Os.GoeC f20: OI.GD =02.GoeC + 03.GoeC f21: OI'S =02'S + 03'S
M = {Ol.a, Ol.b, Ol.e, Ol.d, OI.GA, OI.GB, OI'C, OI.D, OI.S, OI.BD, OI.AC,02.a, 02.b, Ol.e, 02.GoeA, 02.GoeB, 02.GoeC, 02'S, 02.a, 02.b, Ol.e, 02.GoeA, 02.GoeB, 02.GoeC, 02'S,
03.a, 03.b, 03.e, 03.GoeA, 03.GoeB, 03.GoeC, 03'S, 04.a, 04.b, O~.e, 04.GoeA, 04. GoeB, 04.GoeC, 04'S,
Os.a, Os.b, Os.e, Os.GoeA, Os.GoeB, OS, GoeC, Os.S
}
41 Gia thie't (cae s1,1'ki~n da bie't):
A = {Ol.a, OI.b, OI.e, OI.d, OI.GA } 51 Ml;1etieu tinh toan (t~p bie'n e~n tinh) :
B= {OI'S}
Giai theo thu~t giai suy di§n tie'n ta co qua trlnh xern xet cae quail h~ d~ tlrn Wi giai nhu' sau :
Gia thie't : { Ol.a, Ol.b, Ol.e, Ol.d, OI.GA }
L~n lu'dt thli' ap dung cae quail he giua cae d6i tu'dng ta tinh du'de :
02.b, nho ap d1:111gf1 nho ap dl;1ng f3 02.e, 02.GoeA, 03.b, nho a p dl;1ng f4 nho a p dl;1ng f6 03.e, nho ap dl;1ngf7 nho ap dl;1ngflO 04.b, 04.e, nho ap dl;1ng fl1 nho a p dl;1ng fl4 Os.b, Os. e, nho a p dl;1ng f15
L~nlu'dt xet cae d6i tu'dilgtheo thli tu' 01,02, °2" °1~ ta tinh du'de : 02.a, 02.GoeB, 02.GoeC, 02'S, nho ap dl;1ngO2.
OI.BD, nho ap d\lng fl nho ap d\lng f5 03.a,
Lai xet cac d5i tudng theo thu tu 01, °z, °l' °1~ ta tinh dudc : 03.GocA, 03.GocB, 03.GOCC, 03'S, nho ap d\lng 03, Lai xet cac quail he giua cac d5i tudng ta tinh dudc :
OI'C, OI.D,
nho ap d\lng f8 nho ap d\lng f20
OI'S, nho ap d\lng f21
De'n day ta da d:,ttduQC m\lc tieu c~n tinh toan, va c6 mQt loi gi,ii nhusau : { f2, f3, f4, f6, f7, flO, f11, f14, f15, O2, fI, f5, °3, f8, f20, f21}.
Sail khi rut gQn Wi giai tren ta suy ra duQc mQt Wi gic:lit5t nhu sail : { f2, f3, f4, f6, f7, O2, f}, f5, 03, f21}.
TheoWi gic:lin~y, qua trlnh tinh toan di~n tich S cua tu giac nhusau : Tinh 02.b, (c:,tnh AD)
Tinh Oz.c, (c:,tnh AB)
a p d\lng f2 a p d\lng f3 Tinh 02.GocA, (g6c A) Tinh 03.b, (c:,tnh CD) ap d\lng f4 ap d\lng f6 Tinh 03'C, (c:,tnh CB) a p d\lng f7
Tinh 02.a,02'S, (c:,tnhBD,di~n tich tam giac ABD) ap d\lng O2 Tinh OI.BD, (duong cheo BD cua tu giac)
Tinh 03.a, (c:,tnhBD cua tam giac CBD)
ap d\lng fI
a p d\lng f5 Tinh 03'S, (di~n tich tam giac CBD)
Tinh OI'S, (di~n tich tu giac ACBD)
ap d\lng 03 ap d\lng f21.
Vi du 4.7: Trong vi d\l n~y ta xet l:,tibai toan trong vi d\l 4.5-2: Cho hlnh blnh hanh ABCD. Gia su M va N la 2 di~m tren AC saG cho AM =CN. Chung
..
IBili toaD n~y c6 the bieu di~n du'di d~ng bili toaD (0, F) => G nhu' sau: 0 ={ OJ, Oz, 03}
Trang d6 01 la hlnh blnh hanh ABCD, Oz la tam ghie ABM va 03 la tam giae CDN (duQe xfty d11ngtren cae di@mA, B, C, D, M va N). F ={ Oz.b =03.b (e~nh AM =e~nh CN),