Samarqand davlat universiteti raqamli texnologiyalar fakulteti amaliy matematika informatikayo

> draw({T(color=blue),mT(color=red)},style=line,axes=NONE, rinttext=true);

Endi AN bissektirsa tenglamasin ikki xil usulda topish mumkin:

a)
tenglamga asosan aniqlaymiz.
Bu bissektirsa AB va AC tomonlar orasida bo‘lagligi uchun bu tomonlar tenglamalari
AB: 2x + 7y – 41 = 0 va AC: 5x + 6y – 68 = 0.
ga asosan:

bundan:
(A) , (B)
tenglamlardan qaysi biri A burchakning ichki burchagining bissektirsasi AD ekanligini aniqlaymiz. (A) tenglamaga B va C nuqtalarning koordinatalarini qo‘yganda chap va o‘ng kasirlar ishoralari har xil bo‘ladi. Bundan (A) tenglama ABC ning A ichki burchagining bissektrisasi bo‘ladi. (B) tenglamaga B va C nuqtalarning koordinatalari qo‘yilganda bir xil ishorali bo‘lgani uchun (B) tenglama qo‘shni burchak bissektrisasi bo‘ladi.
Ichki burchak bissektrisasi:
> with(geometry):
triangle(ABC, [point(A,10,3), point(B,-4,7), point(C,4,8)]):
define the ``line'' bisector bA
> bisector(bA, A, ABC); bA
> Equation(bA,[x,y]);
> detail(bA); name of the object: bA
form of the object: line2d
equation of the line: 1630.535418-104.0420976*x-196.7048141*y = 0
Qo‘shni burchakning (qo‘shma) bissektrisasi;
> with(geometry):
triangle(ABC,[point(A,10.,3),point(B,-4,7),point(C,4,8)]):
define the external bisector bA
> ExternalBisector(bA, A, ABC); bA
> Equation(bA,[x,y]);
> detail(bA); name of the object: bA
form of the object: line2d
equation of the line: 1654.921848-196.7048141*x+104.0420976*y = 0
> bisector(ibA,A,ABC):
ArePerendicular(bA,ibA); true
b) A burchak bissektrisasini BC tomon bilan kesishish nuqtasi N ning koordinatalarini topamiz. Geometriya kursidan mahlumki, uchburchak burchagining bissektrisasi burchak qarshisidagi tomonni burchakka yopishpgan tomonlarga proportsional bo‘laklarga bo‘ladi.
Demak: dan  dani son qiymatini topib(= ),
,
formulalarga asosan N(x, y) nuqtani topamiz va ikki nuqtadan o‘tuvchi to‘g‘ri chiziq formulasiga asosan: AN bissektrisa tenglamisini tuzamiz:
.
bA bissektrisani BC tomon bilan kesishish nuqtasi N koordinatalari: