Chiziqli tenglamalar sisitemacini yechish

> draw({c,c1,c2},rinttext= true,

view=[-2..4,-2..4]);
Uchburchak tashqi tomonlariga urinuvchi aylanalar:

> restart;

> with(geometry):

s := point(A,1,1),point(B,3,1),

point(C,2,4): triangle(T,[s]); T

>excircle(obj,T, [c1(o1),c2(o2),c3(o3)]);



> draw({o(obj),T},rinttext=true);
Ichki chizilgan aylana:

> with(geometry):

triangle(T, [point(A,0,0), point(B,2,0), point(C,1,3)]):

Gergonnepoint(G, T); G

> detail(G);

name of the object: inc

form of the object: circle2d

name of the center: o

coordinates of the center: [2.748677468, 2.839772364]

radius of the circle: 1.749794557

equation of the circle: 12.55775391+_x^2+_y^2-5.497354936*_x-5.679544728*_y = 0

draw the icture of the above definition for the triangle T

> incircle(c,T):

segment(sg1,A,rojection(H,center(c),line(tm,[B,C]))):

segment(sg2,B,rojection(E,center(c),line(tm,[C,A]))):

segment(sg3,C,rojection(F,center(c),line(tm,[A,B]))):

draw({sg1,sg2,sg3,c(color= blue,style=OINT), G(symbol=DIAMOND),T(color=red)},color=blue,rinttext=true);
Tashqi chizilgan aylana:

> with(geometry):

triangle(T, [point(A,0,0), point(B,2,0), point(C,1,3)]):

circumcircle(Elc, T, 'centername' = OO);

d etail(Elc);

draw({Elc(color=blue),T},printtext=true);

name of the object: Elc

form of the object: circle2d

name of the center: OO

coordinates of the center: [1, 4/3]

radius of the circle: 1/9*25^(1/2)*9^(1/2)

equation of the circle: _x^2+_y^2-2*_x-8/3*_y = 0
Ichki va tashqi chizilgan aylana:

> with(geometry):

t riangle(T, [point(A,-1,3.), point(B,5,2), point(C,1,-1)]): > circumcircle(Elc, T, 'centername' = OO); Elc

Gergonnepoint(G, T); G

> coordinates(OO);



> coordinates(G);



> incircle(c,T); c

> radius(Elc); radius(c);

3.091243298 1.414345456

> detail(G);

name of the object: G

form of the object: point2d

coordinates of the point: [1.391235831, .8742435189]

draw the icture of the above definition for the triangle T

> incircle(c,T):

segment(sg1,A,rojection(H,center(c),line(tm,[B,C]))):

segment(sg2,B,rojection(E,center(c),line(tm,[C,A]))):

segment(sg3,C,rojection(F,center(c),line(tm,[A,B]))):

draw({Elc,sg1,sg2,sg3,c(color=blue,style=line),G(symbol =DIAMOND),T(color=red)},color=blue,rinttext=true);

Aylanadan tashqaridagi nuqtadan o‘tkazilgan urinma tenglamalari:

> restart;

> with(geometry):

point(A,3,1),circle(c,x^2+y^2+8*x+2*y-8=0,[x,y]);

> TangentLine(obj, A, c, [l1, l2]); [l1, l2]

> form(l1), evalf(Equation(l1));



> form(l2), evalf(Equation(l2));