input geometrie2d;
gTRD := 10;
labeloffset := 5pt;

beginfig(1);
    Fenetre(-5,-6,7,7);

    A = Point(0,0);
    B = Point(3,0);
    C = Point(2.1,2.25);

    b1 = Bissectrice(C,A,B);
    b2 = Bissectrice(A,B,C);
    b3 = Bissectrice(B,C,A);

    O = Intersection(b1,b2);

    A' = Intersection(b1,Perpendiculaire(B,b2));
    B' = Intersection(b2,Perpendiculaire(C,b3));
    C' = Intersection(b3,Perpendiculaire(A,b1));

    c1 = Cercle(O,Distance(O,Droite(A,C)));
    c2 = Cercle(A',Distance(A',Droite(C,A)));
    c3 = Cercle(B',Distance(B',Droite(A,B)));
    c4 = Cercle(C',Distance(C',Droite(B,C)));

    T = Triangle(A,B,C);

    trace Droite(A,B);
    trace Droite(B,C);
    trace Droite(C,A);

    remplis T withcolor .8white;
    trace T withpen pencircle scaled 1 ;


    remplis c1 withcolor 0.5(red+white);
    remplis c2 withcolor 0.5(red+white);
    remplis c3 withcolor 0.5(red+white);
    remplis c4 withcolor 0.5(red+white);

    trace c1 withcolor red;
    trace c2 withcolor red;
    trace c3 withcolor red;
    trace c4 withcolor red;

    trace b1 withcolor red;
    trace b2 withcolor red;
    trace b3 withcolor red;


    marque.ulft "O";
    marque.bot  "A";
    marque.llft "B";
    marque.top  "C";
    marque.top  "A'";
    marque.urt  "B'";
    marque.rt   "C'";

endfig;

end