Source : symetriques-cercle-circonscrit.mp

input geometrie2d;
 

beginfig(1);
 
    A = Point(0,0); 
    B = Point(6,0); 
    C = Point(4.5,3);
 
    T = Triangle(A,B,C);
    c = CercleCirconscrit(T);
    O = Centre(C);
 
    M = ptoPoint(point 3 of (Lieu c));
 
    alpha = Symetrique(M,Droite(B,C));
    beta  = Symetrique(M,Droite(C,A));
    gamma = Symetrique(M,Droite(A,B));
 
    c1 = CercleCirconscrit(Triangle(A,beta,C));
    c2 = CercleCirconscrit(Triangle(alpha,B,C));
    c3 = CercleCirconscrit(Triangle(A,B,gamma));
 
    H = Orthocentre(T);
 
    %% Les dessins
    gTRD := 1.7; trace Droite(B,C); gTRD := 1.1;
 
    remplis T withcolor (0.9,0.6,0.6);
    trace T 
	withpen pencircle scaled 1 pt withcolor 0.6red;
    trace c 
	withcolor 0.6white;
 
 
    trace Segment(M,alpha)
	dashed withdots;
    trace Segment(M,beta)
	dashed withdots;
    trace Segment(M,gamma)
	dashed withdots;
 
 
    trace c1
	withpen pencircle scaled 0.2 pt withcolor 0.8white;
    trace c2
	withpen pencircle scaled 0.2 pt withcolor 0.8white;
    trace c3
	withpen pencircle scaled 0.2 pt withcolor 0.8white;
 
    trace Droite(alpha,gamma);
 
    marque.llft "A";
    marque.urt  "B";
    marque.urt  "C";
    marque.ulft "M";
    marque.lrt  "alpha";
    marque.lrt  "beta";
    marque.lft  "gamma";
    marque.bot  "H";
 
endfig;
end