input geometrie2d;

beginfig(1);
    A = Point(0,0); 
    B = Point(8,0); 
    C = Point(6,4);
    
    T = Triangle(A,B,C);
    c = CercleCirconscrit(T);
    O = Centre(c);
    
    M = ptoPoint(point 5.8 of (Lieu c));
    
    alpha = Projection(M,Droite(B,C));
    beta  = Projection(M,Droite(C,A));
    gamma = Projection(M,Droite(A,B));
    
    gTRD := 1.3; 
    trace Droite(B,C); 
    trace Droite(alpha,beta)
	withpen pencircle scaled 1pt withcolor 0.7red+0.2blue;
	
    trace Segment(M,alpha) withpen pencircle scaled 0.5pt;
    trace Segment(M,beta) withpen pencircle scaled 0.5pt;
    trace Segment(M,gamma) withpen pencircle scaled 0.5pt;

    trace T
	withpen pencircle scaled 1pt withcolor 0.6green;
	
    trace c
	withcolor 0.6white;
	
    marque.lft "A";
    marque.rt "B";
    marque.urt "C";
    marque.urt "alpha";
    marque.top  "beta";
    marque.top "gamma";
    marque.bot "M";
    	
    trace SigneOrtho(M,beta,A,0.2);
    trace SigneOrtho(M,gamma,B,0.2);
    trace SigneOrtho(M,alpha,C,0.2);
endfig;
end