% Propriété métrique dans un triangle :
% AB.AC=2.R.AH
% mardi 8 juin 1999
input geometrie2d;


beginfig(1);

    A = Point(3,7.5);
    B = Point(0,0);
    C = Point(9,0);
    H = Point(3,0);
    T = Triangle(A,B,C);
    c = CercleCirconscrit(T);
    O = Centre(c);
    A'= Symetrique(A,O);
    
    trace T
	withcolor (0,0.39,0)
	withpen pencircle scaled 1.5;
    
    trace c
	withcolor black;
	
    trace Segment(A,H)
	withcolor red;

    trace Segment(B,A')
	withcolor 0.4red;
    trace Segment(A,A')
	withcolor 0.4red;
	
    trace SigneOrtho(A,H,C,0.2);
    trace SigneOrtho(A,B,A',0.2);
    
    marque.top "A";
    marque.lft "B";
    marque.lrt "C";
    marque.bot "H";
    marque.urt "O";
    marque.bot "A'";
    R = Milieu(Segment(A,O));
    Etiquette.urt("$R$",1,_Point(R));
	
endfig;

end