# Les droites remarquables

Les médianes

Voici son code :

u:=1cm;
figure (-u,-2u,8u,6u);
pair A,B,C,I,J,K,G;

A=(0,0);
B=(2u,5u);
C=(7u,-u);
I=0.5[B,C];
%I:=milieu(B,C);
J=0.5[A,C];
K=0.5[B,A];

G=whatever[A,I]=whatever[B,J]; %centre de gravité
%G:=(A+B+C)/3;
%G:=iso(A,B,C);

draw A--B--C--cycle;
draw droite(A,I) withcolor red;
draw droite(B,J) withcolor red;
draw droite(C,K) withcolor red;

trace codesegments(B,I,I,C,2);
trace codesegments(A,J,J,C,1);
trace codesegments(B,K,K,A,3);

marque_p:="rien";
label.ulft(btex $A$ etex,A);
label.urt(btex $B$ etex,B);
label.bot(btex $C$ etex,C);
label.top(btex $I$ etex,I);
label.llft(btex $J$ etex,J);
label.ulft(btex $K$ etex,K);
label.urt(btex $G$ etex,G);

label.lrt(btex $(d_1)$ etex, 1.6[G,I]);
label.llft(btex $(d_2)$ etex, 1.4[G,J]);
label.urt(btex $(d_3)$ etex, 1.6[G,K]);

fin;



Les médiatrices

Voici son code :

u:=1cm;
figure (-u,-3u,8u,6u);
pair A,B,C,K,I,J;
pair O;

A=(0,0);
B=(2u,5u);
C=(7u,-u);
I=0.5[C,B];
J=0.5[A,C];
K=0.5[A,B];

draw A--B--C--cycle;

O=CentreCercleC(A,B,C);   %centre du ercle circonscrit

trace codesegments(A,K,K,B,2);
trace codesegments(C,I,I,B,1);
trace codesegments(A,J,J,C,3);

draw droite(I,O) withcolor red;
% draw mediatrice(B,C) withcolor red;
draw droite(J,O) withcolor red;
draw droite(K,O) withcolor red;

trace codeperp(O,I,C,5);
trace codeperp(A,J,O,5);
trace codeperp(O,K,A,5);

draw cercles(O,A) withcolor blue;

marque_p:="rien";
label.llft(btex $A$ etex,A);
label.ulft(btex $B$ etex,B);
label.lrt(btex $C$ etex,C);
label.top(btex $I$ etex,I);
label.llft(btex $J$ etex,J);
label.ulft(btex $K$ etex,K);
label.urt(btex $O$ etex,O);

label.ulft(btex $(d_1)$ etex, 2.5[O,I]);
label.ulft(btex $(d_2)$ etex, 1.7[O,J]);
label.llft(btex $(d_3)$ etex, 1.4[O,K]);


Les hauteurs

Voici son code :

u:=1cm;
figure (-u,-2u,8u,6u);
pair A,B,C,AA,BB,CC,H;

A=(0,0);
B=(2u,5u);
C=(7u,-u);
AA=projection(A,B,C);
BB=projection(B,A,C);
CC=projection(C,B,A);

H=Orthocentre(A,B,C);     % orthocentre

draw A--B--C--cycle;
draw droite(A,AA) withcolor red;
draw droite(B,BB) withcolor red;
draw droite(C,CC) withcolor red;

trace codeperp(A,AA,B,5);
trace codeperp(B,BB,C,5);
trace codeperp(C,CC,A,5);

marque_p:="rien";
label.ulft(btex $A$ etex,A);
label.urt(btex $B$ etex,B);
label.bot(btex $C$ etex,C);
label.rt(btex $H$ etex,H);

label.ulft(btex $(d_1)$ etex, 3.2[A,H]);
label.urt(btex $(d_2)$ etex, 1.6[B,H]);
label.urt(btex $(d_3)$ etex, 1.4[C,H]);

fin;

Les bissectrices

Voici son code :

u:=1cm;
figure (-u,-2u,8u,6u);
pair A,B,C,I,P,Q,R;

A=(0,0);
B=(2u,5u);
C=(7u,-u);
I=CentreCercleI(A,B,C);   % centre du cercle inscrit

draw A--B--C--cycle;
draw droite(A,I) withcolor red;
draw droite(B,I) withcolor red;
draw droite(C,I) withcolor red;

P=projection(I,A,B);
Q=projection(I,B,C);
R=projection(I,A,C);

draw I--P dashed withdots;
draw I--Q dashed withdots;
draw I--R dashed withdots;

trace codeperp(I,P,A,5);
trace codeperp(I,Q,B,5);
trace codeperp(I,R,C,5);

trace cercles(I,P) withcolor blue;

marque_p:="rien";
label.ulft(btex $A$ etex,A);
label.urt(btex $B$ etex,B);
label.bot(btex $C$ etex,C);
label.urt(btex $I$ etex,I);

label.ulft(btex $(d_1)$ etex, 2.2[A,I]);
label.urt(btex $(d_2)$ etex, 2[B,I]);
label.urt(btex $(d_3)$ etex, 1.7[C,I]);

trace marqueangle(C,A,I,1);
trace marqueangle(I,A,B,1);

trace marqueangle(B,C,I,2);
trace marqueangle(I,C,A,2);

trace marqueangle(A,B,I,3);
trace marqueangle(I,B,C,3);

fin;