input geometriesyr12;
figure(-0.5u,-0.5u,8u,5u);
cadre((-0.5,-0.5),(8,5));
trace papiermillimetre withcolor orange;
pair O,A,I,M,N;
O=u*(0.5,3.5);nomme.ulft(O);
A=u*(0.5,0.8);nomme.llft(A);
I=u*(0.5,2.5);nomme.llft(I);
M=u*(2.8,2.5);nomme.llft(M);
N=(abs(A-O)/abs(I-O))[O,M];nomme.urt(N);
draw demidroite(O,A);
draw demidroite(O,N);
  draw I--M;
  trace cotation(O,M,2mm,2mm,btex $b$ etex);
  trace cotation(I,O,2mm,2mm,btex $1$ etex);
  trace cotation(A,O,6mm,2mm,btex $a$ etex);
  draw A--N;
  label.rt(btex $OI=1$, $OA=a$, $OM=b$ etex,u*(3.5,4));
  draw codeperp(M,I,O,5);
  draw codeperp(N,A,O,5);
fin;
end