input geometriesyr12;
figure(0,0,7u,7u);
pair A,B,C,D,E,F,I;
A=u*(1,1);
B=u*(5,1);
C=rotation(A,B,-90);
D=rotation(B,A,90);
trace A--B--C--D--cycle;
E=4/5[D,C];
trace E--(E shifted (B-C));
F=4/5[D,A];
trace F--(F shifted(B-A));
I=(E--(E shifted (B-C))) intersectionpoint (F--(F shifted(B-A)));
trace codeperp(A,B,C,5);
trace codeperp(B,C,E,5);
trace codeperp(C,D,A,5);
trace codeperp(D,A,B,5);
trace codeperp(D,E,I,5);
trace codeperp(D,F,I,5);
trace codeperp(F,I,E,5);
trace cotation(D,E,3mm,2mm,btex $a$ etex);
trace cotation(E,C,3mm,2mm,btex $b$ etex);
trace cotation(A,F,3mm,2mm,btex $b$ etex);
trace cotation(F,D,3mm,2mm,btex $a$ etex);
fin;
end