H2_pic7

import geometry;

size(9cm, 0);
defaultpen(fontsize(8pt));
dotfactor = 4;
point A,B,C,D,M;
A=origin; B=2*dir(75); D=5*dir(0); C=B+D;
line a = bisector(line(A,B), line(A,D));
line b = bisector(line(A,B), line(C,B),false);
line c = bisector(line(B,C), line(C,D));
line d = bisector(line(A,D), line(C,D), false);

point Ap1=intersectionpoint(a,b);
point Ap2=intersectionpoint(a,d);
point Cp1=intersectionpoint(c,b);
point Cp2=intersectionpoint(c,d);
M= intersectionpoint(a, line(B,C));

fill(Ap1--Ap2--Cp2--Cp1--cycle, pink+white);

markangle(Label("$\alpha/2$", Relative(0.5)), radius=0.35cm, D,A,M);
markangle(radius=0.3cm, M,A,B);
markangle(radius=0.35cm, B,M,A);
markangle(radius=0.3cm, M,C,Cp1);
markangle(radius=0.35cm, Cp2,C,D);

markangle(radius=0.35cm,n=2, A,B,Ap1);
markangle(radius=0.3cm, n=2,Ap1,B,M);
markangle(radius=0.3cm, n=2,C,D,Ap2);
markangle(radius=0.35cm, n=2,Ap2,D,A);

markrightangle(size=0.15cm, Ap1, Ap2,Cp2);
markrightangle(size=0.15cm, Ap2, Cp2,Cp1);
markrightangle(size=0.15cm, Cp2, Cp1,Ap1);
markrightangle(size=0.15cm, Cp1, Ap1,Ap2);

draw(A--B^^B--M, white+opacity(0), StickIntervalMarker(1, 2, size=0.15cm));

draw(A--(Ap2+1/2*dir(A--Ap2))^^B--(Cp1+1/2*dir(B--Cp1))^^C--(Cp1+1/2*dir(C--Cp1))^^D--(Ap2+1/2*dir(D--Ap2)));

draw(A--B--C--D--cycle);

dot(A^^B^^C^^D^^M^^Ap1^^Ap2^^Cp1^^Cp2);
label("A", A, S);
label("B", B, N);
label("C", C, N);
label("D", D, S);
label("M", M, N);
label(Label("$a$", Relative(0.5), Rotate(dir(A--B))), B--A);
label(Label("$a$", Relative(0.5), Rotate(dir(B--M))), M--B);
label(Label("$b-a$", Relative(0.3), Rotate(dir(M--C))), C--M);