Homework№1(pic.4)

import geometry;

size(9cm, 0);
defaultpen(fontsize(10pt));
dotfactor = 4;
point A,B,C,D,M, O;

A=(0,0); B= 2*dir(70); D=3*dir(0); C=B+D; M=(B+C)/2;

O=intersectionpoint(line(A,M),line(B,D));


fill(A--O--D--cycle, gray+0.25white);
fill(B--O--M--cycle, gray+0.25white);
markangle(radius=0.45cm, n=1, M, O, B);
markangle(radius=0.45cm, n=1, A, O, D);

markangle(radius=0.45cm, n=2, D, A, M);
markangle(radius=0.45cm, n=2, B, M, A);

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

dot(A); label("$A$", A, S);
dot(B); label("$B$", B, N);
dot(C); label("$C$", C, N);
dot(D); label("$D$", D, S);
dot(M); label("$M$", M, N);
dot(O); label("$O$", O, W);