Homework№1(pic.5)

import geometry;

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

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

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

fill(A--M--B--cycle, gray+0.25white);
fill(C--M--D--cycle, gray+0.25white);


markangle(radius=0.45cm, n=1, C, M, D);
markangle(radius=0.45cm, n=1, A, M, B);

dot(A); label("$A$", A, N);
dot(B); label("$B$", B, S);
dot(C); label("$C$", C, S);
dot(D); label("$D$", D, N);
dot(M); label("$M$", M, 2*N+0.5*E);

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

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

label("$27$", B--A, W);
label("$27$", C--D, E);
label("$29$", C--B, S);
label(Label("$26$", Relative(0.55), Rotate(dir(B--M))), B--M);
label(Label("$26$", Relative(0.4), Rotate(dir(M--D))), M--D, N);