Homework№1(pic.7)

import geometry;

size(9cm, 0);
defaultpen(fontsize(10pt));
dotfactor = 4;
point A,B,C,D,M,Np,K,L,F,A1,B1,M1;

D=(0,0); A= 4*dir(65); B= 5.5*dir(30); C=6*dir(0);
M= point(A--B, 1/5);
Np= point(C--D, 1/3);
line DC = line(D,C);
//line a = perpendicular(A, DC);
line m = perpendicular(M, DC);
line b = perpendicular(B, DC);
K=intersectionpoint(line(D,M),line(A,Np));
L=intersectionpoint(line(C,M),line(B,Np));
//A1=intersectionpoint(DC,a);
A1=projection(D,C)*A;
M1=intersectionpoint(DC,m);
B1=intersectionpoint(DC,b);
F=intersectionpoint(line(A1,B),line(M,M1));

fill(A--K--D--cycle, blue+white);
fill(B--L--C--cycle, blue+white);
fill(K--M--L--Np--cycle, red);

markrightangle(size=7, A, A1, D);
markrightangle(size=7, M, M1, D);
markrightangle(size=7, B, B1, D);

draw(D--M^^M--C);
draw(A--Np^^Np--B);
draw(A1--B);
draw(A--A1^^M--M1^^B--B1);
draw(A--B--C--D--cycle);


dot(A); label("$A$", A, N);
dot(B); label("$B$", B, N);
dot(C); label("$C$", C, S);
dot(D); label("$D$", D, S);
dot(M); label("$M$", M, N);
dot(Np); label("$N$", Np, S);
dot(K); label("$K$", K, 2*S);
dot(L); label("$L$", L, 2*N+0.5*W);
dot(F); label("$F$", F, WNW);
dot(A1); label("$A_1$", A1, S);
dot(B1); label("$B_1$", B1, S);
dot(M1); label("$M_1$", M1, S);