H2_pic4

import geometry;
import patterns;

size(9cm, 0);
defaultpen(fontsize(10pt));
dotfactor = 6;
point A,B,C,A1,B1,C1,T,M,Np,K;
A=origin; B=4*dir(45); C=4*dir(0);
A1=point(B--C, 1/3); B1=point(C--A, 2/5);
C1=point(A--B, 3/7);
line t= parallel(B,line(C,A));
T=intersectionpoint(line(C,C1), t);
M=intersectionpoint(C--C1,A--A1);
K=intersectionpoint(C--C1,B--B1);
Np=intersectionpoint(A--A1,B--B1);

add("diag", hatch(1mm, dir(-45)));
fill(M--Np--K--cycle, pattern("diag"));


markangle(radius=0.4cm, n=1, C,T,B);
markangle(radius=0.4cm, n=1, T,C,A);
markangle(radius=0.3cm, n=2, C,B1,B);
markangle(radius=0.3cm, n=2, T,B,B1);

draw(A--A1^^B--B1);
draw(B--T^^C--T);
draw(A--B--C--cycle, black+pt);


dot(A1^^B1^^C1^^T^^M^^Np^^K);

label("$A$", A, S);
label("$B$", B, N);
label("$C$", C, S);
label("$A1$", A1, NE);
label("$B1$", B1, S);
label("$C1$", C1, 2N);
label("$T$", T, N);
label("$M$", M, N);
label("$N$", Np, SE);
label("$K$", K, WSW);
label(Label("$\frac{15}{2}a$", Relative(0.5)), B--T);
label(Label("$2a$", Relative(0.5)), B1--C);
label(Label("$3a$", Relative(0.5)), A--B1);