import geometry;
defaultpen(fontsize(10pt));
dotfactor = 4;
size(9cm, 0);
point A,B,C, A1, B1, C1;
C=(0,0); B= 4*dir(70); A= 4*dir(0);
A1=(C+B)/3; B1 = 2*(C+A)/3; C1= (B+1/3*A)/(1+1/3);

triangle t = triangle(A,B,C); show(Lc="",Lb="",La="",t);

draw(C1--B1--A1--cycle);
fill(C1--B1--A1--cycle, gray+0.25white);

dot(A); dot(B); dot(C);
dot(A1); label("$A1$", A1, WNW);
dot(B1); label("$B1$", B1, S);
dot(C1); label("$C1$", C1, NE);