Homework№1(pic.6)

import geometry;
size(9cm, 0);
defaultpen(fontsize(10pt));
dotfactor = 4;
point A,B,C,K,A1,B1,C1;

A=(0,0); B=6*dir(60); C=6*dir(0); K=1.5*(A+B+2*C)/(6);
line AB = line(A,B);
line BC = line(B,C);
line AC = line(A,C);
line h1 = perpendicular(K, AB);
line h2 = perpendicular(K, BC);
line h3 = perpendicular(K, AC);

C1 = intersectionpoint(h1, AB);
B1 = intersectionpoint(h3, AC);
A1 = intersectionpoint(h2, BC);

fill(C1--K--B--cycle^^K--A1--C--cycle^^K--B1--A--cycle, green+white);
fill(C1--K--A--cycle^^K--A1--B--cycle^^K--B1--C--cycle, blue+white);

markrightangle(size=7, K, C1, B);
markrightangle(size=7, B, A1, K);
markrightangle(size=7, K, B1, A);

draw(A--B--K--cycle);
draw(C--B--K--cycle);
draw(A--C--K--cycle);
draw(K--C1^^K--B1^^K--A1);

dot(C1^^B1^^A1, UnFill);
dot(A^^B^^C^^K, UnFill);