Homework№1(pic.1)

import geometry;

size(9cm, 0);
defaultpen(fontsize(10pt));
dotfactor = 6;
point A,B,C,O;
A=(0,0); B=4*dir(75); C=5*dir(0);

triangle tABC = triangle(A,B,C);

point L = bisectorpoint (tABC.AC);
point Ep = bisectorpoint (tABC.BC);
point K = foot(tABC.VB);
O=intersectionpoint(line(A,Ep),line(B,L));

markangle(radius=0.5cm, n=2, A, B, L);
markangle(radius=0.57cm, n=2, L, B, C);
markangle(radius=0.5cm, n=1, C, A, Ep);
markangle(radius=0.57cm, n=1, Ep, A, B);
markrightangle(size=7, B, K, A);
draw(B--L);
draw(A--Ep);
draw(B--K);
draw(A--K^^K--L, white+opacity(0), StickIntervalMarker(1, 1, size=0.15cm));

show(Lc="$6a$", Lb="", La= "", tABC);

dot(A^^B^^C^^L^^K^^O^^Ep, UnFill);

label("$O$", O, WNW);
label("$E$", Ep, NE);
label("$K$", K, NE);
label("$L$", L, S);
label(Label("$4a$", Relative(0.5), Rotate(dir(B--O)), align = NE), B--O);
label(Label("$2a$", Relative(0.5), Rotate(dir(O--L)), align = NE), O--L);
label(Label("$3a$", Relative(0.5), align = S), A--L);
label(Label("$b$", Relative(0.5), align = S), C--L);
label(Label("$2b$", Relative(0.6), Rotate(dir(B--C)), align = NE), B--C);