import geometry;
size(7cm);
dotfactor=9;

real grad=15;
point A, B, C, L, E_, K, O, H;
A=6*dir(-90-grad); L=6*dir(-90+grad);
H=1*dir(-90+3*grad);
C=intersectionpoint(line(A,L), line(B,H));
triangle t=triangle(A, B, C);
E_=bisectorpoint(t.BC);
O=intersectionpoint(A--E_, B--L);
K=projection(A,C)*B;

markangle(radius=0.6cm, n=2, A, B, K);
markangle(radius=0.8cm, n=2, K, B, L);
markangle(radius=0.5cm, C, A, E_);
markangle(radius=0.6cm, E_, A, B);
markrightangle(B, K, A, size=5);

draw(A--L, opacity(0), StickIntervalMarker(2, 1, size=0.15cm));
draw(Label("$6a$", Rotate(dir(A--B))), align=1.5*LeftSide,A--B, black+2bp);
draw(Label("$2b$", Rotate(dir(B--C)), position=Relative(0.65)), align=1.5*LeftSide,B--C, black+2bp);
draw(Label("$4a$", Rotate(dir(B--O))),O--B);
draw(Label("$2a$", Rotate(dir(O--L))),L--O);
draw(A--E_^^B--K);
draw(A--C, black+2bp);

label("$A$", A, S);
label("$C$", C, S);
label("$B$", B, N);
label("$L$", L, S);
label("$E$", E_, NE);
label("$O$", O, WNW);
label("$K$", K, NE);
label("$3a$", (A+L)/2, S);
label("$b$", (L+C)/2, S);

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