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import geometry;
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import patterns;
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import markers ;
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//import graph;
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//import three;
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defaultpen(fontsize(11pt));
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dotfactor=5;
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//labelmargin=0.25;
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add ("hatch",hatch (1.2mm , black ));
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point A,B,C,E1,L,O,K;
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point A,B,C,A1,B1,C1;
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A=(0,0); C = 5*dir(0); B=3.5*dir(74);
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C=(0,0); A = 3*dir(0); 
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line AB=line(A,B); line AC = line(A,C);
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B=2.5*dir(60);
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line BC=line(B,C);
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A1 = C + 1/3*(B-C);
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line l1 = bisector(AB,AC);
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B1 = A + 1/3*(C-A);
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line l2 = bisector(AB,BC);
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C1=  B + 1/3*(A-B);
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E1 = intersectionpoint(l1,BC);
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L = intersectionpoint(l2,AC);
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dot(C); dot(A); dot(B); 
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O = intersectionpoint(l1,l2);
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dot(A1); dot(B1); dot(C1);
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K = projection(A,L)*B;
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draw(A--C--B--cycle,black+1bp); draw(A--E1); 
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draw(C--A--B--cycle); 
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draw(B--L); draw(B--K);
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draw(A1--C1--B1--cycle);
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draw(A--L, white+opacity(0), StickIntervalMarker(2, 1, size=0.15cm));
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filldraw(A1--C1--B1--cycle,pattern ("hatch")); 
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dot(A,black+4bp); dot(A,white+3bp);
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dot(B,black+4bp); dot(B,white+3bp);
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dot(C,black+4bp); dot(C,white+3bp);
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label("$C$",C,SW); label("$A$",A,SE); label("$B$",B,N);
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dot(E1,black+4bp); dot(E1,white+3bp);
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label("$A_1$",A1,W); label("$B_1$",B1,S); label("$C_1$",C1,E);
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dot(L,black+4bp); dot(L,white+3bp);
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dot(O,black+4bp); dot(O,white+3bp);
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dot(K,black+4bp); dot(K,white+3bp);
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markangle(1,radius=0.5cm,C,A,E1);
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markangle(1,radius=0.6cm,E1,A,B);
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markangle(2,radius=0.6cm,A,B,L);
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markangle(2,radius=0.4cm,L,B,C);
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markrightangle(size=0.25cm, B,K,A);
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label("$A$",A,SW);  label("$C$",C,SE);  label("$B$",B,N); 
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label("$E$",E1,NE); label("$L$",L,S); label("$O$",O,1.1W);
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label("$K$",K,NE);
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label("$3a$",A--L,S); label("$b$",L--C,S);
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label("$6a$",A--B,W); label("$4a$",B--O,E); label("$2a$",O--L,E);
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label("$2b$",E1--C,2E);