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- import geometry;
- defaultpen(fontsize(10 pt));
- size(9 cm,0);
- point A, B, C, L, K, E, O;
- A=(0,0); B=2*dir(80); C=3*dir(0);
- L=point(A--C,0.3);
- K=point(A--C,0.15);
- E=point(B--C,0.45);
- fill(A--B--L--cycle,green+opacity(0.03));
- O=intersectionpoint(A--E, B--L);
- draw(A--B--C--cycle);
- draw(B--L);
- draw(B--K);
- draw(A--K^^K--L, white+opacity(0), StickIntervalMarker(1,1,size=0.15cm));
- draw(A--E);
- markangle(n=1,radius=0.3cm, O,A,B);
- markangle(n=1,radius=0.4cm, L,A,O);
- markangle(n=2,radius=0.5cm, A,B,L);
- markangle(n=2,radius=0.4cm, L,B,C);
- markrightangle(size=6, B,K,A);
- dot(O, UnFill); dot(K); dot(L); dot(E);
- label("$A$",A,SW);
- label("$B$",B,NNW);
- label("$C$",C,SE);
- label("$L$",L,S);
- label("$E$",E,NE);
- label("$K$",K,NE);
- label("$O$",O,SSW);
- draw ( rotate ( unit (B -A ))* "$6a$", B--A);
- draw ( rotate ( unit (C -L ))* "$b$", L--C);
- draw ( rotate ( unit (A - L ))* "$3a$", A--L);
- draw ( rotate ( unit (B - O ))* "$4a$", O--B);
- draw ( rotate ( unit (O - L ))* "$2a$", L--O);
- draw ( rotate ( unit (B - C ))* "$2b$", C--B);
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