pair A=(0,0), B=(5,4), C=(6,0), I, X1, Y1, X2, Y2, X3, Y3, P1, F1, P2, F2, P3, F3; draw(A--B--C--cycle); X1=expi((angle(B-A)+angle(C-B))/2); Y1=expi((angle(C-A)+angle(B-C))/2); P1=intersectionpoint(B--10*X1+B, C--10*Y1+C);F1=foot(P1, B, C); draw(circle(P1, abs(P1-F1)));draw(2*B-A--B);draw(2*C-A--C); X2=expi((angle(A-B)+angle(C-A))/2); Y2=expi((angle(C-B)+2*pi+angle(A-C))/2); P2=intersectionpoint(A--10*X2+A, C--10*Y2+C);F2=foot(P2, A, C); draw(circle(P2, abs(P2-F2)));draw(2*A-B--A);draw(3*C-2*B--C); X3=expi((angle(A-C)+angle(B-A))/2); Y3=expi((angle(B-C)+2*pi+angle(A-B))/2); P3=intersectionpoint(A--100*X3+A, B--100*Y3+B);F3=foot(P3, A, B); draw(circle(P3, abs(P3-F3)));draw(2*A-C--A);draw(3*B-2*C--B); draw(P1--foot(P1,A,B)..P1--foot(P1,B,C)..P1--foot(P1,A,C)); draw(P2--foot(P2,A,B)..P2--foot(P2,B,C)..P2--foot(P2,A,C)); draw(P3--foot(P3,A,B)..P3--foot(P3,B,C)..P3--foot(P3,A,C)); I=incenter(A,B,C); draw(incircle(A,B,C)); draw(I--foot(I,A,B)..I--foot(I,B,C)..I--foot(I,A,C)); dot(P1^^P2^^P3);