# simelo-math / IMO / 2012 / imo2k12p1_sol1_img2.euk

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61``` ``` frame -5, -5, 15, 10 @../../lib/triangle.euk A B C triangle J = excircle_center(A, B, C) M = intersection(line(B,C), perpendicular(line(B,C), J)) K = intersection(line(A,B), perpendicular(line(A,B), J)) L = intersection(line(A,C), perpendicular(line(A,C), J)) F = intersection(line(L,M), line(B,J)) G = intersection(line(K,M), line(C,J)) S = intersection(line(A,F), line(B,C)) T = intersection(line(A,G), line(B,C)) c0 = excircle(A, B, C) c1 = circle(M, B, K) c2 = circle(M, C, L) H = orthocenter(J, B, C) X = intersection(line(C,H), line(J,B)) Y = intersection(line(B,H), line(J,C)) c3 = circle(J, X, Y) c4 = circle(M.J) % Drawings draw dot A; B; C; J; M; K; L; F; G; S; T; X; Y end draw black line(A,K) half line(A,L) half S.T F.J F.L G.J G.K A.S A.T "C0" K 15: 10 "C1" J 90: 4; "C2" J -15:4 "C3" H 45:; "C4" intersection(line(F,L), line(J,G)) 60: 4 end draw dashed c0 c3; c4 end draw dotted c1; c2 end label A 180:; B -30: 2; C 90: 2; J 0:; M -135:; K -90:; L 135:; F -135:; G 180:; S 0:; T 180:; X -45:; Y 90: end ```