Source

simelo-math / IMO / 2012 / imo2k12p1.euk


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)

% Drawings

draw dot
  A; B; C; J; M; K; L; F; G; S; T
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
end

draw dashed
  J.K
  J.M
  J.L
  c0
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:
end