#
# dati due angoli alfa e beta, costruire un triangolo
# iperbolico di angoli pi/2, alfa, beta (alfa+beta < pi/2)
#

#alfa0 = Point(-4,-2)
#alfa1 = Point(-2,-2)
#Alfa = Angle (alfa1, alfa0, Point(-2, -0.5))
#Beta = Angle (alfa1, alfa0, Point(-2, -1))

#Ass1 = Point(-6,0,internal=True)
#Ass2 = Point(6,0,internal=True)
#assoluto = Line(Ass1, Ass2)

#
# il vertice A puo' essere fissato a piacere
# inoltre decido che un cateto e' diretto
# verticalmente
#
#A = Point (0,1)

#hideobjects()

def trianglebyangles (A, Alfa, Beta):
  vert = Orthogonal(assoluto,A,VISIBLE)
  H = LineLineIntersection(assoluto,vert)

  vertrotalfa = Rotate(vert, A, Alfa)
  l1 = Orthogonal(vertrotalfa,A)
  K = LineLineIntersection(l1,assoluto)
  lato1 = Circle(K,A,VISIBLE)
  l1rotbeta = Rotate(l1,K,Beta)
  l2 = Orthogonal(l1rotbeta,A,HIDDEN)
  M = LineLineIntersection(l2,l1rotbeta)
  seg = Segment(A,M)
  N = MidPoints(H,K)
  c1 = Circle(N,H)
  ct1 = Circle(M,A,internal=True)
  tras1 = Vector(M,K,internal=True)
  c2 = Translate(ct1,tras1)
  R = CircleCircleIntersection(c1,c2,-1)

  l3 = Line(R, H)
  B = ConicLineIntersection(lato1, l3, -1, VISIBLE)
  lato2 = Circle(H,B,VISIBLE)
  C = ConicLineIntersection(lato2, vert, -1, VISIBLE)

  return [B, C, lato1, lato2, vert]