d

Homographie O*

Directions fixes

Involution de Desargues

Coniques dégénérées

F = Point(xAxis)
O = Intersect(xAxis, yAxis)
F' = Mirror(F, O)
S = Point(xAxis)
Γ = If(Distance[O, F] < Distance[O, S], Ellipse[F, F', S], Hyperbola[F, F', S])
ff' = Line(F, F')
oy = OrthogonalLine(O, ff')
F_b = (-1.5037491397998615, 1.4757030891558283)
ff'_b = Line(F_b, O)
S_b = Point(ff'_b)
F'_b = Mirror(F_b, O)
Γ_b = If(Distance[O, F_b] < Distance[O, S_b], Ellipse[F_b, F'_b, S_b], Hyperbola[F_b, F'_b, S_b])
oy_b = OrthogonalLine(O, ff'_b)
D_{1} = (5.607139729142367, -3.5962212295520666)
d = Line(O, D_{1})
d' = Line(O, Midpoint[Intersect[Γ, Line[F, d], 1], Intersect[Γ, Line[F, d], 2]])
d'' = Line(O, Midpoint[Intersect[Γ_b, Line[F_b, d'], 1], Intersect[Γ_b, Line[F_b, d'], 2]])
s1 = true
s2 = false
c'' = Line(O, Midpoint[Intersect[Γ_b, Line[F_b, ff'], 1], Intersect[Γ_b, Line[F_b, ff'], 2]])
a'' = Line(O, Midpoint[Intersect[Γ_b, Line[F_b, oy], 1], Intersect[Γ_b, Line[F_b, oy], 2]])
ω = (2.7124082227386985, 2.0018153359794395)
c = Circle(ω, O)
dd = Mirror(O, OrthogonalLine[ω, d])
dd'' = Mirror(O, OrthogonalLine[ω, d''])
aa = Mirror(O, OrthogonalLine[ω, ff'])
aa'' = Mirror(O, OrthogonalLine[ω, a''])
cc = Mirror(O, OrthogonalLine[ω, oy])
cc'' = Mirror(O, OrthogonalLine[ω, c''])
f = Line(aa, cc'')
g = Line(cc, aa'')
X = Intersect(f, g)
h = Line(cc, dd'')
i = Line(cc'', dd)
X' = Intersect(h, i)
j = Line(X', X)
v, u = Intersect(c, j)
k = Line(O, u)
l = Line(O, v)
A_{1} = (-5.88752292280366, 3.361745298122583)
B_{1} = (1.6821329699412846, -3.3413506607727754)
Δ = Line(A_{1}, B_{1})
s3 = false
s4 = false
M', M = Intersect(Γ, Δ)
M_b, M'_b = Intersect(Γ_b, Δ)
om' = Line(M', O)
om'_b = Line(M'_b, O)
om_b = Line(M_b, O)
om = Line(M, O)
m = Mirror(O, OrthogonalLine[ω, om])
m' = Mirror(O, OrthogonalLine[ω, om'])
m'_b = Mirror(O, OrthogonalLine[ω, om'_b])
m_b = Mirror(O, OrthogonalLine[ω, om_b])
m'm_b = Line(m_b, m')
mm'_b = Line(m, m'_b)
C_{1} = Intersect(m'm_b, mm'_b)
Q = Intersect(l, Δ)
mm_b = Line(m_b, m)
m'm'_b = Line(m'_b, m')
E = Intersect(mm_b, m'm'_b)
xx = Line(C_{1}, E)
X_J, X_I = Intersect(c, xx)
oj_{1} = Line(O, X_J)
I = Intersect(oj_{1}, Δ)
oj = Line(X_I, O)
J = Intersect(oj, Δ)
c_{IJ} = Circle(Midpoint[I, J], I)
T_Q = Intersect(Semicircle[Midpoint[I, J], Q], c_{IJ})
c_Q = Circle(Q, T_Q)
G, H = Intersect(c_Q, Δ)
TQ = Segment(Q, T_Q)
n = Line(G, l)
p = Line(H, l)
B, A = Intersect(Γ_b, n)
C, D = Intersect(Γ_b, p)
Q' = Intersect(Δ, k)
T_Q' = Intersect(Semicircle[Midpoint[I, J], Q'], c_{IJ})
e = Circle(Q', T_Q')
G', H' = Intersect(e, Δ)
q = Line(G', k)
r = Line(H', k)