homographie

axe

solutions

T = (-2.1917548064158967, 0.19175480641589648)
U = (1, 6)
V = (-5.191754806415897, 3.1917548064158963)
tu = Line(T, U)
uv = Line(U, V)
tv = Line(V, T)
P = (-2, 2)
Q = (-1, 4)
R = (-3, 3)
PQ = Segment(P, Q)
QR = Segment(Q, R)
PR = Segment(R, P)
A_1 = Point(tv)
ac_1 = Line(A_1, R)
C_1 = Intersect(uv, ac_1)
bc_1 = Line(C_1, Q)
B_1 = Intersect(tu, bc_1)
ab_1 = Line(B_1, P)
A'_1 = Intersect(tv, ab_1)
AC_1 = Segment(A_1, C_1)
BC_1 = Segment(C_1, B_1)
AB_1 = Segment(B_1, A'_1)
AR_1 = Segment(A_1, R)
CQ_1 = Segment(C_1, Q)
PB_1 = Segment(B_1, P)
A_2 = Point(tv)
ac_2 = Line(R, A_2)
C_2 = Intersect(uv, ac_2)
bc_2 = Line(C_2, Q)
B_2 = Intersect(bc_2, tu)
ab_2 = Line(B_2, P)
A'_2 = Intersect(ab_2, tv)
A_{3} = Point(tv)
ac_3 = Line(A_{3}, R)
C_3 = Intersect(uv, ac_3)
bc_3 = Line(C_3, Q)
B_3 = Intersect(tu, bc_3)
ab_3 = Line(B_3, P)
A'_3 = Intersect(ab_3, tv)
O = (-5.073436808999929, -0.36035001025635716)
S = (-3.7886796060134245, 1.039460076579687)
Γ = Circle(O, S)
sa_1 = Line(A_1, S)
sa'_1 = Line(A'_1, S)
a_1 = Mirror(S, OrthogonalLine[O, sa_1])
a'_1 = Mirror(S, OrthogonalLine[O, sa'_1])
sa_2 = Line(A_2, S)
sa_3 = Line(A_{3}, S)
sa'_2 = Line(A'_2, S)
sa'_3 = Line(S, A'_3)
a_2 = Mirror(S, OrthogonalLine[O, sa_2])
a_3 = Mirror(S, OrthogonalLine[O, sa_3])
a'_3 = Mirror(S, OrthogonalLine[O, sa'_3])
a'_2 = Mirror(S, OrthogonalLine[O, sa'_2])
a_1a'_2 = Line(a_1, a'_2)
a'_1a_2 = Line(a'_1, a_2)
M = Intersect(a'_1a_2, a_1a'_2)
a_2a'_3 = Line(a'_3, a_2)
a'_2a_3 = Line(a'_2, a_3)
M' = Intersect(a_2a'_3, a'_2a_3)
mn = Line(M, M')
A_1s = Ray(A_1, S)
A_2s = Ray(A_2, S)
A_3s = Ray(A_{3}, S)
A'_{4} = Ray(A'_2, S)
A'_1s = Ray(A'_1, S)
A'_2s = Ray(A'_3, S)
m, m' = Intersect(Γ, mn)
ms = Line(m, S)
m's = Line(m', S)
A_m' = Intersect(m's, tv)
A_m = Intersect(ms, tv)
ac_m' = Line(A_m', R)
C_m' = Intersect(ac_m', uv)
bc_m' = Line(C_m', Q)
B_m' = Intersect(tu, bc_m')
AB_m' = Segment(A_m', B_m')
PB_m' = Segment(B_m', P)
BC_m' = Segment(C_m', B_m')
CQ_m' = Segment(C_m', Q)
AC_m' = Segment(A_m', C_m')
AR_m' = Segment(A_m', R)
ac_m = Line(A_m, R)
C_m = Intersect(ac_m, uv)
bc_m = Line(C_m, Q)
B_m = Intersect(bc_m, tu)
AB_m = Segment(A_m, B_m)
AC_m = Segment(A_m, C_m)
BC_m = Segment(B_m, C_m)
AR_m = Segment(A_m, R)
CQ_m = Segment(C_m, Q)
PB_m = Segment(B_m, P)
a = true
b = false
c = false
AA_1: A_1