\text{Zostrojte obraz kružnice }k(O,r) \text{v stredovej kolineácii }\mathscr{K}(S,o,u).

1. \; \text{Zvoľme ľub. }U_1∈u\text{ a dotyčnice }t_1,t_2

2. \; \text{Úbežník }U_2=\overleftrightarrow{T_1T_2}∩u

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3.  \; \text{Bod }(1=1')∈\mathscr{K}(\overleftrightarrow{T_1T_2}) \; ∧ \; \mathscr{K}(\overleftrightarrow{T_1T_2}) ∥\overleftrightarrow{SU_2}=\overrightarrow{v_1}

4. \; \text{Odkiaľ: }\mathscr{K}(T_i)=T'_i; \; i=1,2 

5. \; \text{Obrazy dotyčníc: }\mathscr{K}(t_i)=t'_i; \; t'_i∥\overleftrightarrow{SU_1}=\overrightarrow{v_2}

6. \; \text{Dotyčnice }r_1,r_2\text{ a dotykové body }R_1,R_2

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7. \; \text{Obrazy: }\mathscr{K}(R_i)=R'_i; \;2∈\overleftrightarrow{R_1R_2}∩\overleftrightarrow{R'_1R'_2}\; ∧ \; \mathscr{K}(\overleftrightarrow{R_1R_2}) ∥\overleftrightarrow{SU_1}=\overrightarrow{v_2}

8. \; \text{Obrazy dotyčníc: }\mathscr{K}(r_i)=r'_i; \; r'_i∥\overleftrightarrow{SU_2}=\overrightarrow{v_1}

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9. \; \text{Obraz ľub. bodu: }\mathscr{K}(L)=L' ;  \; \overleftrightarrow{LT_1}∩o=3 \text{ - samodružný

10. \; \text{Kužeľosečka určená bodmi: }T'_1,T'_2,R'_1,R'_2,L'

S = (2.97836, 6.6695)
A = (-3, 1)
B = (11, 1)
o = Line(A, B)
C = (-0.4429581818181716, 4.904701818181829)
u = Line(C, o)
O = (4.33598, 1.29226)
E = (1.80708, 2.33044)
k = Circle(O, E)
U_1 = Point(u)
t_1, t_2 = Tangent(U_1, k)
T_2 = Intersect(k, t_2)
T_1 = Intersect(k, t_1)
n = Segment(T_1, T_2)
j = Line(T_1, T_2)
U_2 = Intersect(u, j)
D = Intersect(o, j)
r = Line(S, U_2)
s = Line(D, r)
U'_2_∞ = Point(r)
v_1 = Vector(U_2, U'_2_∞)
a = Line(S, T_2)
t = Line(S, T_1)
T'_1 = Intersect(s, t)
T'_2 = Intersect(s, a)
k_1 = Line(S, U_1)
U'_1_∞ = Point(k_1)
v_2 = Vector(U_1, U'_1_∞)
t'_1 = Line(T'_1, k_1)
t'_2 = Line(T'_2, t'_1)
b = Segment(T'_1, T'_2)
r_1, r_2 = Tangent(U_2, k)
R_2 = Intersect(k, r_2)
R_1 = Intersect(k, r_1)
q = Line(R_1, R_2)
p = Segment(R_1, R_2)
F = Intersect(o, q)
f = Line(F, k_1)
g = Line(S, R_1)
h = Line(S, R_2)
R'_1 = Intersect(f, g)
R'_2 = Intersect(f, h)
i = Segment(R'_1, R'_2)
r'_1 = Line(R'_1, r)
r'_2 = Line(R'_2, r)
L = Point(k)
h_1 = Line(S, L)
j_1 = Line(T_1, L)
G = Intersect(o, j_1)
l_1 = Line(G, T'_1)
L' = Intersect(h_1, l_1)
c = Conic(T'_1, L', R'_2, T'_2, R'_1)