 \text{V kolineácii }\mathscr{K}(S, o, u) \text{ zostrojte obraz trojuholníka }ABC.  
\\text{              Strany  }AB, AC \text{ pretínajú úbežnicu }u.

S

o

1. \; s_a=\overleftrightarrow{SU_1},c=\overleftrightarrow{AB}

1

2. \; \text{Samodružný }1:(o∩\overleftrightarrow{AB})=1

3. \; \text{Nevlastný bod }U'_1_∞∈\overrightarrow{SU_1}

4. \; c'=\overleftrightarrow{1U'_1_∞}:(c'∥\overleftrightarrow{SU_1})∧(1∈c')

5. \; A': (c'∩\overleftrightarrow{SA})=A'

6. \; \overleftrightarrow{SB}; (c'∩\overleftrightarrow{SB})=B'

2

7. \; \text{Samodružný }2=(o \; ∩\overleftrightarrow{BC})→ \; C'=\overleftrightarrow{2B'} \; ∩\overleftrightarrow{SC}

8. \; BC∩u=\empty⇒\mathscr{K}(BC)=B'C'

9. \; AB∩u≠\empty⇒\mathscr{K}(AB)=\overrightarrow{A'U'_1_∞}∪\overrightarrow{B'U'_1_∞}

C_a∈AU_1:\mathscr{K}(C_a)=C'_a

\mathscr{K}(AU_1)=\overrightarrow{A'U'_1_∞}

10. \; CB∩o≠\empty⇒\mathscr{K}(AC)=\overrightarrow{A'U'_∞}∪\overrightarrow{C'U'_∞}

pohybujte

11. \; ΔA'B'C' \text{ tvorený z polpriamok } \overrightarrow{A'U_∞},\overrightarrow{CU_∞}

B = (-0.07002123198130548, 0.10663498470672747)
A = (-0.5017448740055387, -0.3477582980908317)
mnohouholník1, f, h, i, C = Polygon(A, B, 3)
U_2 = Point(mnohouholník1)
S = (-0.37120709770837135, 0.05360930412097645)
Q = (0.7577468451822877, 0.05193496449749518)
P = (-0.7851065914831531, -0.5435523268470609)
o = Line(P, Q)
u = Line(U_2, o)
c = Line(B, A)
U_1 = Intersect(u, c)
s_u = Line(S, A)
D = Intersect(o, c)
k = Line(S, U_1)
U'_1_∞ = Point(k)
H = Point(k)
v_1 = Vector(H, U'_1_∞)
c' = Line(D, k)
A' = Intersect(c', s_u)
r_{1} = Line(S, B)
B' = Intersect(c', r_{1})
s = Line(S, C)
p = Line(C, B)
E = Intersect(o, p)
q = Line(B', E)
C' = Intersect(s, q)
m = Line(A', C')
t = Segment(B', C')
g = Segment(A, U_1)
C_a = Point(g)
l = Line(S, C_a)
C'_a = Intersect(c', l)
h_1 = Ray(A', C'_a)
i_1 = Segment(U_1, B)
C_b = Point(i_1)
j_1 = Line(C_b, S)
C'_b = Intersect(c', j_1)
k_1 = Ray(B', C'_b)
j = Line(S, U_2)
I = Point(j)
U'_2_∞ = Point(j)
v_2 = Vector(I, U'_2_∞)
f_1 = Ray(A', v_2)
g_1 = Ray(C', Vector[(-v_2)])
r = 0.504 (slider from 0 to Distance[B, C], step 0.002)
d = Circle(B, r)
A_r, W = Intersect(d, p)
n = Line(A_r, S)
A'_r = Intersect(q, n)
l_1 = Segment(A, A_r)
a = Line(A', A'_r)
G = Intersect(u, l_1)
w = Vector(S, G)
m_1 = Ray(A', w)
n_1 = Ray(A'_r, Vector[(-w)])