\; \text{Zostrojte pravouholník }ABCD\; \text{ s vrcholmi }A, C, D\; \text{ postupne na priamkach }a, c, \overleftrightarrow{P B}. } 

\text{Rozbor

D∈\overleftrightarrow{PB}⇒S∈\overleftrightarrow{PB}

∀ \; ABCD \text{ sú rovnoľahlé v }\mathcal{H}=(P,κ)⇒ \text{ zvolíme ľub. }S'

 \text{Postup} 

1.  \; \text{Zvolíme ľub. } S'∈\overleftrightarrow{PB}

2.  \; \text{ Stredová súmernosť }  ρ_S':b→b'; \; A'=a∩b',A'→C'

3.  \; \text{Pravouholník } A'B'C'D'

4.  \; \mathcal{H}(A'B'C'D')=ABCD

P = (1.5710917441373902, 4.117718766494666)
Q = (7.544064521502573, 8.821074141907829)
b = Line(P, Q)
R = (10.09772679588334, 2.1123003702295438)
a = Line(P, R)
B = (9.520627976814241, 5.329626286539775)
h = Line(P, B)
E = (-4, 6)
F = (2, 6)
S' = Point(h)
b' = Mirror(b, S')
A' = Intersect(a, b')
C' = Mirror(A', S')
f = Line(A', C')
c = Circle(S', A')
D', B' = Intersect(c, h)
q1, a', g, c', d' = Polygon(A', B', C', D')
PB = Distance(P, B)
PB' = Distance(P, B')
KO: PB / PB'
A = Dilate(A', KO, P)
B'' = Dilate(B', KO, P)
C = Dilate(C', KO, P)
D = Dilate(D', KO, P)
q1', a'', b'', c'', d'' = Polygon(A, B'', C, D)