 \text{ Poincaré Disc: } ω=\left\{ x^2+y^2<1; x,y∈\mathbb{R} \right\} 

 \text{ Zostrojte hyperbolickú kružnicu určenú stredom }A  \text{ a bodom }B: φ(A, r≅AB).

1.  \text{ Oblúk } α=AB; A' -  \text{ obraz v kruhovej inverzii }ω

2.  \text{ Oblúk }δ⟂α \;  ; \; ( \overleftrightarrow{PS_1}⟂\overleftrightarrow{OA} )∧ (P=\overleftrightarrow{S_1S_2}∩\overleftrightarrow{PQ})

3.  \;  B' -  \text{ obraz bodu }B \text{ v kruhovej inverzii }δ

4.  \text{ Dotyčnice }t_B,t_B'  \text{ k oblúku }ε \text{ cez }B, B'

5. \text{ Stred euklidovskej kružnice je } S=t_B∩t_B' 

6.  \; φ=(S, r=SB...≅AB)

O = Point(yAxis)
M = Point(xAxis)
ω = Circle(O, M)
A = (0.4515549556747038, -0.0921178096492436)
B = (0.25108626535342715, 0.5882596858179157)
A' = Mirror(A, ω)
d = Circle(A', A, B)
P = Intersect(ω, d, 1)
Q = Intersect(ω, d, 2)
S_{1} = Center(d)
α = CircleArc(S_{1}, P, Q)
h = Ray(O, A)
i = OrthogonalLine(S_{1}, h)
j = Line(P, Q)
S_2 = Intersect(i, j)
δ_{1} = Circle(S_2, A)
Q_2 = Intersect(ω, δ_{1}, 1)
P_2 = Intersect(ω, δ_{1}, 2)
δ = CircleArc(S_2, Q_2, P_2)
k = Tangent(A, δ_{1})
l = Tangent(A, d)
B' = Mirror(B, δ_{1})
B'' = Mirror(B', ω)
c_{1} = Circle(B'', B', B)
S_1 = Center(c_{1})
C_{1}, D = Intersect(c_{1}, ω)
t_B' = Tangent(B', c_{1})
t_B = Tangent(B, c_{1})
S = Intersect(t_B', t_B)
φ = Circle(S, B)