\text{Je daný bod } S \text{ ležiaci vo vnútri ostrého uhla } KVM.

\text{Zostrojte štvorec } ABCD \text{ taký, že } S \text{ je jeho stredom, bod } A \text{ leží na polpriamke } VK \text{ a bod }C \text{ na polpriamke } VM.

\text{Postup:}

\text{1. }p=ρ_{S}\left(\overleftrightarrow{VK}\right)

\text{2. } C=p∩\overrightarrow{VM}

3.\ A=ρ_S(C)

4.\; i\colon i⟂AC,\ S∈AC

5.\; k\colon k(S;r=SA)

6.\; B,D∈i∩k

7.\ \square\ ABCD

α = 1.0471975511965976 rad (slider from 1° to 90°, step 0.017453292519943295)
V = (7.5, -3.96)
M = (19.28, -3.94)
f = Line(V, M)
K = Rotate(M, α, V)
β = Angle(M, V, K)
g = Line(V, K)
S = (12.94, -0.42)
p = Mirror(g, S)
C = Intersect(f, p)
A = Mirror(C, S)
h = Line(A, C)
i = OrthogonalLine(S, h)
k = Circle(S, C)
D = Intersect(k, i, 2)
B = Intersect(k, i, 1)
q1, a, b, c_1, d = Polygon(A, B, C, D)