\; \text{Určte }GMS \text{ priesečníkov }S= AC∩ BD \text{ všetkých pravouholníkov }ABCD. }

\triangle AKL \text{ je ostrouhlý}

K∈BC; \; L∈CD

 \text{Postup} 

1.  \; \text{Keďže } \triangle KCL:∡C=90°  \text{, tak }C∈τ(KL)\text{ Tálesova.polkružnica

$\math τ$

2.  \; \text{ Musí platiť } μ(AEC) \text{ odkiaľ }τ⊂\overrightarrow{KLA}^★\text{ - opačná polrovina }

$\math τ'$

3.  \; \text{Rovnoľahlosť } \mathcal{H}=\left( A,κ=\frac{1}{2}  \right)  \text{ zobrazí: }τ→\red {GMS} \red {\text{ polkružnica}}

4.  \; \mathcal{H}=\left( A,κ=\frac{1}{2} \right) (K)=K' \text{ - stred }AK

5.  \; \mathcal{H}=\left( A,κ=\frac{1}{2} \right) (L)=L' \text{ - stred }AL

A = (2, 2)
K = (9.145513744419326, 4.536115410319766)
L = (6.0724625328763695, 6.16641957418997)
t1, c, a, b = Polygon(A, K, L)
d = Semicircle(L, K)
C = Point(d)
f = Line(C, K)
g = Line(C, L)
h = OrthogonalLine(A, f)
i = OrthogonalLine(A, h)
B = Intersect(f, h)
D = Intersect(g, i)
j = Segment(A, B)
k = Segment(B, C)
l = Segment(C, D)
m = Segment(D, A)
n = Segment(A, C)
p = Segment(B, D)
S = Intersect(n, p)
q = Circle(L, C, K)
τ = Semicircle(L, K)
E = Intersect(a, n)
e(x, y) = (y(Vector[K, L]) * (x - x(K))) - (x(Vector[K, L]) * (y - y(K))) ≥ 0
τ' = Dilate(τ, 1 / 2, A)
K' = Dilate(K, 1 / 2, A)
L' = Dilate(L, 1 / 2, A)