\text{ Kolmica } k \text{ idúca bodom } M\text{ na rovinu }α 

α

\text{Postup

1. \;  \text{Ľub. priamka } a⊂α

a

β

2. \;  \text{Rovina } β=(M,a)

b

3. \;  \text{Kolmica  } b \; ⟂ \; a;  \; ( M∈b \; ∧ \; b⊂β) ... \text{\small Euklid T/XII

4. \;  \text{Priesečník } P=a∩β

5. \;  \text{Kolmica  } c \; ⟂ \; a;  \; ( P∈c \; ∧ \; c⊂α) ... \text{\small Euklid T/XI

c

6. \;  \text{Rovina } γ=(M,c)

7. \;  \text{Kolmica  } k \; ⟂ \; α;  \; ( M∈k \; ∧ \; k⊂γ)

a = 6 (slider from 5 to 8, step 0.2)
A: (((-a)) / 2, ((-a)) / 2, -2)
B = PointIn(Sphere[A, a])
C = Point(Circle[B, Distance[A, B], Segment[A, B]])
α = Plane(A, B, C)
b, D, E, F, G, H, stenaABCD, stenaADHE, stenaABFE, stenaBCGF, stenaCDHG, stenaEFGH, hranaAD, hranaAB, hranaBC, hranaCD, hranaAE, hranaDH, hranaEH, hranaEF, hranaBF, hranaFG, hranaCG, hranaGH = Cube(A, B, C)
f = Segment(A, B)
M = (0.33254588124880513, 0.09879067937788477, 2.0313799791607376)
g = Line(B, C)
β = Plane(M, g)
h = Line(B, A)
j = OrthogonalLine(M, g, space)
K = Point(j)
P = Intersect(j, α)
i = OrthogonalLine(M, α)
I = Intersect(j, g)
J = Intersect(i, α)
l = Line(I, J)
p = Plane(l, j)
k = OrthogonalLine(M, α)
R = Intersect(k, α)