C = (5.32, 2.12)
B = (6.4, -1.36)
A = (-0.5, 0.54)
triangulo, b, a, c = Polygon(A, C, B)
P = (5.5, 3.72)
F = Fermat(triangulo)
d = Segment(P, A)
e = Segment(P, C)
f = Segment(P, B)
g = Segment(A, F)
h = Segment(F, B)
i = Segment(F, C)
texto1: "AF + BF + CF = " + (g + i + h) + " ≤ " + (d + e + f) + " = AP + BP + CP"
α = Angle(B, A, C)
β = Angle(A, B, C)
γ = Angle(B, C, A)
texto2: "\hat {A}\;=\;" + α + "\;\;\;\;\;\;\;\;\;\;\;" + "\hat {B}\;=\;" + β + "\;\;\;\;\;\;\;\;\;\;\;" + "\hat {C}\;=\;" + γ

Tool: X14
Triángulo
Input: polígono1
Output: X14

A = (0.3, -0.78)
B = (3.6, 0)
C = (6.140000000000001, -1.5)
polígono1, c, a, b = Polygon(A, B, C)
A' = Intersect(c, b)
B' = Intersect(a, c)
C' = Intersect(a, b)
q = Circle(C', A')
g = LineBisector(b)
f = LineBisector(a)
E = Midpoint(b)
e = Line(B', E)
D = Midpoint(a)
d = Line(A', D)
F = Intersect(d, e)
i = OrthogonalLine(F, g)
G = Intersect(g, i)
k = Ray(E, G)
K = Intersect(q, k, 1.0)
l = Line(K, B')
h = OrthogonalLine(F, f)
H = Intersect(f, h)
p = Circle(C', B')
j = Ray(D, H)
J = Intersect(p, j, 1.0)
m = Line(J, A')
X14 = Intersect(l, m)

Tool: Fermat (punto) (command Fermat)
Triángulo
Input: polígono1
Output: Fermat

A = (-0.5, 0.54)
B = (5.32, 2.12)
C = (6.4, -1.36)
polígono1, c, a, b = Polygon(A, B, C)
A' = Intersect(c, b)
B' = Intersect(a, c)
C' = Intersect(a, b)
q = Circle(C', A')
g = LineBisector(b)
f = LineBisector(a)
E = Midpoint(b)
e = Line(B', E)
D = Midpoint(a)
d = Line(A', D)
F = Intersect(d, e)
F' = Mirror(F, E)
i = OrthogonalLine(F', g)
G = Intersect(g, i)
k = Ray(E, G)
K = Intersect(q, k, 1.0)
l = Line(K, B')
F'_1 = Mirror(F, D)
h = OrthogonalLine(F'_1, f)
H = Intersect(f, h)
p = Circle(C', B')
j = Ray(D, H)
J = Intersect(p, j, 1.0)
m = Line(J, A')
α = Angle(B', A', C')
β = Angle(C', B', A')
γ = Angle(A', C', B')
δ = Max({α, β, γ})
Vertice = If(δ ≟ α, A', If[δ ≟ β, B', C'])
I = Intersect(l, m)
Fermat = If(δ < 2.0 * 3.141592653589793 / 3.0, I, Vertice)