$\scalebox{2} {%n}$

$\scalebox{2} {%n}$

$\scalebox{2} {%n}$

$\scalebox{2} {%n}$

$\scalebox{2} {%n}$

$\scalebox{2} {%n}$

$\scalebox{2} {%n}$

$\scalebox{2} {%n}$

$\scalebox{2} {%n}$

$\scalebox{2} {%n}$

$\scalebox{2} {%n}$

$\scalebox{2} {%n}$

$\scalebox{2} {%n}$

$$
\frac{AF}{FB}\times\frac{BD}{DC}\times\,
\frac{CE}{EA}\
=\frac{a}{b}\times \frac{b}{c}\times \frac{c}{a}=1
$$

$\scalebox{3} {%n}$

$\scalebox{3} {%n}$

$\scalebox{3} {%n}$

A = (-0.86, -1.64)
B = (2.76, -1.66)
C = (1.1, 1.86)
t1, c_3, a_2, b_2 = Polygon(A, B, C)
f = Segment(C, A)
g = Segment(A, B)
h = Segment(B, C)
i = Ray(A, B)
E = Point(f)
D = Point(h)
j = Ray(E, D)
F = Intersect(i, j)
A' = (11.9634204254115, 4.16522355826676)
k = Line(A', i)
F' = Point(k)
d = Circle(A', F')
e = Circle(F', A')
B' = Intersect(e, k, 2)
p = Circle(B', F')
D' = Intersect(p, k, 2)
q = Circle(D', B')
C' = Intersect(q, k, 2)
r = Circle(C', D')
E' = Intersect(r, k, 2)
s = Circle(E', C')
A'' = Intersect(s, k, 2)
l = Segment(A', A'')
m = Line(E, F)
n = OrthogonalLine(A, m)
t = OrthogonalLine(C, m)
f_1 = OrthogonalLine(B, m)
G = Intersect(m, n)
H = Intersect(m, t)
I = Intersect(m, f_1)
t2, a_1, e_1, g_1 = Polygon(E, G, A)
t3, c_1, e_2, h_1 = Polygon(E, H, C)
t4, d_1, c_2, h_2 = Polygon(C, H, D)
t5, i_1, d_2, b_1 = Polygon(D, B, I)
α = Angle(D, H, C)
β = Angle(D, I, B)
J = Point(m)
γ = Angle(J, G, A)
a = Segment(A, G)
c = Segment(C, H)
b = Segment(I, B)