Ipotesi\!:\ C\^BD\ angolo\ esterno\ a\ \^B\
Tesi\!:\ C\^BD > A\^CB;\ C\^BD > C\^AB

1\ -\ \overline{CE} \cong \overline{CB};\ 
\overline{AE} \cong \overline{AF}\ -\ Costruzione

2\ -\ \triangle ACE \cong \triangle BFE\ -\ 
I\ criterio: \overline{CE} \cong \overline{CB}\ (1);\ 
\overline{AE} \cong \overline{AF}\ (1);\ \
\ \ \ \ \ \ \ A\^EC \cong B\^EF\ opposti\ al\ vertice

3\ -\ A\^CE \cong F\^BE\ -\ Per\ (2)

4\ -\ F \notin \overline{BC}\ -\ Altrimenti\ 
F \equiv E \equiv A,\ incompatibile\ con\ 
A \notin \overline{BC}

5\ -\ F \notin \overline{AD}\ -\ Altrimenti\ 
E \equiv B \equiv C,\ incompatibile\ con\ 
B \not\equiv C

6\ -\ F\ è\ interno\ a\ C\^BD\ -\ Per\ (4)\ e\ (5)

7\ -\ C\^BD > C\^BF\ -\ Per\ (6)

8\ -\ C\^BD > A\^CB\ -\ Per\ (7),\ (3)\ e\ 
proprietà\ transitiva\ -\ Prima\ parte\ della\ tesi

9\ -\ A\^BH \cong C\^BD\ -\ Opposti\ al\ vertice

10\ -\ C\^BD > C\^AB\ -\ Dimostrazione\ 
analoga\ alla\ precedente\ utilizzando\ 
A\^BH\
Q.E.D.

http://www.profcortese.net

A = (0.28, -0.24)
B = (5.14, -0.24)
C = (1.22, 3.56)
poli1, c, a, b = Polygon(A, B, C)
d = Ray(A, B)
D = Point(d)
α = Angle(D, B, C)
β = Angle(A, C, B)
γ = Angle(B, A, C)
E = Midpoint(B, C)
j = Segment(C, E)
k = Segment(E, B)
e = Ray(A, E)
f = Circle(E, A)
F = Intersect(f, e, 2)
g = Segment(A, E)
l = Segment(E, F)
h = Segment(F, B)
poli2, b_1, e_1, f_1 = Polygon(E, F, B)
poli3, e_2, a_1, c_1 = Polygon(A, C, E)
i = Ray(C, B)
H = Point(i)