Les droites (BC) et (MN) sont parallèles.
Fais glisser le point M sur la droite (AB) 
et observe les quotients.

Quelle conjecture peux tu faire sur les quotients?

A = (0, -1)
a = Line(A, xAxis)
B = (10, -1)
C = (5.477631656634599, 3.3926498931503186)
b = Line(A, C)
c = Segment(A, B)
d = Segment(A, C)
e = Segment(C, B)
M = Point(a)
f = Segment(A, M)
g = Line(M, e)
h = Line(A, C)
N = Intersect(g, h)
i = Segment(A, C)
j = Segment(N, C)
k = Segment(N, M)
cf: (c * f)
l = Segment(A, N)
poly1, b_1, a_1, c_1 = Polygon(A, C, B)
poly2, m, a_2, n = Polygon(A, N, M)
texte1: "\frac{AB}{AM}=\frac {" + (LaTeX[c]) + "}{" + (LaTeX[f]) + "} = " + (LaTeX[c / f]) + ""
texte2: "\frac{AC}{AN} =\frac{" + (LaTeX[d]) + "}{" + (LaTeX[l]) + "} =  " + (LaTeX[d / l]) + ""
texte3: "\frac{AB}{MN} =\frac{" + (LaTeX[e]) + "}{" + (LaTeX[k]) + "} =  " + (LaTeX[e / k]) + ""