Le\;grand\;huit

A

B

C

D

O

M

Conjecture:\
Lorsque \;le\;point\;C\;décrit \;le\; cercle\;\mathscr{C},\;le\;point\;M\;décrit\; la\
 réunion \;de \;deux \;cercles \;de\; diamètres\; respectifs\;\left [OB'  \right ]\;et\;\left [OA'  \right ] \
\left( où\;\left [ A'B' \right ] est\;le\;diamètre\;de\;\mathscr{C}\;perpendiculaire \;à\;\left [ AB \right ]   \right)  

\mathscr{C}

O = (4.82, 0.42)
B = (9.02, 0.38)
β = 0.7504915783575616 rad (slider from 0 to 6.283185307179586, step 0.017453292519943295)
c = Circle(O, B)
A = Mirror(B, O)
a = Segment(A, B)
C = Rotate(B, β, O)
b = Segment(O, C)
d = OrthogonalLine(C, a)
D = Intersect(d, a)
e = Segment(D, C)
f = Circle(O, e)
M = Intersect(f, b, 1)
g = Segment(O, M)
α = Angle(C, D, O)
E = Point(c)
γ = Angle(O, D, C)