Un\; angle \;constant

C

D

O

B

A

J

I

Commande\; de\; x: \;côté \;du \;carré

a = 7.3 (slider from 1 to 10, step 0.1)
O = (0, 0)
B: (a, 0)
C: (a, a)
D: (0, a)
poly1, o, b, c, d = Polygon(O, B, C, D)
I = Midpoint(B, O)
J = Midpoint(B, C)
e = Segment(C, I)
f = Segment(O, J)
A = Intersect(e, f)
α = Angle(O, A, I)
P_s: Vector[A, O] * Vector[A, I]
d_1 = Distance(A, O)
d_2 = Distance(A, I)
q_1: P_s / (d_1 * d_2)
α': acos(q_1)
α'': (α' * 180) / π
texte3: "x=" + (LaTeX[a]) + ""
u = Vector(A, O)
v = Vector(A, I)
texte2: "\;\;\;\;\;\;\;Vérification\;par\;le\;calcul\\
cos\left( \widehat{OAI} \right) =\frac{\overrightarrow{AO}.\overrightarrow{AI}}{AO.AI}=\frac{" + (LaTeX[P_s]) + "}{" + (LaTeX[d_1]) + "×" + (LaTeX[d_2]) + "}=" + (LaTeX[q_1]) + "\\
\\
\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;alors\;\;\;\widehat{OAI}=" + (LaTeX[α'']) + ""