Angle droit et cercle
Author: db iufm V
Date: 30 Mai 2013

Observe bien la figure. Tire sur n'importe quelle poignée orange.
L'angle droit reste un angle droit.
Maintenant : que peux-tu dire du point D ?
Vérifie tes hypothèses en faisant apparaître les traits auxiliaires.

Traits auxiliaires :

Invisibles

Visibles

A = (4.6, -5.12)
B = (7.58, -2.42)
a = Segment(A, B)
b = OrthogonalLine(B, a)
C = Point(b)
D = Midpoint(A, C)
c = Circle(D, B)
d = Segment(B, C)
α = Angle(A, B, C)
e = Segment(A, D)
f = Segment(D, B)
g = Segment(D, C)
E = (13.8, 1.08)
F = (17.14, 1.06)
G = (17.16, -0.66)
H = (13.8, -0.7)
poly1, e_1, f_1, g_1, h = Polygon(E, F, G, H)
I = (15.14, 0.28)
J = (15.14, -0.18)
I': (x(I), y(I))
J': (x(J), y(J))

Tool: Carré
1 point 1 point
Input: A, B
Output: C, D, poly1, a, b, c, d

poly1, a, b, c, d, C, D = Polygon(A, B, 4)

Tool: Carré Centré (command Carré_Centré)
Le centre puis un sommet
Input: O, A
Output: poly1, B, C, D, a, b, c, d

B = Rotate(A, 90*°, O)
D = Mirror(B, O)
C = Mirror(A, O)
poly1, d, a, b, c = Polygon(D, A, B, C)

Tool: Rectangle
2 sommets un segment
Input: A, B, u
Output: C, D, poly1, a_1, b_1, e_1, f

U_1 = (0.37, 6.965)
U_2 = (1.75, 6.935)
u = Segment(U_1, U_2)
B' = Rotate(B, 90*°, A)
b = Ray(A, B')
c = Circle(A, u)
D = Intersect(c, b)
d = OrthogonalLine(D, b)
e = OrthogonalLine(B, d)
C = Intersect(e, d)
poly1, a_1, b_1, f, e_1 = Polygon(A, B, C, D)

Tool: parallélogramme
Clic sur trois points A, B, C
Input: A, B, C
Output: poly1

u = Vector(A, B)
C' = Translate(C, u)
poly1, a, b, c', c = Polygon(A, B, C', C)