10e ES20 Droite d'Euler

le triangle

l'orthocentre

le centre du cercle circonscrit

le centre de gravité

le centre du cercle inscrit

l'alignement

G

X

O

H

cas général

A = (-4.1, 6.66)
B = Point(Circle[A, 8])
a = Segment(A, B)
c = Circle(A, 10)
d = Circle(B, 12)
C = Intersect(c, d, 1)
b = Segment(A, C)
e = Segment(B, C)
f = false
g = OrthogonalLine(A, e)
h = OrthogonalLine(B, b)
H = Intersect(g, h)
i = OrthogonalLine(C, a)
D = Intersect(i, a)
E = Intersect(h, b)
F = Intersect(g, e)
α = Angle(C, F, A)
β = Angle(A, E, B)
γ = Angle(B, D, C)
j = false
k = LineBisector(e)
l = LineBisector(b)
O = Intersect(k, l)
m = LineBisector(a)
I = Intersect(m, a)
J = Intersect(l, b)
K = Intersect(k, e)
δ = Angle(C, K, O)
ε = Angle(A, J, O)
ζ = Angle(B, I, O)
n = false
p = Line(A, K)
q = Line(J, B)
G = Intersect(p, q)
r = Line(I, C)
o = false
s = AngularBisector(B, A, C)
t = AngularBisector(B, C, A)
X = Intersect(s, t)
a_1 = AngularBisector(C, B, A)
u = false
b_1 = Segment(H, O)
v = false
L = (4.48, 6.74)
M = (4.14, 5.62)
N = (6.86, 6.54)
poly1, n_1, l_1, m_1 = Polygon(L, M, N)
P = Centroid(poly1)
Q = Center(Incircle[M, N, L])
c_1 = LineBisector(l_1)
d_1 = LineBisector(m_1)
R = Intersect(c_1, d_1)
e_1 = OrthogonalLine(L, l_1)
f_1 = OrthogonalLine(M, m_1)
S = Intersect(e_1, f_1)
g_1 = Segment(R, S)
w = false