Eulergerade

Konstruiere:
(1) Ein Dreieck
(2) Umkreismittelpunkt des Dreiecks
(3) Schwerpunkt des Dreiecks
(4) Höhenschnittpunkt des Dreiecks
Was fällt auf?

A = (-2, -1)
B = (1, -2)
C = (4, 1)
poly1, c, a, b = Polygon(A, B, C)
A_1 = (5, -1)
B_1 = (8, -2)
C_1 = (11, 1)
poly1_1, c_1, a_1, b_1 = Polygon(A_1, B_1, C_1)
A_2 = (12, -1)
B_2 = (15, -2)
C_2 = (18, 1)
poly1_2, c_2, a_2, b_2 = Polygon(A_2, B_2, C_2)
f = LineBisector(b_1)
g = LineBisector(c_1)
h = LineBisector(a_1)
i = OrthogonalLine(C, c)
j = OrthogonalLine(B, b)
k = OrthogonalLine(A, a)
D = Midpoint(b_2)
E = Midpoint(c_2)
F = Midpoint(a_2)
l = Line(C_2, E)
m = Line(B_2, D)
n = Line(A_2, F)
G = Intersect(j, b)
H = Intersect(i, j)
p = Segment(G, H)
q = Segment(C, H)
r = Segment(H, A)
I = Intersect(g, c_1)
J = Intersect(f, g)
s = Segment(I, J)
K = Intersect(f, b_1)
t = Segment(K, J)
L = Intersect(h, a_1)
d = Segment(L, J)
e = Segment(E, C_2)
f_1 = Segment(F, A_2)
g_1 = Segment(B_2, D)