Théorème de Feuerbach
Author: Yvan Monka

Cercle inscrit

Cercle d'Euler

Cercle ex-inscrit

Cercle ex-inscrit

Cercle ex-inscrit

A = (-0.9666666666666667, -5.2)
B = (4.760081040620082, 1.625279336350872)
C = (14.433333333333334, -4.033333333333333)
P, c, a, b = Polygon(A, B, C)
d = LineBisector(A, C)
e = LineBisector(B, C)
f = LineBisector(A, B)
M_3 = Intersect(c, f)
M_1 = Intersect(a, e)
M_2 = Intersect(d, b)
g = Segment(B, M_2)
h = Segment(A, M_1)
i = Segment(C, M_3)
j = AngularBisector(B, C, A)
k = AngularBisector(A, B, C)
l = AngularBisector(B, A, C)
m = OrthogonalLine(B, b)
n = OrthogonalLine(A, a)
p = OrthogonalLine(C, c)
O = Intersect(f, d)
H = Intersect(p, n)
K = Intersect(k, j)
G = Intersect(i, g)
q = Circle(O, A)
r = OrthogonalLine(K, b)
K_1 = Intersect(r, b)
s = Circle(K, K_1)
t = Line(H, O)
D = Midpoint(H, O)
c_1 = Circle(D, M_3)
a_1 = Line(B, C)
b_1 = Line(C, A)
d_1 = Line(A, B)
e_1, f_1 = AngularBisector(d_1, a_1)
g_1, h_1 = AngularBisector(b_1, a_1)
E = Intersect(e_1, g_1)
i_1 = OrthogonalLine(E, a_1)
F = Intersect(a_1, i_1)
k_1 = Circle(E, F)
j_1, l_1 = AngularBisector(a_1, d_1)
m_1, n_1 = AngularBisector(b_1, d_1)
I = Intersect(j_1, m_1)
p_1 = OrthogonalLine(I, d_1)
J = Intersect(p_1, d_1)
q_1 = Circle(I, J)
r_1, s_1 = AngularBisector(a_1, b_1)
t_1, a_2 = AngularBisector(d_1, b_1)
L = Intersect(r_1, t_1)
b_2 = OrthogonalLine(L, d_1)
M = Intersect(d_1, b_2)
c_2 = Circle(L, M)