Théorème de Feuerbach :
Dans un triangle,
le cercle des 9 points d'Euler 
est tangent aux cercles inscrit et exinscrits.

A = (5.813682041757958, 5.023534731203875)
B = (-2.602382863021802, -4.795207657705835)
C = (11.493376116841565, -2.35776809511935)
a = Line(A, B)
b = Line(B, C)
c = Line(C, A)
d = AngularBisector(B, A, C)
e = AngularBisector(C, B, A)
D = Point(a)
f = AngularBisector(C, B, D)
E = Intersect(d, f)
F = Intersect(d, e)
g = OrthogonalLine(F, b)
h = OrthogonalLine(E, b)
G = Intersect(b, g)
H = Intersect(b, h)
k = Circle(F, G)
p = Circle(E, H)
I = Midpoint(B, C)
J = Midpoint(C, A)
K = Midpoint(A, B)
q = Circle(J, K, I)
L = Intersect(q, a, 2.0)
M = Intersect(q, c, 2.0)
N, O = Intersect(q, b)
i = Segment(A, O)
j = Segment(B, M)
l = Segment(C, L)
α = Angle(B, M, C)
β = Angle(B, L, C)
γ = Angle(C, O, A)
P = Intersect(q, j, 2.0)
Q = Intersect(q, l, 2.0)
R = Intersect(q, i, 2.0)