EULER LINE

The Euler line passes through many
triangle centers, including these:

X(2), the centroid, G
X(3), the circumcenter, O
X(4), the orthocenter, H
X(5), the nine-point center, N

Sketch contributed by Michael Stairs, 
January 2018.

Drag A, B, C.

OH/ON

A = (2.6026223107145516, 4.433148528179771)
B = (-0.5384617004849285, 1.639430632208674)
C = (3.2353946234151647, 1.6615567949017633)
f = Segment(B, A)
g = Segment(A, C)
h = Segment(C, B)
i = AngularBisector(B, C, A)
j = AngularBisector(C, B, A)
C'_1 = Midpoint(f)
B'_1 = Midpoint(g)
A'_1 = Midpoint(h)
m = OrthogonalLine(A'_1, h)
D_1 = Point(m)
k = OrthogonalLine(A, h)
l = OrthogonalLine(C, f)
n = OrthogonalLine(B, g)
H = Intersect(k, l)
p = LineBisector(h)
q = LineBisector(g)
r = LineBisector(f)
O = Intersect(p, q)
s = Ray(B, H)
t = Ray(A, H)
a = Ray(C, H)
A' = Intersect(h, t)
B' = Intersect(g, s)
b = Segment(A', B')
C' = Intersect(f, a)
c = Segment(B', C')
d = Segment(C', A')
D = Midpoint(B, C)
E = Midpoint(C, A)
F = Midpoint(A, B)
e = Segment(O, H)
f_1 = Segment(F, D)
g_1 = Segment(D, E)
h_1 = Segment(E, F)
N = Midpoint(O, H)
c_1 = Circle(N, E)
H_1 = Midpoint(B, C)
I = Midpoint(A, C)
J = Midpoint(A, B)
i_1 = Segment(A, H_1)
j_1 = Segment(C, J)
k_1 = Segment(I, B)
G = Intersect(i_1, j_1)
l_1 = Segment(O, H)
m_1 = Line(O, H)
n_1 = Line(A, C)
p_1 = Line(C, B)
q_1 = Line(B, A)
distanceOH = Distance(O, H)
distanceON = Distance(O, N)
TextON: Name[O] + (Name[N]) + " = " + distanceON
o_1 = Distance(O, H)
TextOH: Name[O] + (Name[H]) + " = " + o_1
OH_1 = Distance(O, H)
ON = Distance(O, N)
OH: OH_1 / ON