X(20)   DE LONGCHAMPS POINT

The De Longchamps point, labeled 20, is 
the reflection of X(4) in X(3).

Also, X(20) is the orthocenter of the 
anticomplementary triangle, A'B'C'.

Sketch provided by Michael Stairs, January 2018.

Drag A, B, C.

4

3

20

A = (2.5578517361249316, 4.08067085022401)
B = (-0.2573193160656448, 1.9093847328680538)
C = (3.641627457866125, 1.8472026016204806)
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 = Point(m)
k = OrthogonalLine(C, f)
l = OrthogonalLine(A, h)
n = OrthogonalLine(B, g)
E = Intersect(l, h)
p = Ray(E, A)
F = Intersect(k, n)
c = Circle(A, B, C)
G = Midpoint(A, C)
H = Midpoint(C, B)
I = Midpoint(B, A)
q = OrthogonalLine(G, g)
r = OrthogonalLine(H, h)
s = OrthogonalLine(I, f)
J = Intersect(q, r)
t = Line(J, F)
a = OrthogonalLine(J, t)
F' = Mirror(F, a)
b = Line(A, h)
d = Line(C, f)
e = Line(B, g)
B' = Intersect(b, d)
f_1 = OrthogonalLine(B', e)
A' = Intersect(d, e)
g_1 = OrthogonalLine(A', b)
C' = Intersect(b, e)
h_1 = OrthogonalLine(C', d)
i_1 = Segment(C', B')
j_1 = Segment(B', A')
k_1 = Segment(A', C')
N = Intersect(f_1, k_1)
l_1 = Segment(B', N)
O = Intersect(h_1, j_1)
m_1 = Segment(C', O)
P = Intersect(g_1, i_1)
n_1 = Segment(A', P)