X(23)    FAR-OUT POINT

The far-out point, labeled 23, is 
the inverse-in-circumcircle of X(2).

Sketch contributed by Michael 
Stairs, March 2018.

Drag A, B, C.

3

2

23

A = (-25.31944125127233, 7.1262862808888805)
B = (-32.77591630324163, 6.214343288921415)
C = (-25.10012368481123, 6.232609648377382)
t1, c, a, b = Polygon(A, B, C)
D = Midpoint(A, C)
E = Midpoint(B, C)
F = Midpoint(A, B)
f = OrthogonalLine(E, a)
g = OrthogonalLine(D, b)
h = OrthogonalLine(F, c)
G = Intersect(f, g)
i = Line(E, A)
j = Line(B, D)
k = Line(C, F)
l = LineBisector(c)
m = LineBisector(b)
n = LineBisector(a)
H = Intersect(l, m)
d = Circle(H, A)
I = Midpoint(B, C)
J = Midpoint(C, A)
K = Midpoint(A, B)
p = Segment(A, I)
q = Segment(J, B)
L = Intersect(p, q)
r = Line(H, L)
s = OrthogonalLine(L, r)
M = Intersect(d, s, 1)
N = Intersect(d, s, 2)
t = Tangent(N, d)
e = Tangent(M, d)
O = Intersect(r, t)