X(75)    ISOTOMIC CONJUGATE OF INCENTER

X(75), labeled 75, is the isotomic conjugate of the incenter,
X(1), of triangle ABC. A full definition of how to find a point's isotomic
conjugate can be found in the Encyclopedia of Triangle Centers glossary.

Sketch contributed by Michael Stairs, January 2018.

Drag A, B, C.

1

75

A = (-1.0750612341708714, 3.0897192877161688)
B = (-0.9862271309128487, -0.15272548120165125)
C = (3.011307515698166, -0.1194126924798928)
f = Segment(B, A)
g = Segment(A, C)
h = Segment(C, B)
i = AngularBisector(B, C, A)
j = AngularBisector(C, B, A)
I = Intersect(i, j)
k = OrthogonalLine(I, h)
D = Intersect(k, h)
l = Segment(I, D)
c = Circle(I, D)
m = Ray(B, I)
n = Ray(C, I)
p = Line(A, I)
q = Line(B, I)
r = Line(C, I)
A' = Intersect(p, h)
B' = Intersect(q, g)
C' = Intersect(r, f)
Mid_1 = Midpoint(B, A)
Mid_2 = Midpoint(A, C)
Mid = Midpoint(C, B)
A'' = Mirror(A', Mid)
C'' = Mirror(C', Mid_1)
B'' = Mirror(B', Mid_2)
s = Segment(A, A')
t = Segment(C, C')
a = Segment(B, B')
b = Line(A, A'')
d = Line(C, C'')
e = Line(B, B'')
E = Intersect(b, d)