X(26)    CIRCUMCENTER OF THE TANGENTIAL TRIANGLE

Triangle A'B'C' is the tangential triangle of ABC, and 
X(26), labeled 26, is its circumcenter.

Sketch contributed by Michael Stairs, March 2018.

Drag A, B, C.

3

26

A = (-2.669018110468939, 5.65363985708836)
B = (-7.49536143929982, -2.0246336205970983)
f = Segment(A, B)
C = (-0.12421890072174772, -2.0246336205970983)
g = Segment(B, C)
h = Segment(C, A)
i = OrthogonalLine(A, g)
j = OrthogonalLine(C, f)
k = OrthogonalLine(B, h)
b = LineBisector(f)
c = LineBisector(g)
l = LineBisector(f)
m = LineBisector(h)
D = Intersect(l, m)
d = Circle(D, A)
n = Segment(A, D)
p = Segment(B, D)
q = Segment(D, C)
r = Tangent(A, d)
s = Tangent(C, d)
t = Tangent(B, d)
B' = Intersect(r, s)
A' = Intersect(s, t)
a = Segment(B', A')
C' = Intersect(r, t)
e = Segment(A', C')
f_1 = Segment(C', B')
g_1 = LineBisector(f_1)
h_1 = LineBisector(e)
E = Intersect(g_1, h_1)
c_1 = Circle(E, B')
i_1 = Segment(C', E)
j_1 = Segment(E, A')
k_1 = Segment(E, B')
l_1 = Segment(A, B)
m_1 = Segment(B, C)
n_1 = Segment(C, A)