X(54)    KOSNITA POINT

The Kosnita Point, labeled 54, is here constructed 
as X(3)-of-reflection-triangle-of-X(5). 

A'B'C' = reflection-triangle-of-X(5)

Sketch contributed by Michael Stairs, March 2018.

Drag A, B, C. 

4

3

5

54

A = (0.16208230954842687, 5.0045203202984245)
B = (-2.8842123751452826, 2.2320413289649723)
C = (0.9470383054621359, 2.2316213231618773)
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)
E_1 = Intersect(k, l)
p = LineBisector(h)
q = LineBisector(g)
r = LineBisector(f)
F_1 = Intersect(p, q)
s = Ray(B, E_1)
t = Ray(A, E_1)
a = Ray(C, E_1)
e = Segment(F_1, E_1)
G = Midpoint(F_1, E_1)
B' = Mirror(G, g)
A' = Mirror(G, h)
C' = Mirror(G, f)
b = Segment(C', A')
c = Segment(A', B')
d = Segment(B', C')
f_1 = LineBisector(d)
g_1 = LineBisector(b)
D = Intersect(f_1, g_1)
c_1 = Circle(D, B')
h_1 = LineBisector(b)
i_1 = LineBisector(d)
j_1 = LineBisector(c)