X(22)    EXETER POINT

The Exeter point, labeled 22, is 
the perspector of the circum-medial 
triangle, A'B'C', and the tangential 
triangle, A''B''C''.

Sketch contributed by Michael 
Stairs, March 2018.

Drag A, B, C.

22

A = (-17.323016163367583, 9.612381609200089)
B = (-22.95044417873308, 4.660270314924074)
C = (-15.370444178733083, 4.560270314924074)
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)
d = Circle(G, C)
i = Line(E, A)
j = Line(B, D)
k = Line(C, F)
C' = Intersect(d, k, 2)
B' = Intersect(d, j, 2)
l = Segment(C', B')
A' = Intersect(d, i, 1)
m = Segment(B', A')
n = Segment(A', C')
p = Tangent(A, d)
q = Tangent(C, d)
r = Tangent(B, d)
C'' = Intersect(p, r)
A'' = Intersect(q, r)
s = Segment(C'', A'')
B'' = Intersect(p, q)
t = Segment(A'', B'')
e = Segment(B'', C'')
f_1 = Line(B'', B')
g_1 = Line(A'', A')
h_1 = Line(C'', C')
H = Intersect(f_1, g_1)
i_1 = Segment(B'', H)
j_1 = Segment(A'', H)
k_1 = Segment(C'', H)