X(24)

X(24)    PERSPECTOR OF ABC AND 
ORTHIC-OF-ORTHIC TRIANGLE

This perspector, labeled 24, is also
constructed here as the point of 
intersection of lines X(2)X(3) and X(6)X(54).

A'B'C' = orthic-of-orthic triangle.

Sketch contributed by Michael Stairs, March 2018.

Drag A, B, C.

24

2

3

6

4

5

54

A_2 = (-27.26429969465668, 11.262109314745985)
B = (-33.15620440581753, 1.1277556043994788)
C = (-18.48465097622328, 1.1277556043994788)
t1, c, a, b = Polygon(A_2, B, C)
D = Midpoint(A_2, C)
E = Midpoint(B, C)
F = Midpoint(A_2, B)
f = OrthogonalLine(E, a)
g = OrthogonalLine(D, b)
h = OrthogonalLine(F, c)
G = Intersect(f, g)
i = Line(E, A_2)
j = Line(B, D)
k = Line(C, F)
l = LineBisector(c)
m = LineBisector(b)
n = LineBisector(a)
I = Midpoint(B, C)
J = Midpoint(C, A_2)
K = Midpoint(A_2, B)
p = Segment(A_2, I)
q = Segment(J, B)
r = OrthogonalLine(A_2, a)
s = OrthogonalLine(C, c)
t = OrthogonalLine(B, b)
H = Intersect(s, c)
L = Intersect(t, b)
d = Segment(H, L)
M = Intersect(r, a)
e = Segment(L, M)
f_1 = Segment(M, H)
g_1 = OrthogonalLine(H, e)
h_1 = OrthogonalLine(M, d)
i_1 = OrthogonalLine(L, f_1)
A' = Intersect(i_1, f_1)
B' = Intersect(g_1, e)
k_1 = Segment(A', B')
m_1 = OrthogonalLine(M, d)
C' = Intersect(m_1, d)
n_1 = Segment(A', C')
p_1 = Segment(C', B')
q_1 = Line(C', A_2)
r_1 = Line(A', B)
s_1 = Line(B', C)
N = Intersect(q_1, r_1)
O = Midpoint(B, C)
P = Midpoint(C, A_2)
Q = Midpoint(A_2, B)
t_1 = Segment(A_2, O)
a_1 = Segment(P, B)
R = Intersect(t_1, a_1)
S = Midpoint(B, C)
T = Midpoint(C, A_2)
b_1 = OrthogonalLine(T, b)
c_1 = OrthogonalLine(S, a)
U = Intersect(b_1, c_1)
d_1 = Segment(A_2, S)
e_1 = Segment(T, B)
f_2 = AngularBisector(C, B, A_2)
g_2 = AngularBisector(B, A_2, C)
A = Mirror(A_2, g_2)
S' = Mirror(S, g_2)
h_2 = Segment(A, S')
T' = Mirror(T, f_2)
B'_1 = Mirror(B, f_2)
i_2 = Segment(T', B'_1)
V = Intersect(h_2, i_2)
j_2 = Line(U, R)
k_2 = OrthogonalLine(A_2, a)
l_2 = OrthogonalLine(B, b)
m_2 = OrthogonalLine(C, c)
W = (-27.281346337081242, 6.233204077927492)
n_2 = OrthogonalLine(A_2, a)
p_2 = OrthogonalLine(B, b)
Z = Intersect(j_2, n_2)
A_1 = Midpoint(Z, U)
B_1 = Mirror(A_1, b)
C_1 = Mirror(A_1, c)
D_1 = Mirror(A_1, a)
q_2 = Segment(C_1, D_1)
r_2 = Segment(D_1, B_1)
s_2 = Segment(B_1, C_1)
t_2 = LineBisector(q_2)
a_2 = LineBisector(s_2)
E_1 = Intersect(t_2, a_2)
b_2 = Line(E_1, V)