X(35)   {X(1),X(3)}-HARMONIC CONJUGATE OF X(36)

X(35), labeled 35, is constructed here as the point of
intersection of lines X(1)X(3) and X(10)X(21).

Sketch contributed by Michael Stairs, March 2018.

Drag A, B, C.

1

21

3

10

35

A = (1.536632656936772, 2.3385379728381723)
B = (-3.0414940147950293, 0.25389293964099713)
C = (3.147683510085133, 0.29354448113962284)
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)
p = LineBisector(h)
q = LineBisector(g)
r = LineBisector(f)
b = AngularBisector(B, A, C)
c = AngularBisector(A, B, C)
d = AngularBisector(A, C, B)
D = Intersect(d, f)
E_1 = Intersect(c, g)
F = Intersect(b, h)
s = AngularBisector(B, A, C)
t = AngularBisector(A, B, C)
a = AngularBisector(A, C, B)
G = Incenter(A, B, C)
e = Segment(A, G)
f_1 = Segment(B, G)
g_1 = Segment(G, C)
triangle1, a_1, b_1, g_2 = Polygon(B, G, A)
triangle2, g_3, b_2, c_1 = Polygon(B, C, G)
h_1 = Line(A, C)
i_1 = Line(C, B)
j_1 = Line(B, A)
k_1 = OrthogonalLine(A, g_3)
l_1 = OrthogonalLine(B, g)
m_1 = OrthogonalLine(C, g_2)
H = Intersect(k_1, l_1)
I = Centroid(A, B, C)
E = Line(I, H)
J = Centroid(A, G, C)
K = Orthocenter(A, G, C)
E_B = Line(K, J)
L = Orthocenter(A, G, B)
M = Centroid(A, G, B)
E_C = Line(M, L)
N = Orthocenter(B, G, C)
O = Centroid(G, B, C)
E_A = Line(O, N)
P = Intersect(E, E_B)
n_1 = Segment(B, C)
p_1 = Segment(A, B)
q_1 = LineBisector(p_1)
r_1 = LineBisector(g)
Q = Intersect(q_1, r_1)
R = Midpoint(p_1)
S = Midpoint(g)
T = Midpoint(n_1)
s_1 = Segment(R, S)
t_1 = Segment(S, T)
d_1 = Segment(T, R)
e_1 = AngularBisector(T, R, S)
f_2 = AngularBisector(S, T, R)
U = Intersect(e_1, f_2)
h_2 = Line(Q, G)
i_2 = Line(U, P)
V = Intersect(h_2, i_2)

Tool: Centroid
Input: A, B, C
Output: G

D = Midpoint(A, B)
E = Midpoint(B, C)
s = Segment(C, D)
t = Segment(A, E)
G = Intersect(s, t)

Tool: Incenter
Input: A, B, C
Output: I

s = AngularBisector(B, A, C)
t = AngularBisector(A, B, C)
I = Intersect(s, t)

Tool: Incircle
Input: A, B, C
Output: c_1

g = Segment(A, C)
s = AngularBisector(B, A, C)
t = AngularBisector(A, B, C)
I = Intersect(s, t)
e = OrthogonalLine(I, g)
G = Intersect(e, g)
c_1 = Circle(I, G)

Tool: Orthocenter
Input: A, B, C
Output: H

g = Segment(A, C)
G = Incenter(A, B, C)
triangle2, g_3, b_2, c_1 = Polygon(B, C, G)
k_1 = OrthogonalLine(A, g_3)
l_1 = OrthogonalLine(B, g)
H = Intersect(k_1, l_1)