X(28)    CEVAPOINT OF X(19) AND X(25)

The cevapoint of X(19) and X(25), labeled 28,
is constructed here as the point of intersection 
of lines X(1)X(19) and X(2)X(3).

Sketch contributed by Michael Stairs, March 2018.

Drag A, B, C.

1

19

2

3

1

28

A = (2.7436107367713123, 0.20387035296205402)
B = (-0.47288146120199914, -0.12671356738095482)
C = (3.011307515698166, -0.1194126924798928)
f = Segment(B, A)
g = Segment(A, C)
h = Segment(C, B)
i = AngularBisector(B, C, A)
j = AngularBisector(C, B, A)
I = Intersect(i, j)
k = OrthogonalLine(I, h)
D = Intersect(k, h)
l = Segment(I, D)
c = Circle(I, D)
m = Ray(B, I)
n = Ray(C, I)
p = Line(A, I)
q = Line(B, I)
r = Line(C, I)
A'_1 = Intersect(p, h)
B'_1 = Intersect(q, g)
C'_1 = Intersect(r, f)
Mid_1 = Midpoint(B, A)
Mid_2 = Midpoint(A, C)
Mid = Midpoint(C, B)
A''_1 = Mirror(A'_1, Mid)
C''_1 = Mirror(C'_1, Mid_1)
B''_1 = Mirror(B'_1, Mid_2)
s = Segment(A, A'_1)
t = Segment(C, C'_1)
a = Segment(B, B'_1)
b = Line(A, A''_1)
d = Line(C, C''_1)
e = Line(B, B''_1)
E = Intersect(b, d)
f_1 = AngularBisector(C, B, A)
g_1 = AngularBisector(B, A, C)
h_1 = AngularBisector(A, C, B)
d' = Mirror(d, h_1)
e' = Mirror(e, f_1)
b' = Mirror(b, g_1)
F = Intersect(d', e')
G = Intersect(b, h)
i_1 = Segment(A, G)
H = Intersect(e, g)
j_1 = Segment(B, H)
J = Intersect(d, f)
k_1 = Segment(C, J)
K = Intersect(e', g)
l_1 = Segment(B, K)
L = Intersect(d', f)
m_1 = Segment(C, L)
M = Intersect(b', h)
n_1 = Segment(A, M)
N = Point(h_1)
p_1 = Ray(C, N)
O = Point(f_1)
q_1 = Ray(B, O)
P = Point(g_1)
r_1 = Ray(A, P)
s_1 = AngularBisector(B, A, C)
t_1 = AngularBisector(A, C, B)
a_1 = AngularBisector(A, B, C)
Q = Intersect(s_1, t_1)
b_1 = Line(A, Q)
c_1 = Line(C, Q)
d_1 = Line(B, Q)
C' = Intersect(c_1, f)
A' = Intersect(b_1, h)
B' = Intersect(d_1, g)
triangle1, t_2, r_2, s_2 = Polygon(C', A', B')
e_1 = Line(A', C')
f_2 = Line(C', B')
g_2 = Line(B', A')
h_2 = Line(A', F)
i_2 = Line(F, C')
j_2 = Line(B', F)
B'' = Intersect(e_1, j_2)
A'' = Intersect(f_2, h_2)
C'' = Intersect(g_2, i_2)
k_2 = Line(A, A'')
l_2 = Line(C, C'')
m_2 = Line(B, B'')
B_2 = Intersect(k_2, l_2)
R = Midpoint(h)
S = Midpoint(f)
n_2 = Segment(A, R)
p_2 = Segment(C, S)
T = Intersect(n_2, p_2)
q_2 = LineBisector(f)
a_2 = LineBisector(h)
U = Intersect(q_2, a_2)
b_2 = AngularBisector(A, C, B)
c_2 = AngularBisector(A, B, C)
V = Intersect(b_2, c_2)
d_2 = Line(U, T)
e_2 = Line(B_2, V)
W = Intersect(d_2, e_2)